Nonlinear vibroacoustic wave modulations for structural damage detection: an overview
---
paper_title: Nonlinear Mesoscopic Elasticity: Evidence for a New Class of Materials

paper_content:

A squash ball almost doesn't bounce; a Superball bounces first left then right, seeming to have a mind of its own. Remarkable and complex elastic behavior isn't confined to sports equipment and toys. Indeed, it can be found in some surprising places. When the elastic behavior of a rock is probed, for instance, it shows extreme nonlinearity hysteresis and discrete memory (the Flint‐stones could have had a computer that used a sandstone for random‐access memory). Rocks are an example of a class of unusual elastic materials that includes sand. soil, cement, concrete, ceramics and, it turns out, damaged materials, Many members of this class are the blue‐collar materials of daily life: They are in the bridges we cross on the way to work, the roofs over our heads and the ground beneath our cities—such as the Los Angeles basin (home to many earthquakes). The elastic behavior of these materials is of more than academic interest.
---
paper_title: Fatigue damage assessment by nonlinear ultrasonic materials characterization

paper_content:

The ultimate strength of most structural materials is mainly limited by the presence of microscopic imperfections serving as nuclei of the fracture process. Since these nuclei are considerably shorter than the acoustic wavelength at the frequencies normally used in ultrasonic nondestructive evaluation (NDE), linear acoustic characteristics are not sufficiently sensitive to this kind of microscopic degradation of the material's integrity. On the other hand, even very small imperfections can produce very significant excess nonlinearity which can be orders of magnitude higher than the intrinsic nonlinearity of the intact material. The excess nonlinearity is produced mainly by the strong local nonlinearity of microcracks whose opening is smaller than the particle displacement. Parametric modulation via crack-closure significantly increases the stress-dependence of fatigued materials. A special experimental technique was introduced to measure the second-order acousto-elastic coefficient in a great variety of materials including plastics, metals, composites and adhesives. Experimental results are presented to illustrate that the nonlinear acoustic parameters are earlier and more sensitive indicators of fatigue damage than their linear counterparts.
---
paper_title: Nonlinear Interaction of Acoustical Waves Due to Cracks and Its Possible Usage for Cracks Detection

paper_content:

An interaction of a CW acoustic wave and a powerful acoustic pulse due to nonlinear properties of a crack-type discontinuity in a solid is considered. Characteristics of nonstationary variations of the reflected wave amplitude and the phase of the transmitted wave, which are induced by the powerful pulse, are determined. The effects should allow one to distinguish cracks from other scatterers and can be used as a base of a new method of crack detection and positioning. Demonstrative signal estimates based on two simplified crack models are presented.
---
paper_title: Handbook of Nondestructive Evaluation

paper_content:

Chapter 1: Introduction to Nondestructive Testing Chapter 2: Dicontinuities - Origins and Classification Chapter 3: Visual Testing Chapter 4: Penetrant Testing Chapter 5: Magnetic Particle Testing Chapter 6: Radiographic Testing New - Digital Radiography Chapter 7: Ultrasonic Testing New - Phased Array Ultrasonics New - Guided Wave Ultrasonics Chapter 8: Eddy current Testing Chapter 9: Thermal Infrared Testing Chapter 10: Acoustic Emission Testing
---
paper_title: A Baseline and Vision of Ultrasonic Guided Wave Inspection Potential

paper_content:

Ultrasonic guided wave inspection is expanding rapidly to many different areas of manufacturing and in-service inspection. The purpose of this paper is to provide a vision of ultrasonic guided wave inspection potential aswe move forward into the new millennium. An increased understanding of the basic physics and wave mechanics associated with guided wave inspection has led to an increase in practical nondestructive evaluation and inspection problems. Some fundamental concepts and a number of different applications that are currently being considered will be presented in the paper along with a brief description of the sensor and software technology that will make ultrasonic guided wave inspection commonplace in the next century.
---
paper_title: Structural Health Monitoring Using Guided Ultrasonic Waves

paper_content:

Maintenance of air, land and sea structures is an important engineering activity in a wide range of industries including transportation and Civil Engineering. Effective maintenance minimises not only the cost of ownership of structures but also improves safety and the perception of safety. Inspection for material/structural damage, such as fatigue cracks and corrosion in metallics or delamination in composites, is an essential part of maintenance.
---
paper_title: Dynamic nonlinear elasticity in geomaterials

paper_content:

This invention relates to a lens for presbyopia free from distortional aberration for use in correcting an old-age eyesight. In the lens for presbyopia with a front lens surface having a smaller radius of curvature than a rear lens face, a lens surface has a refractive power successively corrected as the lens surface extends radially outwardly away from a geometric center of the lens so that lateral magnifications for all principal rays always equal a lateral magnification for a paraxial range. This construction is entirely free from distortional aberration, and secures a greatly enlarged range of distinct vision.
---
paper_title: Nonlinear Response of a Weakly Damaged Metal Sample: A Dissipative Modulation Mechanism of Vibro-Acoustic Interaction

paper_content:

The nonlinear vibro-acoustic response of solid samples containing quite a small amount of defects can be anomalously high in magnitude compared to the case of undamaged intact solids. Functional de pendencies of the nonlinear effects exhibit rather interesting behavior. In this paper, experimental results on nonlinearity-induced cross-modulation of a high-frequency (HF) f = 15 — 30 kHz signal by a low-frequency (LF) F = 20 - 60 Hz vibration in an aluminum plate with a small single crack are reported. Comparison with a reference sample (the identical plate without a crack) has proven that the presence of such a small defect can be easily detected due to its nonlinear manifestations. It is demonstrated that under proper choice of the sounding signal parameters, the effect level can be so pronounced that the amplitude of the modulation side-lobes originated due to the nonlinearity exceeds the amplitude of the fundamental harmonic of the HF signal. Main functional features of the observed phenomena are analyzed, and a new physical explana tion is suggested based on a dissipative mechanism of vibro-acoustic interaction. Results of the numerical simulation of the effect are also presented.
---
paper_title: Investigation of Nonlinear Vibro-Acoustic Wave Modulation Mechanisms in Composite Laminates

paper_content:

This paper investigates the effect of low-frequency vibration and the related temperature field on nonlinear vibro-acoustic wave modulations. Experimental modal analysis was used to find natural frequencies and mode shapes of a composite laminate plate with seeded delamination. Temperature distribution was analyzed with a thermographic camera in the vicinity of damage for the identified vibration modes. These frequencies of these vibration modes were then used for low-frequency excitation in nonlinear acoustic tests. The correlation between the thermal field and the observed wave modulations was analyzed.
---
paper_title: Luxemburg-Gorky Effect Retooled for Elastic Waves: A Mechanism and Experimental Evidence

paper_content:

A new mechanism is proposed for the linear and amplitude-dependent dissipation due to elastic-wavecrack interaction. We have observed one of its strong manifestations in a direct elastic-wave analog of the Luxemburg-Gorky effect consisting of the cross modulation of radio waves at the dissipative nonlinearity of the ionosphere plasma. The counterpart acoustic mechanism implies, first, a drastic enhancement of the thermoelastic coupling at high-compliance microdefects, and, second, the high stress-sensitivity of the defects leads to a strong stress dependence of the resultant dissipation.
---
paper_title: Observation of the “Luxemburg–Gorky effect” for elastic waves

paper_content:

An experimental observation of a new nonlinear-modulation effect for longitudinal elastic waves is reported. The phenomenon is a direct elastic wave analogy with the so-called Luxemburg–Gorky (L–G) effect known over 60 years for radio waves propagating in the ionosphere. The effect consists of the appearance of modulation of a weaker initially non-modulated wave propagating in a nonlinear medium in the presence of an amplitude-modulated stronger wave that produces perturbations in the medium properties on the scale of its modulation frequency. The reported transfer of modulation from one elastic wave to another was observed in a resonator cut of a glass rod containing a few small cracks. Presence of such a small damage drastically enhances the material nonlinearity compared to elastic atomic nonlinearity of homogeneous solids, so that the pronounced L– G type cross-modulation could be observed at strain magnitude in the stronger wave down to 10 7 and smaller. Main features of the effect are pointed out and physical mechanism of the observed phenomena is discussed. 2002 Elsevier Science B.V. All rights reserved.
---
paper_title: Thermoelastic Mechanism for Logarithmic Slow Dynamics and Memory in Elastic Wave Interactions with Individual Cracks

paper_content:

Logarithmic-in-time slow dynamics has been found for individual cracks in a solid. Furthermore, this phenomenon is observed during both the crack acoustic conditioning and the subsequent relaxation. A thermoelastic mechanism is suggested which relates the log-time behavior to the essentially 2D character of the heating and cooling of the crack perimeter and inner contacts. Nonlinear perturbation of the contacts by a stronger (pump) wave causes either softening or hardening of the sample, and induces either additional absorption or transparency for a weaker (probe) acoustic wave depending on frequency of the latter. DOI: 10.1103/PhysRevLett.90.075501
---
paper_title: Nonlinear acoustics for fatigue crack detection – experimental investigations of vibro-acoustic wave modulations

paper_content:

Vibro-acoustic nonlinear wave modulations are investigated experimentally in a cracked aluminum plate. The focus is on the effect of low-frequency vibration excitation on modulation intensity and associated nonlinear wave interaction mechanisms. The study reveals that energy dissipation – not opening–closing crack action – is the major mechanism behind nonlinear modulations. The consequence is that relatively weak strain fields can be used for crack detection in metallic structures. A clear link between modulations and thermo-elastic coupling is also demonstrated, providing experimental evidence for the recently proposed non-classical, nonlinear vibro-acoustic wave interaction mechanism.
---
paper_title: Instability, chaos, and "memory" in acoustic-wave-crack interaction.

paper_content:

A new class of nonlinear acoustic phenomena has been observed for acoustic wave interactions with cracked defects in solids. Parametric modulation of crack stiffness results in fractional acoustic subharmonics, wave instability, and generation of chaotic noiselike acoustic excitations. Acoustic-wave impact on a crack is shown to exhibit amplitude hysteresis and storage for parametric and nonlinear acoustic effects. The measured storage time amounts to several hours and is believed to be due to a long-term relaxation of thermally induced microstrain within a crack area.
---
paper_title: CAN: an example of nonclassical acoustic nonlinearity in solids.

paper_content:

A new class of nonlinear acoustic phenomena has been observed for acoustic wave interaction with simulated and realistic nonbonded contact interfaces (cracked defects) in solids. "Nonclassical" effects are due to substantially asymmetric stiffness characteristics of the interface for normal stress that results in specific contact acoustic nonlinearity (CAN). The asymmetry in the contact restoring forces causes the stiffness parametric modulation and instability of oscillations, which results in acoustic wave fractional subharmonic generation. The CAN subharmonics and higher harmonics reveal threshold dynamic behaviour, evident hysteresis, and instability effects.
---
paper_title: Dynamic nonlinear elasticity in geomaterials

paper_content:

