Acceleration, a

Any change in velocity with respect to time, given as a vector;
Written: (dv/dt). The second time derivative