This invention relates to a lens for presbyopia free from distortional aberration for use in correcting an old-age eyesight. In the lens for presbyopia with a front lens surface having a smaller radius of curvature than a rear lens face, a lens surface has a refractive power successively corrected as the lens surface extends radially outwardly away from a geometric center of the lens so that lateral magnifications for all principal rays always equal a lateral magnification for a paraxial range. This construction is entirely free from distortional aberration, and secures a greatly enlarged range of distinct vision.
---
paper_title: Nonlinear Elastic Wave Spectroscopy (NEWS) Techniques to Discern Material Damage, Part I: Nonlinear Wave Modulation Spectroscopy (NWMS)

paper_content:

Abstract. The level of nonlinearity in the elastic response of materials containing structural damage is far greater than in materials with no structural damage. This is the basis for nonlinear wave diagnostics of damage, methods which are remarkably sensitive to the detection and progression of damage in materials. Nonlinear wave modulation spectroscopy (NWMS) is one exemplary method in this class of dynamic nondestructive evaluation techniques. The method focuses on the application of harmonics and sum and difference frequency to discern damage in materials. It consists of exciting a sample with continuous waves of two separate frequencies simultaneously, and inspecting the harmonics of the two waves, and their sum and difference frequencies (sidebands). Undamaged materials are essentially linear in their response to the two waves, while the same material, when damaged, becomes highly nonlinear, manifested by harmonics and sideband generation. We illustrate the method by experiments on uncracked and cracked Plexiglas and sandstone samples, and by applying it to intact and damaged engine components.
---
paper_title: Nonlinear modulation technique for NDE with air-coupled ultrasound

paper_content:

Abstract The present study is aimed at expanding flexibility and application area of nonlinear acoustic modulation (NAM-) technique by combining the benefits of noncontact ultrasound excitation (remote locating and imaging of defects) with sensitivity of nonlinear methods in a new air-coupled NAM-version. A pair of focused air-coupled transducers was used to generate and receive (high-frequency) longitudinal or flexural waves in plate-like samples. Low-frequency (LF-) vibrations were excited with a shaker or a loudspeaker. Temporal and spectral analysis of the output signal revealed an extremely efficient nonlinear amplitude modulation and multiple frequency side-bands for sound transmission and flexural wave propagation through cracked defects. On the contrary, a negligible modulation was observed for large and medium scale inclusions and material inhomogeneities (linear defects). A new subharmonic mode of the NAM was observed at high excitation levels. It was also shown for the first time that nonlinear vibrations of cracks resulted in radiation of a very high-order harmonics (well above 100) of the driving excitation in air that enabled imaging of cracks remotely by registration their highly nonlinear “acoustic emission” with air-coupled transducers.
---
paper_title: Scattering of Sound by Sound

paper_content:

As a preliminary to an investigation of the scattering of sound by turbulence, the scattering of one sound beam by another is studied using the Lighthill formulation. The scattered sound is predicted to be composed in part of components with frequency equal to the sum or difference of those in the primary beams. These components of the scattered field have been isolated in measurements using a selective receiver and their angular distributions are compared with those predicted. This work was supported in part by the NACA.
---
paper_title: Scattering of Sound by Sound

paper_content:

Earlier studies [J. Acoust. Soc. Am. 29, 199 (1957)] of the mutual nonlinear interaction of two plane waves of sound with each other are extended to encompass arbitrary directions of travel of one wave with respect to the other; an exact solution to the first‐order scattering process is obtained.
---
paper_title: Nonlinear acoustics in Nizhni Novgorod (A review)

paper_content:

This article reviews the development of nonlinear acoustics in Nizhni Novgorod from the days when the idea of parametric transmission and reception was conceived until the present time.
---
paper_title: Dynamic nonlinear elasticity in geomaterials

paper_content:

This invention relates to a lens for presbyopia free from distortional aberration for use in correcting an old-age eyesight. In the lens for presbyopia with a front lens surface having a smaller radius of curvature than a rear lens face, a lens surface has a refractive power successively corrected as the lens surface extends radially outwardly away from a geometric center of the lens so that lateral magnifications for all principal rays always equal a lateral magnification for a paraxial range. This construction is entirely free from distortional aberration, and secures a greatly enlarged range of distinct vision.
---
paper_title: Vibro-acoustic modulation nondestructive evaluation technique

paper_content:

Nonlinear acoustic technique has been recently introduced as a new tool for nondestructive inspection and evaluation of fatigued, defective, and fractured materials. Various defects such as cracks, debonding, fatigue, etc. lead to anomalous high level of nonlinearity as compared with flawless structures. One of the acoustic manifestations of such nonlinearity is the modulation of ultrasound by low frequency vibration. Two methods employing the nonlinear interaction of ultrasound and vibration were developed, namely vibro-modulation (VM) and impact-modulation (IM) methods. VM method employs forced harmonic vibration of a structure tested, while IM method uses impact excitation of structure natural modes of vibration. The feasibility tests were carried out for different objects and demonstrated high sensitivity of the methods for detection of cracks in steel pipes and pins, bonding quality in titanium and thermoplastic plates used for airspace applications, cracks in combustion engine, adhesion flaws in bonded composite structures, and cracks and corrosion in reinforced concrete. The model of the crack allowing to describe the modulation of sound by vibration is discussed. The developed nonlinear technique demonstrated certain advantages as compared with the conventional linear acoustic technique, specifically discrimination capabilities, sensitivity, and applicability to highly inhomogeneous structures.
---
paper_title: Impact damage detection in composite laminates using nonlinear acoustics

paper_content:

The paper demonstrates the application of nonlinear acoustics for impact damage detection in composite laminates. A composite plate is monitored for damage resulting from a low-velocity impact. The plate is instrumented with bonded low-profile piezoceramic transducers. A high-frequency acoustic wave is introduced to one transducer and picked up by a different transducer. A low-frequency flexural modal excitation is introduced to the plate at the same time using an electromagnetic shaker. The damage induced by impact is exhibited in a power spectrum of the acoustic response by a pattern of sidebands around the main acoustic harmonic. The results show that the amplitude of sidebands is related to the severity of damage. The study investigates also the effect of boundary conditions on the results.
---
paper_title: Modelling of nonlinear crack–wave interactions for damage detection based on ultrasound—A review

paper_content:

Abstract The past decades have been marked by a significant increase in research interest in nonlinearities in micro-cracked and cracked solids. As a result, a number of different nonlinear acoustic methods have been developed for damage detection. A general consensus is that – under favourable conditions – nonlinear effects exhibited by cracks are stronger than crack-induced linear phenomena. However, there is still limited understanding of physical mechanisms related to various nonlinearities. This problem remains essential for implementation of nonlinear acoustics for damage-detection applications. This paper reviews modelling approaches used for nonlinear crack–wave interactions. Various models of classical and nonclassical crack-induced elastic, thermo-elastic and dissipative nonlinearities have been discussed.
---
paper_title: Nonlinear Elastic Wave Spectroscopy (NEWS) Techniques to Discern Material Damage, Part I: Nonlinear Wave Modulation Spectroscopy (NWMS)

paper_content:

Abstract. The level of nonlinearity in the elastic response of materials containing structural damage is far greater than in materials with no structural damage. This is the basis for nonlinear wave diagnostics of damage, methods which are remarkably sensitive to the detection and progression of damage in materials. Nonlinear wave modulation spectroscopy (NWMS) is one exemplary method in this class of dynamic nondestructive evaluation techniques. The method focuses on the application of harmonics and sum and difference frequency to discern damage in materials. It consists of exciting a sample with continuous waves of two separate frequencies simultaneously, and inspecting the harmonics of the two waves, and their sum and difference frequencies (sidebands). Undamaged materials are essentially linear in their response to the two waves, while the same material, when damaged, becomes highly nonlinear, manifested by harmonics and sideband generation. We illustrate the method by experiments on uncracked and cracked Plexiglas and sandstone samples, and by applying it to intact and damaged engine components.
---
paper_title: Nonlinear modulation technique for NDE with air-coupled ultrasound

paper_content:

Abstract The present study is aimed at expanding flexibility and application area of nonlinear acoustic modulation (NAM-) technique by combining the benefits of noncontact ultrasound excitation (remote locating and imaging of defects) with sensitivity of nonlinear methods in a new air-coupled NAM-version. A pair of focused air-coupled transducers was used to generate and receive (high-frequency) longitudinal or flexural waves in plate-like samples. Low-frequency (LF-) vibrations were excited with a shaker or a loudspeaker. Temporal and spectral analysis of the output signal revealed an extremely efficient nonlinear amplitude modulation and multiple frequency side-bands for sound transmission and flexural wave propagation through cracked defects. On the contrary, a negligible modulation was observed for large and medium scale inclusions and material inhomogeneities (linear defects). A new subharmonic mode of the NAM was observed at high excitation levels. It was also shown for the first time that nonlinear vibrations of cracks resulted in radiation of a very high-order harmonics (well above 100) of the driving excitation in air that enabled imaging of cracks remotely by registration their highly nonlinear “acoustic emission” with air-coupled transducers.
---
paper_title: Nonlinear acoustic interaction on contact interfaces and its use for nondestructive testing

paper_content:

Recent theoretical and experimental studies demonstrated that a weakly or incompletely bonded interfaces exhibit highly nonlinear behavior. One of acoustic manifestations of such nonlinearity is the modulation of a probing high-frequency ultrasonic wave by low-frequency vibration. The vibration varies the contact area modulating the phase and amplitude of higher frequency probing wave passing through the interface. In the frequency domain, the result of this modulation manifests itself as side-band spectral components with respect to the frequency of the probing wave. This modulation effect has been observed experimentally for various materials (metals, composites, concrete, sandstone, glass) with various types of contact-type defects (interfaces): cracks, debondings, delaminations, and microstructural material damages. Study of this phenomenon revealed correlation between the developed modulation criterion and the quantitative characteristics of the interfaces, such as its size, loading condition, and bonding strength. These findings have been used for the development of an innovative nondestructive evaluation technique, namely Vibro-Acoustic Modulation Technique. Two modifications of this technique have been developed: Vibro-Modulation (VM) and Impact-Modulation (IM), employing CW and impact-induced vibrations, respectively. The examples of applications of these methods include crack detection in steel pipes, aircraft and auto parts, bonded composite plates etc. These methods also proved their effectiveness in the detection of cracks in concrete.
---
paper_title: Experimental Study of Impact-Damage Detection in Composite Laminates using a Cross-Modulation Vibro-Acoustic Technique

paper_content:

The paper demonstrates the application of cross-modulation vibro-acoustic technique for impact-damage detection in composite laminates. A composite plate is monitored for damage resulting from a low-velocity impact. The plate is excited simultaneously with two harmonic signals: a slow amplitude-modulated vibration pumping wave and a constant amplitude-probing wave. The frequency of both the excitation signals coincides with the resonances of the plate. An electromagnetic shaker is used to introduce the pumping wave to the plate. Two surface-bonded, low-profile piezoceramic transducers are used for probing-wave excitation and measurement. The wave modulation is transferred from the pumping wave to the probing wave in the presence of impact damage. This effect is exhibited in a power spectrum of the probing wave by a pattern of sidebands around the carrier harmonic. The results show that the amplitude of the sidebands is related to the severity of damage. The study also investigates also the effect of bound...
---
paper_title: Peridynamic model for dynamic fracture in unidirectional fiber-reinforced composites

paper_content:

Abstract We propose a computational method for a homogenized peridynamics description of fiber-reinforced composites and we use it to simulate dynamic brittle fracture and damage in these materials. With this model we analyze the dynamic effects induced by different types of dynamic loading on the fracture and damage behavior of unidirectional fiber-reinforced composites. In contrast to the results expected from quasi-static loading, the simulations show that dynamic conditions can lead to co-existence of and transitions between fracture modes; matrix shattering can happen before a splitting crack propagates. We observe matrix–fiber splitting fracture, matrix cracking, and crack migration in the matrix, including crack branching in the matrix similar to what is observed in recent dynamic experiments. The new model works for arbitrary fiber orientation relative to a uniform discretization grid and also works with random discretizations. The peridynamic composite model captures significant differences in the crack propagation behavior when dynamic loadings of different intensities are applied. An interesting result is branching of a splitting crack into two matrix cracks in transversely loaded samples. These cracks branch as in an isotropic material but here they migrate over the “fiber bonds”, without breaking them. This behavior has been observed in recent experiments. The strong influence that elastic waves have on the matrix damage and crack propagation paths is discussed. No special criteria for splitting mode fracture (Mode II), crack curving, or crack arrest are needed, and yet we obtain all these modes of material failure as a direct result of the peridynamic simulations.
---
paper_title: Luxemburg-Gorky Effect Retooled for Elastic Waves: A Mechanism and Experimental Evidence

paper_content:

A new mechanism is proposed for the linear and amplitude-dependent dissipation due to elastic-wavecrack interaction. We have observed one of its strong manifestations in a direct elastic-wave analog of the Luxemburg-Gorky effect consisting of the cross modulation of radio waves at the dissipative nonlinearity of the ionosphere plasma. The counterpart acoustic mechanism implies, first, a drastic enhancement of the thermoelastic coupling at high-compliance microdefects, and, second, the high stress-sensitivity of the defects leads to a strong stress dependence of the resultant dissipation.
---
paper_title: Observation of the “Luxemburg–Gorky effect” for elastic waves

paper_content:

An experimental observation of a new nonlinear-modulation effect for longitudinal elastic waves is reported. The phenomenon is a direct elastic wave analogy with the so-called Luxemburg–Gorky (L–G) effect known over 60 years for radio waves propagating in the ionosphere. The effect consists of the appearance of modulation of a weaker initially non-modulated wave propagating in a nonlinear medium in the presence of an amplitude-modulated stronger wave that produces perturbations in the medium properties on the scale of its modulation frequency. The reported transfer of modulation from one elastic wave to another was observed in a resonator cut of a glass rod containing a few small cracks. Presence of such a small damage drastically enhances the material nonlinearity compared to elastic atomic nonlinearity of homogeneous solids, so that the pronounced L– G type cross-modulation could be observed at strain magnitude in the stronger wave down to 10 7 and smaller. Main features of the effect are pointed out and physical mechanism of the observed phenomena is discussed. 2002 Elsevier Science B.V. All rights reserved.
---
paper_title: Nonlinear acoustics for fatigue crack detection – experimental investigations of vibro-acoustic wave modulations

paper_content:

Vibro-acoustic nonlinear wave modulations are investigated experimentally in a cracked aluminum plate. The focus is on the effect of low-frequency vibration excitation on modulation intensity and associated nonlinear wave interaction mechanisms. The study reveals that energy dissipation – not opening–closing crack action – is the major mechanism behind nonlinear modulations. The consequence is that relatively weak strain fields can be used for crack detection in metallic structures. A clear link between modulations and thermo-elastic coupling is also demonstrated, providing experimental evidence for the recently proposed non-classical, nonlinear vibro-acoustic wave interaction mechanism.
---
paper_title: Non-local modeling and simulation of wave propagation and crack growth

paper_content:

The paper presents the results of numerical analyses carried out for 2D models of aluminum plates undergoing crack propagation. Different types of numerical analyses were performed to show the area of applicability of a non-local discrete formulation of mechanical continua for NDE and QNDE. The authors’ interests dealt with: Lamb wave propagation, higher harmonics generation, the phenomenon of clapping, and wave generation and its propagation for growing crack. In the first case a 2D model allowed to find the displacements for the vertical cross-section along the direction of wave propagation and therefore assess its disturbance when introducing a notch. In-plane components of the displacements were considered for the latter 3 cases, in turn. The above cases and elaborated non-local numerical models were discussed in terms of detection of propagating crack. Apart from theoretical aspects of the presented work, the obtained results seem to be of great importance for improvement of experiments in terms of sensor distribution and required accuracy.The paper presents the results of numerical analyses carried out for 2D models of aluminum plates undergoing crack propagation. Different types of numerical analyses were performed to show the area of applicability of a non-local discrete formulation of mechanical continua for NDE and QNDE. The authors’ interests dealt with: Lamb wave propagation, higher harmonics generation, the phenomenon of clapping, and wave generation and its propagation for growing crack. In the first case a 2D model allowed to find the displacements for the vertical cross-section along the direction of wave propagation and therefore assess its disturbance when introducing a notch. In-plane components of the displacements were considered for the latter 3 cases, in turn. The above cases and elaborated non-local numerical models were discussed in terms of detection of propagating crack. Apart from theoretical aspects of the presented work, the obtained results seem to be of great importance for improvement of experiments in terms of s...
---
paper_title: Theoretical investigation of nonlinear ultrasonic wave modulation spectroscopy at crack interface

paper_content:

Abstract This paper studies theoretical results of a nonlinear ultrasonic method based on interaction of two elastic waves of different frequencies. A virtual Nonlinear Wave Modulation Spectroscopy experiment is performed in the vicinity of a crack described by a model combining classical and hysteretic nonlinearity. Quasistatic response to two frequency excitation was computed and harmonic and intermodulation components were studied. The influence of driving signal parameters and nonlinear parameters on the response is thoroughly discussed. A general way of hysteretic response description based on scaling properties is explained. In case of the combined nonlinear model, an analysis of nonlinear spectral components is performed in complex plane. Based on the complex interaction of classical and hysteretic parts, a method of their separation is proposed.
---
paper_title: Impact damage detection in composite chiral sandwich panels using nonlinear vibro-acoustic modulations

paper_content:

This paper reports an application of nonlinear acoustics to impact damage detection in a composite chiral sandwich panel. The panel is built from a chiral honeycomb and two composite skins. High-frequency ultrasonic excitation and low-frequency modal excitation were used to observe nonlinear modulations in ultrasonic waves due to structural damage. Low-profile, surface-bonded piezoceramic transducers were used for ultrasonic excitation. Non-contact laser vibrometry was applied for ultrasonic sensing. The work presented focuses on the analysis of the modulation intensities and damage-related nonlinearities. The paper demonstrates that the method can be used for impact damage detection in composite chiral sandwich panels.
---
paper_title: Vibro‐Acoustic Modulation NDE Technique. Part 2: Experimental Study

paper_content:

The crack detection capability of the Vibro‐Acoustic Modulation NDE technique is experimentally investigated over a broad range of ultrasonic frequencies. The generation of low frequency modes of the samples is performed using harmonic excitation applied by a shaker or by tapping. For both excitation methods the effect of different strain levels on the sideband activity is analyzed. The implementation of practical and reliable supports for testing the specimens is also considered in this study, as well as examples of results on industrial components.
---
paper_title: Impact damage detection in laminated composites by non-linear vibro-acoustic wave modulations

paper_content:

Abstract The paper presents an application of nonlinear acoustics for impact damage detection in composite laminates. Two composite plates were analysed. A low-velocity impact was used to damage one of the plates. Ultrasonic C-scan was applied to reveal the extent of barely visible impact damage. Finite element modelling was used to find vibration mode shapes of the plates and to estimate the local defect resonance frequency in the damaged plate. A delamination divergence study was performed to establish excitation parameters for nonlinear acoustics tests used for damage detection. Both composite plates were instrumented with surface-bonded, low-profile piezoceramic transducers that were used for the high-frequency ultrasonic excitation. Both an arbitrary frequency and a frequency corresponding to the local defect resonance were investigated. The low-frequency modal excitation was applied using an electromagnetic shaker. Scanning laser vibrometry was applied to acquire the vibro-acoustic responses from the plates. The study not only demonstrates that nonlinear vibro-acoustic modulations can successfully reveal the barely visible impact damage in composite plates, but also that the entire procedure can be enhanced when the ultrasonic excitation frequency corresponds to the resonant frequency of damage.
---
paper_title: Non-linear techniques for ultrasonic micro-damage diagnostics: A Simulation Approach

paper_content:

In the field of ultrasonic micro-damage diagnostics, nonlinear techniques seem to possess an enormous potential for applications. In fact, whenever mesoscopic features (e.g. mechanical inhomogeneities which are very small with respect to the acoustic wavelength, but much larger than interatomic spacings) are present, acoustic nonlinearity may be up to four orders of magnitude higher than in a perfect monocrystal. Correspondingly, nonlinear parameters are much more sensitive to the presence of micro-inhomogeneities and, in particular, of microdamage. Reliable techniques, such as Single Mode Nonlinear Resonance Acoustic Spectroscopy (SIMONRAS) and Nonlinear Wave Modulation Spectroscopy (NWMS), have been developed in order to quantify the acoustic nonlinearity of laboratory samples. A comparison with theoretical predictions is, however, extremely difficult due to the complexity of the phenomena involved (e.g. hysteretic behavior and end point memory). For this purpose an extension of the Local Interaction Si...
---
paper_title: N-SCAN: new vibromodulation system for detection and monitoring of cracks and other contact-type defects

paper_content:

In recent years, innovative vibro-modulation technique has been introduced for detection of contact-type interfaces such as cracks, debondings, and delaminations. The technique utilizes the effect of nonlinear interaction of ultrasound and vibrations at the interface of the defect. Vibration varies on the contact area of the interface modulating passing through ultrasonic wave. The modulation manifests itself as additional side-band spectral components with the combination frequencies in the spectrum of the received signal. The presence of these components allows for detection and differentiation of the contact-type defects from other structural and material inhomogeneities. Vibro-modulation technique has been implemented in N-SCAN damage detection system. The system consists of a digital synthesizer, high and low frequency amplifiers, a magnetostrictive shaker, ultrasonic transducers and a PC-based data acquisition/processing station with N-SCAN software. The ability of the system to detect contact-type defects was experimentally verified using specimens of simple and complex geometries made of steel, aluminum, composites and other structural materials. N-SCAN proved to be very effective for nondestructive testing of full-scale structures ranging from 24 foot-long gun barrels to stainless steel pipes used in nuclear power plants. Among advantages of the system are applicability for the wide range of structural materials and for structures with complex geometries, real time data processing, convenient interface for system operation, simplicity of interpretation of results, no need for sensor scanning along structure, onsite inspection of large structures at a fraction of time as compared with conventional techniques. This paper describes the basic principles of nonlinear vibro-modulation NDE technique, some theoretical background for nonlinear interaction and justification of signal processing algorithm. It is also presents examples of practical implementation and application of the technique.
---
paper_title: Dynamic nonlinear elasticity in geomaterials

paper_content:

This invention relates to a lens for presbyopia free from distortional aberration for use in correcting an old-age eyesight. In the lens for presbyopia with a front lens surface having a smaller radius of curvature than a rear lens face, a lens surface has a refractive power successively corrected as the lens surface extends radially outwardly away from a geometric center of the lens so that lateral magnifications for all principal rays always equal a lateral magnification for a paraxial range. This construction is entirely free from distortional aberration, and secures a greatly enlarged range of distinct vision.
---
paper_title: Peridynamic Theory and Its Applications

paper_content:

Introduction.- Peridynamic Theory.- Peridynamics for Local Interactions.- Peridynamics for Isotropic Materials.- Peridynamics for Laminated Composite Materials.- Damage Prediction.- Numerical Solution Methods.- Benchmark Problems.- Nonimpact Problems.- Impact Problems.- Coupling of the Peridynamic Theory and Finite Element Methods.- Peridynamic Thermal Diffusion.- Fully Coupled Peridynamic Thermomechanics.
---
paper_title: Time reversal and non-linear elastic wave spectroscopy (TR NEWS) techniques

paper_content:

Non-linear elastic wave spectroscopy (NEWS) has been shown to exhibit a high degree of sensitivity to both distributed and isolated nonlinear scatterers in solids. In the case of an isolated non-linear scatterer such as a crack, by combining the elastic energy localization of time reversal (TR) with NEWS, it is shown that one can isolate non-linear scatterers in solids. The experiments reviewed here present two distinct methods of combining TR and NEWS for this purpose. The techniques each have there own advantages and disadvantages, with respect to each other and other non-linear methods, which are discussed. 2008 Published by Elsevier Ltd.
---
paper_title: Nonlinear modulation technique for NDE with air-coupled ultrasound

paper_content:

Abstract The present study is aimed at expanding flexibility and application area of nonlinear acoustic modulation (NAM-) technique by combining the benefits of noncontact ultrasound excitation (remote locating and imaging of defects) with sensitivity of nonlinear methods in a new air-coupled NAM-version. A pair of focused air-coupled transducers was used to generate and receive (high-frequency) longitudinal or flexural waves in plate-like samples. Low-frequency (LF-) vibrations were excited with a shaker or a loudspeaker. Temporal and spectral analysis of the output signal revealed an extremely efficient nonlinear amplitude modulation and multiple frequency side-bands for sound transmission and flexural wave propagation through cracked defects. On the contrary, a negligible modulation was observed for large and medium scale inclusions and material inhomogeneities (linear defects). A new subharmonic mode of the NAM was observed at high excitation levels. It was also shown for the first time that nonlinear vibrations of cracks resulted in radiation of a very high-order harmonics (well above 100) of the driving excitation in air that enabled imaging of cracks remotely by registration their highly nonlinear “acoustic emission” with air-coupled transducers.
---
paper_title: Combined Photoacoustic–Acoustic Technique for Crack Imaging

paper_content:

Nonlinear imaging of a crack by combination of a common photoacoustic imaging technique with additional acoustic loading has been performed. Acoustic signals at two different fundamental frequencies were launched in the sample, one photoacoustically through heating of the sample surface by the intensity-modulated scanning laser beam and another by a piezoelectrical transducer. The acoustic signal at mixed frequencies, generated due to system nonlinearity, has been detected by an accelerometer. Different physical mechanisms of the nonlinearity contributing to the contrast in linear and nonlinear photoacoustic imaging of the crack are discussed.
---
paper_title: Nonlinear acoustic interaction on contact interfaces and its use for nondestructive testing

paper_content:

Recent theoretical and experimental studies demonstrated that a weakly or incompletely bonded interfaces exhibit highly nonlinear behavior. One of acoustic manifestations of such nonlinearity is the modulation of a probing high-frequency ultrasonic wave by low-frequency vibration. The vibration varies the contact area modulating the phase and amplitude of higher frequency probing wave passing through the interface. In the frequency domain, the result of this modulation manifests itself as side-band spectral components with respect to the frequency of the probing wave. This modulation effect has been observed experimentally for various materials (metals, composites, concrete, sandstone, glass) with various types of contact-type defects (interfaces): cracks, debondings, delaminations, and microstructural material damages. Study of this phenomenon revealed correlation between the developed modulation criterion and the quantitative characteristics of the interfaces, such as its size, loading condition, and bonding strength. These findings have been used for the development of an innovative nondestructive evaluation technique, namely Vibro-Acoustic Modulation Technique. Two modifications of this technique have been developed: Vibro-Modulation (VM) and Impact-Modulation (IM), employing CW and impact-induced vibrations, respectively. The examples of applications of these methods include crack detection in steel pipes, aircraft and auto parts, bonded composite plates etc. These methods also proved their effectiveness in the detection of cracks in concrete.
---
paper_title: Global crack detection using bispectral analysis

paper_content:

This paper describes a global non-destructive testing technique for detecting fatigue cracking in engineering components. The technique measures the mixing of two ultrasonic sinusoidal waves which are excited by a small piezoceramic disc bonded to the test structure. This input signal excites very high-order modes of vibration of the test structure within the ultrasonic frequency range. The response of the structure is measured by a second piezoceramic disc and the received waveform is analysed using the bispectrum signal processing technique. Frequency mixing occurs as a result of nonlinearities within the test structure and fatigue cracking is shown to produce a strong mixing effect. The bispectrum is shown to be particularly suitable for this application due to its known insensitivity to noise. Experimental results on steel beams are used to show that fatigue cracks, corresponding to a reduction in the beam section of 8%, can be detected. It is also shown that the bispectrum can be used to quantify the extent of the cracking. A simple nonlinear spring model is used to interpret the results and demonstrate the robustness of the bispectrum for this application.
---
paper_title: Non-contact nonlinear ultrasound scan of a CFRP plate with manufactured damages

paper_content:

A Carbon Fibre Reinforced Plastic plate was manufactured to have internal damages of different types. A nonlinear ultrasound technique was used to scan the plate. Non-contact transmitters of own design were used as transducer, and a contact sensor was used to measure the wave in the composite. Scanning was made perpendicularly with the sensor being on the same side as the transducer. The technique can be adapted in accuracy and speed.
---
paper_title: Impact damage detection in light composite sandwich panels using piezo-based nonlinear vibro-acoustic modulations

paper_content:

The nonlinear vibro-acoustic modulation technique is used for impact damage detection in light composite sandwich panels. The method utilizes piezo-based low-frequency vibration and high-frequency ultrasonic excitations. The work presented focuses on the analysis of modulation intensity. The results show that the method can be used for impact damage detection reliably separating damage-related from vibro-acoustic modulations from other intrinsic nonlinear modulations.
---
paper_title: Crack detection using nonlinear acoustics and piezoceramic transducers—instantaneous amplitude and frequency analysis

paper_content:

This paper investigates the nonlinear vibro-acoustic modulation technique for damage detection in metallic structures. Surface-bonded, low-profile piezoceramic actuators are used to introduce a high-frequency ultrasonic wave and low-frequency modal vibration into an aluminium specimen. The response of the vibro-acoustic interaction is monitored by a third low-profile piezoceramic transducer. In contrast to previous applications analysing the response in the frequency domain, current investigations focus on the instantaneous characteristics of the response using the Hilbert?Huang transform. The study shows that both modulations, i.e.?amplitude and frequency, are present in the acoustical responses when the aluminium plate is cracked. The intensity of amplitude modulation correlates far better with crack lengths than the intensity of frequency modulations.
---
paper_title: Vibro-acoustic modulation–based damage identification in a composite skin–stiffener structure

paper_content:

The vibro-acoustic modulation method is applied to a composite skin-stiffener structure to investigate the possibilities to utilise this method for damage identification in terms of detection, localisation and damage quantification. The research comprises a theoretical part and an experimental part. An impact load is applied to the skin-stiffener structure, resulting in a delamination underneath the stiffener. The structure is interrogated with a low frequency pump excitation and a high frequency carrier excitation. The analysis of the response in a frequency band around the carrier frequency is employed to assess the damage identification capabilities and to gain a better understanding of the modulations occurring and the underlying physical phenomena. Though vibro-acoustic is shown to be a sensitive method for damage identification, the complexity of the damage, combined with a high modal density, complicate the understanding of the relation between the physical phenomena and the modulations occurring.
---
paper_title: Nonlinear acoustics for fatigue crack detection – experimental investigations of vibro-acoustic wave modulations

paper_content:

Vibro-acoustic nonlinear wave modulations are investigated experimentally in a cracked aluminum plate. The focus is on the effect of low-frequency vibration excitation on modulation intensity and associated nonlinear wave interaction mechanisms. The study reveals that energy dissipation – not opening–closing crack action – is the major mechanism behind nonlinear modulations. The consequence is that relatively weak strain fields can be used for crack detection in metallic structures. A clear link between modulations and thermo-elastic coupling is also demonstrated, providing experimental evidence for the recently proposed non-classical, nonlinear vibro-acoustic wave interaction mechanism.
---
paper_title: Vibro-Acoustic Modulation Utilizing a Swept Probing Signal for Robust Crack Detection

paper_content:

One practical issue that must be addressed prior to the implementation of a vibration-based structural health monitoring system is the influence that variations in the structure’s environmental and boundary conditions can have on the vibration response of the structure. This issue is especially prominent in the structural health monitoring of aircraft, which operate in a wide variety of different environmental conditions and possess complex structural components connected through various boundary conditions. However, many types of damage introduce nonlinear stiffness and damping restoring forces, which may be used to detect damage even in the midst of these varying conditions. Vibro-acoustic modulation is a nondestructive evaluation technique that is highly sensitivity to the presence of nonlinearities. One factor that complicates the use of vibro-acoustic modulation as a structural health monitoring technique is that the amount of measured modulation has been shown to be dependent on the frequency of the...
---
paper_title: Nonlinear Elastic Wave NDE II. Nonlinear Wave Modulation Spectroscopy and Nonlinear Time Reversed Acoustics

paper_content:

This paper presents the second part of the review of Nonlinear Elastic Wave Spectroscopy (NEWS) in NDE, and describe two different methods of nonlinear NDE that provide not only damage detection but location as well. Nonlinear Wave Modulation Spectroscopy is based on the application of an ultrasonic probe signal modulated by a low frequency vibration. Damage location can be obtained by application of Impulse Modulation Techniques that exploit the modulation of a short pulse reflected from a damage feature (e.g. crack) by low frequency vibration. Nonlinear Time Reversed Acoustic methods provide the means to focus acoustic energy to any point in a solid. In combination, we are applying the focusing properties of TRA and the nonlinear properties of cracks to locate them.
---
paper_title: Noncontact fatigue crack visualization using nonlinear ultrasonic modulation

paper_content:

Abstract This paper presents a complete noncontact fatigue crack visualization technique based on nonlinear ultrasonic wave modulation and investigates the main source of nonlinear modulation generation. Two distinctive frequency input signals are created by two air-coupled transducers and the corresponding ultrasonic responses are scanned using a 3D laser Doppler vibrometer. The effectiveness of the proposed technique is tested using aluminum plates with different stages of fatigue crack formation such as micro and macro-cracks. Furthermore, the main source of nonlinear modulation is discussed based on the visualization results and the microscopic images.
---
paper_title: Impact damage detection in laminated composites by non-linear vibro-acoustic wave modulations

paper_content:

Abstract The paper presents an application of nonlinear acoustics for impact damage detection in composite laminates. Two composite plates were analysed. A low-velocity impact was used to damage one of the plates. Ultrasonic C-scan was applied to reveal the extent of barely visible impact damage. Finite element modelling was used to find vibration mode shapes of the plates and to estimate the local defect resonance frequency in the damaged plate. A delamination divergence study was performed to establish excitation parameters for nonlinear acoustics tests used for damage detection. Both composite plates were instrumented with surface-bonded, low-profile piezoceramic transducers that were used for the high-frequency ultrasonic excitation. Both an arbitrary frequency and a frequency corresponding to the local defect resonance were investigated. The low-frequency modal excitation was applied using an electromagnetic shaker. Scanning laser vibrometry was applied to acquire the vibro-acoustic responses from the plates. The study not only demonstrates that nonlinear vibro-acoustic modulations can successfully reveal the barely visible impact damage in composite plates, but also that the entire procedure can be enhanced when the ultrasonic excitation frequency corresponds to the resonant frequency of damage.
---
paper_title: N-SCAN: new vibromodulation system for detection and monitoring of cracks and other contact-type defects

paper_content:

In recent years, innovative vibro-modulation technique has been introduced for detection of contact-type interfaces such as cracks, debondings, and delaminations. The technique utilizes the effect of nonlinear interaction of ultrasound and vibrations at the interface of the defect. Vibration varies on the contact area of the interface modulating passing through ultrasonic wave. The modulation manifests itself as additional side-band spectral components with the combination frequencies in the spectrum of the received signal. The presence of these components allows for detection and differentiation of the contact-type defects from other structural and material inhomogeneities. Vibro-modulation technique has been implemented in N-SCAN damage detection system. The system consists of a digital synthesizer, high and low frequency amplifiers, a magnetostrictive shaker, ultrasonic transducers and a PC-based data acquisition/processing station with N-SCAN software. The ability of the system to detect contact-type defects was experimentally verified using specimens of simple and complex geometries made of steel, aluminum, composites and other structural materials. N-SCAN proved to be very effective for nondestructive testing of full-scale structures ranging from 24 foot-long gun barrels to stainless steel pipes used in nuclear power plants. Among advantages of the system are applicability for the wide range of structural materials and for structures with complex geometries, real time data processing, convenient interface for system operation, simplicity of interpretation of results, no need for sensor scanning along structure, onsite inspection of large structures at a fraction of time as compared with conventional techniques. This paper describes the basic principles of nonlinear vibro-modulation NDE technique, some theoretical background for nonlinear interaction and justification of signal processing algorithm. It is also presents examples of practical implementation and application of the technique.
---
paper_title: Structural Health Monitoring Using Guided Ultrasonic Waves

paper_content:

Maintenance of air, land and sea structures is an important engineering activity in a wide range of industries including transportation and Civil Engineering. Effective maintenance minimises not only the cost of ownership of structures but also improves safety and the perception of safety. Inspection for material/structural damage, such as fatigue cracks and corrosion in metallics or delamination in composites, is an essential part of maintenance.
---
paper_title: Vibro-acoustic modulation nondestructive evaluation technique

paper_content:

Nonlinear acoustic technique has been recently introduced as a new tool for nondestructive inspection and evaluation of fatigued, defective, and fractured materials. Various defects such as cracks, debonding, fatigue, etc. lead to anomalous high level of nonlinearity as compared with flawless structures. One of the acoustic manifestations of such nonlinearity is the modulation of ultrasound by low frequency vibration. Two methods employing the nonlinear interaction of ultrasound and vibration were developed, namely vibro-modulation (VM) and impact-modulation (IM) methods. VM method employs forced harmonic vibration of a structure tested, while IM method uses impact excitation of structure natural modes of vibration. The feasibility tests were carried out for different objects and demonstrated high sensitivity of the methods for detection of cracks in steel pipes and pins, bonding quality in titanium and thermoplastic plates used for airspace applications, cracks in combustion engine, adhesion flaws in bonded composite structures, and cracks and corrosion in reinforced concrete. The model of the crack allowing to describe the modulation of sound by vibration is discussed. The developed nonlinear technique demonstrated certain advantages as compared with the conventional linear acoustic technique, specifically discrimination capabilities, sensitivity, and applicability to highly inhomogeneous structures.
---
paper_title: Elastic-wave modulation approach to crack detection: Comparison of conventional modulation and higher-order interactions

paper_content:

Abstract Comparison of recent theoretical estimates with experiments has indicated that the ultimate sensitivity of the conventional modulation technique of crack detection is mainly determined by the background modulation produced by the quadratic component of the atomic nonlinearity of the matrix material. Much smaller level of masking nonlinear effects is typical of higher-order interactions due to cubic and higher-order components in the power-series expansion of the background nonlinearity of the solid. In contrast, the level of formally higher-order components originated due to nonlinearity of crack-like defects can be comparable with that of the first-order components. Such strongly increased efficiency of higher-order interactions is due to the fact that crack-like defects often demonstrate non-analytic (non power-law) nonlinearity even for moderate acoustic amplitudes. Besides the increased level, the higher-order components arisen due to non-analytic nonlinearity of cracks can demonstrate significantly different functional behavior compared to manifestations of the atomic nonlinearity. This difference can also help to discriminate the contributions of the defects and the background atomic nonlinearity. Here, we focus on the main differences between the modulation components arisen due to cubic terms in the power-series expansion of the atomic nonlinearity and similar components generated by clapping Hertzian nonlinearity of inner contacts in cracks. We also examine experimental examples of higher-order modulation interactions in damaged samples. These examples clearly indicate non-analytical character of the defects’ nonlinearity and demonstrate that the use of higher-order modulation effects can significantly improve the ultimate sensitivity and reliability of the modulation approach to detection of crack-like defects.
---
paper_title: Nonlinear Elastic Wave Spectroscopy (NEWS) Techniques to Discern Material Damage, Part I: Nonlinear Wave Modulation Spectroscopy (NWMS)

paper_content:

Abstract. The level of nonlinearity in the elastic response of materials containing structural damage is far greater than in materials with no structural damage. This is the basis for nonlinear wave diagnostics of damage, methods which are remarkably sensitive to the detection and progression of damage in materials. Nonlinear wave modulation spectroscopy (NWMS) is one exemplary method in this class of dynamic nondestructive evaluation techniques. The method focuses on the application of harmonics and sum and difference frequency to discern damage in materials. It consists of exciting a sample with continuous waves of two separate frequencies simultaneously, and inspecting the harmonics of the two waves, and their sum and difference frequencies (sidebands). Undamaged materials are essentially linear in their response to the two waves, while the same material, when damaged, becomes highly nonlinear, manifested by harmonics and sideband generation. We illustrate the method by experiments on uncracked and cracked Plexiglas and sandstone samples, and by applying it to intact and damaged engine components.
---
paper_title: Nonlinear acoustic interaction on contact interfaces and its use for nondestructive testing

paper_content:

Recent theoretical and experimental studies demonstrated that a weakly or incompletely bonded interfaces exhibit highly nonlinear behavior. One of acoustic manifestations of such nonlinearity is the modulation of a probing high-frequency ultrasonic wave by low-frequency vibration. The vibration varies the contact area modulating the phase and amplitude of higher frequency probing wave passing through the interface. In the frequency domain, the result of this modulation manifests itself as side-band spectral components with respect to the frequency of the probing wave. This modulation effect has been observed experimentally for various materials (metals, composites, concrete, sandstone, glass) with various types of contact-type defects (interfaces): cracks, debondings, delaminations, and microstructural material damages. Study of this phenomenon revealed correlation between the developed modulation criterion and the quantitative characteristics of the interfaces, such as its size, loading condition, and bonding strength. These findings have been used for the development of an innovative nondestructive evaluation technique, namely Vibro-Acoustic Modulation Technique. Two modifications of this technique have been developed: Vibro-Modulation (VM) and Impact-Modulation (IM), employing CW and impact-induced vibrations, respectively. The examples of applications of these methods include crack detection in steel pipes, aircraft and auto parts, bonded composite plates etc. These methods also proved their effectiveness in the detection of cracks in concrete.
---
paper_title: Nonlinear ultrasonic wave modulation for online fatigue crack detection

paper_content:

Abstract This study presents a fatigue crack detection technique using nonlinear ultrasonic wave modulation. Ultrasonic waves at two distinctive driving frequencies are generated and corresponding ultrasonic responses are measured using permanently installed lead zirconate titanate (PZT) transducers with a potential for continuous monitoring. Here, the input signal at the lower driving frequency is often referred to as a ‘pumping’ signal, and the higher frequency input is referred to as a ‘probing’ signal. The presence of a system nonlinearity, such as a crack formation, can provide a mechanism for nonlinear wave modulation, and create spectral sidebands around the frequency of the probing signal. A signal processing technique combining linear response subtraction (LRS) and synchronous demodulation (SD) is developed specifically to extract the crack-induced spectral sidebands. The proposed crack detection method is successfully applied to identify actual fatigue cracks grown in metallic plate and complex fitting-lug specimens. Finally, the effect of pumping and probing frequencies on the amplitude of the first spectral sideband is investigated using the first sideband spectrogram (FSS) obtained by sweeping both pumping and probing signals over specified frequency ranges.
---
paper_title: Nonlinear acoustics for fatigue crack detection – experimental investigations of vibro-acoustic wave modulations

paper_content:

Vibro-acoustic nonlinear wave modulations are investigated experimentally in a cracked aluminum plate. The focus is on the effect of low-frequency vibration excitation on modulation intensity and associated nonlinear wave interaction mechanisms. The study reveals that energy dissipation – not opening–closing crack action – is the major mechanism behind nonlinear modulations. The consequence is that relatively weak strain fields can be used for crack detection in metallic structures. A clear link between modulations and thermo-elastic coupling is also demonstrated, providing experimental evidence for the recently proposed non-classical, nonlinear vibro-acoustic wave interaction mechanism.
---
paper_title: Vibro-Acoustic Modulation Utilizing a Swept Probing Signal for Robust Crack Detection

paper_content:

One practical issue that must be addressed prior to the implementation of a vibration-based structural health monitoring system is the influence that variations in the structure’s environmental and boundary conditions can have on the vibration response of the structure. This issue is especially prominent in the structural health monitoring of aircraft, which operate in a wide variety of different environmental conditions and possess complex structural components connected through various boundary conditions. However, many types of damage introduce nonlinear stiffness and damping restoring forces, which may be used to detect damage even in the midst of these varying conditions. Vibro-acoustic modulation is a nondestructive evaluation technique that is highly sensitivity to the presence of nonlinearities. One factor that complicates the use of vibro-acoustic modulation as a structural health monitoring technique is that the amount of measured modulation has been shown to be dependent on the frequency of the...
---
paper_title: Nonlinear Elastic Wave NDE II. Nonlinear Wave Modulation Spectroscopy and Nonlinear Time Reversed Acoustics

paper_content:

This paper presents the second part of the review of Nonlinear Elastic Wave Spectroscopy (NEWS) in NDE, and describe two different methods of nonlinear NDE that provide not only damage detection but location as well. Nonlinear Wave Modulation Spectroscopy is based on the application of an ultrasonic probe signal modulated by a low frequency vibration. Damage location can be obtained by application of Impulse Modulation Techniques that exploit the modulation of a short pulse reflected from a damage feature (e.g. crack) by low frequency vibration. Nonlinear Time Reversed Acoustic methods provide the means to focus acoustic energy to any point in a solid. In combination, we are applying the focusing properties of TRA and the nonlinear properties of cracks to locate them.
---
paper_title: Nonlinear elastic wave spectroscopy identification of impact damage on a sandwich plate

paper_content:

Fragility of composite material to impact loading limits their application in aircraft structures. There is the need to develop reliable monitoring devices capable of localizing and assessing impact damage. At this aim, a new technique, non-linear elastic wave spectroscopy (NEWS), developed for geophysics applications, is investigated and presented in this paper. The NEWS damage detection based technique consists in the analysis of the spectrum of a signal acquired from the structure under investigation excited by a bi-harmonic signal. In pristine conditions, the signal spectrum presents two picks at the excitation frequencies. In presence of damages, the material starts to behave non-linearly and sidebands and harmonics of the excited frequencies are generated. In this study, experimental findings on a sandwich plate are presented in order to understand the capability of the NEWS technique to detect impact damages.
---
paper_title: Vibro-acoustic modulation technique for micro-crack detection in pipeline

paper_content:

For the poor sensitivity of traditional ultrasonic technique for micro crack detection, a kind of ::: nonlinear ultrasonic technique, vibro-acoustic modulation technique, is used for micro crack detection ::: in pipes. The influence of the frequency and amplitude of vibration on the modulation index (MI) is ::: experimentally investigated. The experiment results prove that the vibro-acoustic modulation technique ::: can be used for crack detection in pipes. The modulation index is influenced by the frequency and ::: amplitude of vibration, therefore it is important to choose the appropriate parameters in order to get ::: higher sensitivity in crack detection.
---
paper_title: Nonlinear acoustics with low-profile piezoceramic excitation for crack detection in metallic structures

paper_content:

Structural damage detection is one of the major maintenance activities in a wide range of industries. A variety of different methods have been developed for detection of fatigue cracks in metallic structures over the last few decades. This includes techniques based on stress/acoustic waves propagating in monitored structures. Classical ultrasonic techniques used in nondestructive testing and evaluation are based on linear amplitude and/or phase variations of reflected, transmitted or scattered waves. In recent years a range of different techniques utilizing nonlinear phenomena in vibration and acoustic signals have been developed. It appears that these techniques are more sensitive to damage alterations than other techniques used for damage detection based on linear behaviour. The paper explores the use of low-profile piezoceramic actuators with low-frequency excitation in nonlinear acoustics. The method is used to detect a fatigue crack in an aluminium plate. The results are compared with modal/vibration excitation performed with an electromagnetic shaker. The study shows that piezoelectric excitation with surface-bonded low-profile piezoceramic transducers is suitable for crack detection based on nonlinear acoustics.
---
paper_title: Comparison between a type of vibro-acoustic modulation and damping measurement as NDT techniques

paper_content:

The sensitivities of the conventional damping test and a particular implementation of the emerging vibro-acoustic modulation NDT technique have been compared on three types of cracked specimens: (1) a set of mild steel beams cracked in the laboratory, (2) a perspex beam also cracked in the laboratory and (3) an industrial component made of a nickel-based alloy. The latter was forged and cracked in the forging process. The comparison showed very similar performances on the specimens used. Both techniques work best for lightly damped specimens and in setups such that the influence of the support can be minimised. Their sensitivity is severely affected when these two conditions are not satisfied which significantly lower their appeal for many practical situations. (c) 2005 Published by Elsevier Ltd.
---
paper_title: N‐Scan®: New Vibro‐Modulation System for Crack Detection, Monitoring and Characterization

paper_content:

In recent years, an innovative vibro‐modulation technique has been introduced for the detection of contact‐type interfaces such as cracks, debondings, and delaminations. The technique utilizes the effect of nonlinear interaction of ultrasound and vibrations at the interface of the defect. Vibration varies the contact area of the interface, modulating a passing ultrasonic wave. The modulation manifests itself as additional side‐band spectral components with the combination frequencies in the spectrum of the received signal. The presence of these components allows for the detection and differentiation of the contact‐type defects from other structural and material inhomogeneities. The vibro‐modulation technique has been implemented in the N‐SCAN® damage detection system providing a cost effective solution for the complex NDT problems. N‐SCAN® proved to be very effective for damage detection and characterization in structures and structural components of simple and complex geometries made of steel, aluminum, ...
---
paper_title: A study of the vibro-acoustic modulation technique for the detection of cracks in metals

paper_content:

One implementation of the vibro-modulation technique involves monitoring the amplitude modulation of an ultrasonic vibration field transmitted through a cracked specimen undergoing an additional low frequency structural vibration. If the specimen is undamaged and appropriately supported, the two vibration fields do not interact. This phenomenon could be used as the basis for a nondestructive testing technique. In this paper, the sensitivity of the technique is investigated systematically on a set of mild steel beams with cracks of different sizes and shapes. A damage index was measured for each crack. The correlation obtained between the crack size and the strength of the modulation is fairly poor. The technique proved extremely sensitive to the initial state of opening and closing of the crack and to the setup due to the modulating effects of contacts between the specimens and the supports. A simple model is proposed which explains the main features observed and approximately predicts the level of sideband obtained experimentally.
---
paper_title: Vibro‐Acoustic Modulation NDE Technique. Part 2: Experimental Study

paper_content:

The crack detection capability of the Vibro‐Acoustic Modulation NDE technique is experimentally investigated over a broad range of ultrasonic frequencies. The generation of low frequency modes of the samples is performed using harmonic excitation applied by a shaker or by tapping. For both excitation methods the effect of different strain levels on the sideband activity is analyzed. The implementation of practical and reliable supports for testing the specimens is also considered in this study, as well as examples of results on industrial components.
---
paper_title: N-SCAN: new vibromodulation system for detection and monitoring of cracks and other contact-type defects

paper_content:

In recent years, innovative vibro-modulation technique has been introduced for detection of contact-type interfaces such as cracks, debondings, and delaminations. The technique utilizes the effect of nonlinear interaction of ultrasound and vibrations at the interface of the defect. Vibration varies on the contact area of the interface modulating passing through ultrasonic wave. The modulation manifests itself as additional side-band spectral components with the combination frequencies in the spectrum of the received signal. The presence of these components allows for detection and differentiation of the contact-type defects from other structural and material inhomogeneities. Vibro-modulation technique has been implemented in N-SCAN damage detection system. The system consists of a digital synthesizer, high and low frequency amplifiers, a magnetostrictive shaker, ultrasonic transducers and a PC-based data acquisition/processing station with N-SCAN software. The ability of the system to detect contact-type defects was experimentally verified using specimens of simple and complex geometries made of steel, aluminum, composites and other structural materials. N-SCAN proved to be very effective for nondestructive testing of full-scale structures ranging from 24 foot-long gun barrels to stainless steel pipes used in nuclear power plants. Among advantages of the system are applicability for the wide range of structural materials and for structures with complex geometries, real time data processing, convenient interface for system operation, simplicity of interpretation of results, no need for sensor scanning along structure, onsite inspection of large structures at a fraction of time as compared with conventional techniques. This paper describes the basic principles of nonlinear vibro-modulation NDE technique, some theoretical background for nonlinear interaction and justification of signal processing algorithm. It is also presents examples of practical implementation and application of the technique.
---
paper_title: Impact damage detection in composite laminates using nonlinear acoustics

paper_content:

The paper demonstrates the application of nonlinear acoustics for impact damage detection in composite laminates. A composite plate is monitored for damage resulting from a low-velocity impact. The plate is instrumented with bonded low-profile piezoceramic transducers. A high-frequency acoustic wave is introduced to one transducer and picked up by a different transducer. A low-frequency flexural modal excitation is introduced to the plate at the same time using an electromagnetic shaker. The damage induced by impact is exhibited in a power spectrum of the acoustic response by a pattern of sidebands around the main acoustic harmonic. The results show that the amplitude of sidebands is related to the severity of damage. The study investigates also the effect of boundary conditions on the results.
---
paper_title: Damage detection in an aircraft foam sandwich panel using nonlinear elastic wave spectroscopy

paper_content:

A novel damage detection technique, based on nonlinear elastic wave spectroscopy (NEWS) approach, is presented in this paper. This technique detects the presence of structural changes by monitoring the presence of harmonics and sidebands generated by the interaction between a low frequency and a high frequency harmonic excitation signal, due to the nonlinear material behaviour caused by the presence of damage. The proposed methodology was tested on a sandwich plate after being impacted by a foreign object under low velocity impact conditions. The high frequency signal was modulated in amplitude and the changes of the structural response, in terms of harmonic and sidebands amplitude, were recorded. The spectra and time frequency representation (TFR) were evaluated using wavelet transformations (WT). The experimental harmonic and sidebands amplitude resulted in close agreement with the theoretical behaviour of nonlinear behaviour of damaged materials. More specifically, the 3rd harmonics of the low frequency signal component showed a quadratic dependence with the low frequency response amplitude, as predicted by the theory for a hysteretic nonlinear material. Differently, the experimental second sidebands of the high frequency signal resulted bounded by curves representing the second sideband behaviour for pure hysteretic material (lower bound) and classical nonlinear material (upper bound). In particular, for small low frequency response amplitudes, the experimental second sidebands tended to be closer to the classical nonlinear material curve, while for the largest amplitudes investigated the response resembled a hysteretic material behaviour. The results showed that the proposed methodology was capable of detecting successfully the presence of impact damage and can be used as a first assessment of the presence of damage in aircraft structures where the presence of damage should be quickly estimated.
---
paper_title: Detecting barely visible impact damage detection on aircraft composites structures

paper_content:

Composites have many advantages as aircraft structural materials and for this reason their use is becoming increasingly widespread. Fragility of composite material to impact loading limits their application in aircraft structures. In particular, low velocity impacts can cause a significant amount of delamination, even though the only external indication of damage may be a very small surface indentation. This type of damage is often referred to as barely visible impact damage (BVID), and it can cause significant degradation of structural properties. If the damaged laminate is subjected to high compressive loading, buckling failure may occur. Therefore, there is the need to develop improved and more efficient means of detecting such damage. In this work a new NDT approach is presented, based on the monitoring of the nonlinear elastic material behaviour of damaged material. Two methods were investigated: a single-mode nonlinear resonance ultrasound (NRUS) and a nonlinear wave modulation spectroscopy (NWMS). The developed methods were tested on different composite plates with unknown mechanical properties and damage size and magnitude. The presence of the nonlinearities introduced by the damage was clearly identified using both techniques. The results showed that the proposed methodology appear to be highly sensitive to the presence of damage with very promising future applications.
---
paper_title: Crack detection technique for operating wind turbine blades using Vibro-Acoustic Modulation

paper_content:

This article presents a new technique for identifying cracks in wind turbine blades undergoing operational loads using the Vibro-Acoustic Modulation technique. Vibro-Acoustic Modulation utilizes a low-frequency pumping excitation signal in conjunction with a high-frequency probing excitation signal to create the modulation that is used to identify cracks. Wind turbines provide the ideal conditions in which Vibro-Acoustic Modulation can be utilized because wind turbines experience large low-frequency structural vibrations during operation which can serve as the low-frequency pumping excitation signal. In this article, the theory for the vibro-acoustic technique is described, and the proposed crack detection technique is demonstrated with Vibro-Acoustic Modulation experiments performed on a small Whisper 100 wind turbine in operation. The experimental results are also compared with two other conventional vibro-acoustic techniques in order to validate the new technique. Finally, a computational study is demo...
---
paper_title: Nonlinear elastic wave spectroscopy identification of impact damage on a sandwich plate

paper_content:

Fragility of composite material to impact loading limits their application in aircraft structures. There is the need to develop reliable monitoring devices capable of localizing and assessing impact damage. At this aim, a new technique, non-linear elastic wave spectroscopy (NEWS), developed for geophysics applications, is investigated and presented in this paper. The NEWS damage detection based technique consists in the analysis of the spectrum of a signal acquired from the structure under investigation excited by a bi-harmonic signal. In pristine conditions, the signal spectrum presents two picks at the excitation frequencies. In presence of damages, the material starts to behave non-linearly and sidebands and harmonics of the excited frequencies are generated. In this study, experimental findings on a sandwich plate are presented in order to understand the capability of the NEWS technique to detect impact damages.
---
paper_title: N‐Scan®: New Vibro‐Modulation System for Crack Detection, Monitoring and Characterization

paper_content:

In recent years, an innovative vibro‐modulation technique has been introduced for the detection of contact‐type interfaces such as cracks, debondings, and delaminations. The technique utilizes the effect of nonlinear interaction of ultrasound and vibrations at the interface of the defect. Vibration varies the contact area of the interface, modulating a passing ultrasonic wave. The modulation manifests itself as additional side‐band spectral components with the combination frequencies in the spectrum of the received signal. The presence of these components allows for the detection and differentiation of the contact‐type defects from other structural and material inhomogeneities. The vibro‐modulation technique has been implemented in the N‐SCAN® damage detection system providing a cost effective solution for the complex NDT problems. N‐SCAN® proved to be very effective for damage detection and characterization in structures and structural components of simple and complex geometries made of steel, aluminum, ...
---
paper_title: Delamination detection in composites using wave modulation spectroscopy with a novel active nonlinear acousto-ultrasonic piezoelectric sensor

paper_content:

A novel structural health monitoring (SHM) methodology, based on nonlinear wave modulation spectroscopy, is presented for the detection of delamination cracks in composites. The basic element is a novel active nonlinear acousto-ultrasonic piezoelectric sensor enabling low-cost and wide-frequency operational bandwidth. The active sensor configuration involves two piezoceramic wafer actuators, each one excited with a low- and high-frequency signal respectively, and a piezoceramic sensor, all permanently bonded on the tested structure. Experiments are conducted on two sets of composite strips containing delamination cracks of different sizes. Measured results illustrate first the efficiency of the nonlinear ultrasonics methodology to detect delamination cracks, as well as, the potential and benefits of the new active sensor. The sensitivity of the active sensor response to the crack size and the applied high-frequency carrier signals at the actuators, vary at various frequency and voltage levels indicating t...
---
paper_title: Impact Damage Detection in Composite Chiral Sandwich Panels

paper_content:

This paper demonstrates impact damage detection in a composite sandwich panel. The panel is built from a chiral honeycomb and two composite skins. Chiral structures are a subset of auxetic solids exhibiting counterintuitive deformation mechanism and rotative but not reflective symmetry. Damage detection is performed using nonlinear acoustics,involves combined vibro-acoustic interaction of high-frequency ultrasonic wave and low-frequency vibration excitation. High-and low-frequency excitations are introduced to the panel using a low-profile piezoceramic transducer and an electromagnetic shaker, respectively. Vibro-acoustic modulated responses are measured using laser vibrometry. The methods used for impact damage detection clearly reveal de-bonding in the composite panel. The high-frequency weak ultrasonic wave is also modulated by the low-frequency strong vibration wave when nonlinear acoustics is used for damage detection. As a result frequency sidebands can be observed around the main acoustic harmonic in the spectrum of the ultrasonic signal.
---
paper_title: Impact damage detection in composite chiral sandwich panels using nonlinear vibro-acoustic modulations

paper_content:

This paper reports an application of nonlinear acoustics to impact damage detection in a composite chiral sandwich panel. The panel is built from a chiral honeycomb and two composite skins. High-frequency ultrasonic excitation and low-frequency modal excitation were used to observe nonlinear modulations in ultrasonic waves due to structural damage. Low-profile, surface-bonded piezoceramic transducers were used for ultrasonic excitation. Non-contact laser vibrometry was applied for ultrasonic sensing. The work presented focuses on the analysis of the modulation intensities and damage-related nonlinearities. The paper demonstrates that the method can be used for impact damage detection in composite chiral sandwich panels.
---
paper_title: Nonlinear wave structural health monitoring method using an active nonlinear piezoceramic sensor for matrix cracking detection in composites

paper_content:

A structural health monitoring methodology, based on nonlinear wave modulation spectroscopy, is presented and aims to detect matrix cracks in composites. Experiments were conducted on cross-ply carbon/epoxy strips containing matrix cracks, induced via three-point bending. Damage in all tested specimens was categorized according to the acoustic emission hits recorded during loading. The nonlinear ultrasonics methodology is applied via an active nonlinear acousto-ultrasonic piezoelectric sensor, enabling low-cost and wide-frequency operational bandwidth. This active sensor configuration involves two piezoceramic wafer actuators, one excited with a low- and the other with a high-frequency signal, and a piezoceramic sensor, all permanently bonded on the tested structure. The sensitivity of the nonlinear active sensor response at specific high carrier frequencies is depicted and damage indices are proposed. The experimental results illustrate the effectiveness of the nonlinear ultrasonic wave mixing method in ...
---
paper_title: Impact damage detection in laminated composites by non-linear vibro-acoustic wave modulations

paper_content:

Abstract The paper presents an application of nonlinear acoustics for impact damage detection in composite laminates. Two composite plates were analysed. A low-velocity impact was used to damage one of the plates. Ultrasonic C-scan was applied to reveal the extent of barely visible impact damage. Finite element modelling was used to find vibration mode shapes of the plates and to estimate the local defect resonance frequency in the damaged plate. A delamination divergence study was performed to establish excitation parameters for nonlinear acoustics tests used for damage detection. Both composite plates were instrumented with surface-bonded, low-profile piezoceramic transducers that were used for the high-frequency ultrasonic excitation. Both an arbitrary frequency and a frequency corresponding to the local defect resonance were investigated. The low-frequency modal excitation was applied using an electromagnetic shaker. Scanning laser vibrometry was applied to acquire the vibro-acoustic responses from the plates. The study not only demonstrates that nonlinear vibro-acoustic modulations can successfully reveal the barely visible impact damage in composite plates, but also that the entire procedure can be enhanced when the ultrasonic excitation frequency corresponds to the resonant frequency of damage.
---
paper_title: Nonlinear Elastic Wave Spectroscopy (NEWS) Techniques to Discern Material Damage, Part I: Nonlinear Wave Modulation Spectroscopy (NWMS)

paper_content:

Abstract. The level of nonlinearity in the elastic response of materials containing structural damage is far greater than in materials with no structural damage. This is the basis for nonlinear wave diagnostics of damage, methods which are remarkably sensitive to the detection and progression of damage in materials. Nonlinear wave modulation spectroscopy (NWMS) is one exemplary method in this class of dynamic nondestructive evaluation techniques. The method focuses on the application of harmonics and sum and difference frequency to discern damage in materials. It consists of exciting a sample with continuous waves of two separate frequencies simultaneously, and inspecting the harmonics of the two waves, and their sum and difference frequencies (sidebands). Undamaged materials are essentially linear in their response to the two waves, while the same material, when damaged, becomes highly nonlinear, manifested by harmonics and sideband generation. We illustrate the method by experiments on uncracked and cracked Plexiglas and sandstone samples, and by applying it to intact and damaged engine components.
---
paper_title: Acoustic techniques for concrete evaluation: Improvements, comparisons and consistency

paper_content:

Abstract In civil engineering, the testing of structures allows a large number of chemical, mechanical and micro–macro structural parameters to be determined. Within the scope of ultrasonic Non-Destructive Testing (NDT), which is often used to evaluate concrete, many different techniques can be employed to generate, propagate, and receive the ultrasound waves, and to process the corresponding signals. The SENSO project, developed by nine partners, provided an opportunity to test a large number of principles related to the material’s characteristics and properties. Concerning the acoustic techniques, the first approach was based on linear propagation with bulk waves and surface waves, or with backscattered waves. The second method involved nonlinear analysis using wave modulation. One aim of the SENSO project was to compare these different techniques, in order to select that having the most promising performance in the laboratory, before transferring the measurement techniques to the field. The objectives were to evaluate the porosity, degree of saturation, modulus of elasticity and compressive strength of concrete. In the present paper, the measurement techniques and measured parameters are presented, together with the improvements developed within the context of the SENSO project. The methodology used to classify and select the ultrasonic techniques is described. It takes into account the sensitivity of the method to changes in the material and associates measurement uncertainties. Finally, the most significant results to evaluate porosity, mechanical characteristics and degree of saturation of various concretes, are developed. The consistency of the results of the measurements is analysed. The advantages and drawbacks of each technique are discussed.
---
paper_title: Observation of the “Luxemburg–Gorky effect” for elastic waves

paper_content:

An experimental observation of a new nonlinear-modulation effect for longitudinal elastic waves is reported. The phenomenon is a direct elastic wave analogy with the so-called Luxemburg–Gorky (L–G) effect known over 60 years for radio waves propagating in the ionosphere. The effect consists of the appearance of modulation of a weaker initially non-modulated wave propagating in a nonlinear medium in the presence of an amplitude-modulated stronger wave that produces perturbations in the medium properties on the scale of its modulation frequency. The reported transfer of modulation from one elastic wave to another was observed in a resonator cut of a glass rod containing a few small cracks. Presence of such a small damage drastically enhances the material nonlinearity compared to elastic atomic nonlinearity of homogeneous solids, so that the pronounced L– G type cross-modulation could be observed at strain magnitude in the stronger wave down to 10 7 and smaller. Main features of the effect are pointed out and physical mechanism of the observed phenomena is discussed. 2002 Elsevier Science B.V. All rights reserved.
---
paper_title: Crack detection in glass plates using nonlinear acoustics with low-profile piezoceramic transducers

paper_content:

The paper demonstrates application of nonlinear acoustics for crack detection in a glass plate. FE analysis is performed ::: to establish structural resonances of the glass plate. Simulation analysis and experimental tests are used to select ::: ultrasonic frequencies. Finally, nonlinear acoustic tests are performed to detect cracks. A high-frequency ultrasonic ::: signal is introduced to the glass plate. At the same time the plate is modally excited using selected resonance frequencies. ::: Surface-bonded, low-profile piezoceramic transducers are used for low- and high-frequency excitation. The experiments lead to vibro-acoustic wave modulations. The presence of modulation indicates damage and the intensity of modulation describes its severity.
---
paper_title: Nonlinear Elastic Wave NDE II. Nonlinear Wave Modulation Spectroscopy and Nonlinear Time Reversed Acoustics

paper_content:

This paper presents the second part of the review of Nonlinear Elastic Wave Spectroscopy (NEWS) in NDE, and describe two different methods of nonlinear NDE that provide not only damage detection but location as well. Nonlinear Wave Modulation Spectroscopy is based on the application of an ultrasonic probe signal modulated by a low frequency vibration. Damage location can be obtained by application of Impulse Modulation Techniques that exploit the modulation of a short pulse reflected from a damage feature (e.g. crack) by low frequency vibration. Nonlinear Time Reversed Acoustic methods provide the means to focus acoustic energy to any point in a solid. In combination, we are applying the focusing properties of TRA and the nonlinear properties of cracks to locate them.
---
paper_title: Micro-damage diagnostics using nonlinear elastic wave spectroscopy (NEWS)

paper_content:

Nonlinear elastic wave spectroscopy (NEWS) represents a class of powerful tools which explore the dynamic nonlinear stress–strain features in the compliant bond system of a micro-inhomogeneous material and link them to micro-scale damage. Hysteresis and nonlinearity in the constitutive relation (at the micro-strain level) result in acoustic and ultrasonic wave distortion, which gives rise to changes in the resonance frequencies as a function of drive amplitude, generation of accompanying harmonics, nonlinear attenuation, and multiplication of waves of different frequencies. The sensitivity of nonlinear methods to the detection of damage features (cracks, flaws, etc.) is far greater than can be obtained with linear acoustical methods (measures of wavespeed and wave dissipation). We illustrate two recently developed NEWS methods, and compare the results for both techniques on roofing tiles used in building construction.
---
paper_title: N‐Scan®: New Vibro‐Modulation System for Crack Detection, Monitoring and Characterization

paper_content:

In recent years, an innovative vibro‐modulation technique has been introduced for the detection of contact‐type interfaces such as cracks, debondings, and delaminations. The technique utilizes the effect of nonlinear interaction of ultrasound and vibrations at the interface of the defect. Vibration varies the contact area of the interface, modulating a passing ultrasonic wave. The modulation manifests itself as additional side‐band spectral components with the combination frequencies in the spectrum of the received signal. The presence of these components allows for the detection and differentiation of the contact‐type defects from other structural and material inhomogeneities. The vibro‐modulation technique has been implemented in the N‐SCAN® damage detection system providing a cost effective solution for the complex NDT problems. N‐SCAN® proved to be very effective for damage detection and characterization in structures and structural components of simple and complex geometries made of steel, aluminum, ...
---
paper_title: Potential of Nonlinear Ultrasonic Indicators for Nondestructive Testing of Concrete

paper_content:

In the context of a growing need for safety and reliability in Civil Engineering, acoustic methods of nondestructive testing provide answers to a real industrial need. Linear indicators (wave speed and attenuation) exhibit a limited sensitivity, unlike nonlinear ones which usually have a far greater dynamic range. This paper illustrates the potential of these indicators, and evaluates its potential for in situ applications. Concrete, a structurally heterogeneous and volumetrically, mechanically damaged material, is an example of a class of materials that exhibit strong multiple scattering as well as significant elastic nonlinear response. In the context of stress monitoring in pre-stressed structures, we show that intense scattering can be applied to robustly determine velocity changes at progressively increasing applied stress using coda wave interferometry and thereby extract nonlinear coefficients. In a second part, we demonstrate the high sensitivity of nonlinear parameters to thermal damage as regard with linear ones. Then, the influence of water content and porosity on these indicators is quantified allowing to uncouple the effect of damage from environmental or structural parameters.
---
paper_title: Dynamic nonlinear elasticity in geomaterials

paper_content:

This invention relates to a lens for presbyopia free from distortional aberration for use in correcting an old-age eyesight. In the lens for presbyopia with a front lens surface having a smaller radius of curvature than a rear lens face, a lens surface has a refractive power successively corrected as the lens surface extends radially outwardly away from a geometric center of the lens so that lateral magnifications for all principal rays always equal a lateral magnification for a paraxial range. This construction is entirely free from distortional aberration, and secures a greatly enlarged range of distinct vision.
---
paper_title: Impact damage detection in light composite sandwich panels using piezo-based nonlinear vibro-acoustic modulations

paper_content:

The nonlinear vibro-acoustic modulation technique is used for impact damage detection in light composite sandwich panels. The method utilizes piezo-based low-frequency vibration and high-frequency ultrasonic excitations. The work presented focuses on the analysis of modulation intensity. The results show that the method can be used for impact damage detection reliably separating damage-related from vibro-acoustic modulations from other intrinsic nonlinear modulations.
---
paper_title: Sensor validation for smart structures

paper_content:

Structures with a large number of embedded sensors are becoming more common, and this refined spatial information can be used to advantage in damage location and model validation. These sensors could be accelerometers, strain gauges, piezoceramic patches, PVDF film sensors, or optical fibre sensors. This approach requires that the sensors are functioning correctly, which on a smart structure operating in the field should be continuous and automatically monitored. This paper considers possible approaches to sensor validation, based on the assumption that a model of the structure is available. The aim is to make use of the natural data redundancy since there will more sensors than modes in the data. The validation approaches considered are based on hypothesis testing based on a number of techniques, such as modal filtering. The methods are demonstrated on simple examples that exercise their strengths and weaknesses.
---
paper_title: Sensor validation for structural systems with multiplicative sensor faults

paper_content:

Structures with a large number of sensors and actuators are becoming more common, with applications that vary from active control to damage location. This large amount of spatial information should be used to the advantage of the analyst, which requires, for correct functioning, the continuous in-operation monitoring of the sensors. Errors introduced by faulty sensors can cause a loss of performance and erroneous conclusions. Most of the currently available techniques seem to work well under the assumption of additive fault conditions, while seem to fail under the condition of multiplicative faults. In this work, we propose a new residual generation and evaluation technique for sensor validation that works for both additive and multiplicative faults. A correlation index is proposed which isolates the faulty sensors. The approach is experimentally validated on a subframe structure.
---
paper_title: Handbook of Nondestructive Evaluation

paper_content:

Chapter 1: Introduction to Nondestructive Testing Chapter 2: Dicontinuities - Origins and Classification Chapter 3: Visual Testing Chapter 4: Penetrant Testing Chapter 5: Magnetic Particle Testing Chapter 6: Radiographic Testing New - Digital Radiography Chapter 7: Ultrasonic Testing New - Phased Array Ultrasonics New - Guided Wave Ultrasonics Chapter 8: Eddy current Testing Chapter 9: Thermal Infrared Testing Chapter 10: Acoustic Emission Testing
---

Title: Nonlinear vibroacoustic wave modulations for structural damage detection: an overview

Section 1: Introduction
Description 1: Introduce the importance of structural integrity, the role of nondestructive testing (NDT), the limitations of existing techniques, and the promising role of nonlinear vibroacoustic wave modulation (VAM) for structural damage detection.

Section 2: Background
Description 2: Provide historical context and the theoretical foundations of classical and nonclassical nonlinear acoustics that underscore the nonlinear VAM technique.

Section 3: Nonlinear Vibroacoustic Wave Modulations
Description 3: Explain the different experimental arrangements and the basic principles of the nonlinear VAM technique including the use of pump and probe waves.

Section 4: Modeling
Description 4: Discuss the theoretical and numerical modeling approaches used to understand and simulate nonlinear acoustics, focusing on VAM.

Section 5: Sensors and Actuators
Description 5: Describe the various types of excitation and sensing methods used in VAM experiments, detailing the configurations and specific actuators applied.

Section 6: Signal Processing
Description 6: Detail the signal processing techniques employed to analyze the response signals in VAM, along with commonly used damage indicators and their computation.

Section 7: Application Examples
Description 7: Present examples of VAM applications across various materials, geometries, and types of damage, showcasing the technique's versatility and effectiveness.

Section 8: Selected Application Case
Description 8: Provide a detailed case study demonstrating the VAM technique applied to composite sandwich panels, discussing experimental setup, results, and implications.

Section 9: Summary and Final Conclusions
Description 9: Summarize the findings, discuss the current state of the VAM technique, its potential, challenges, and future research directions.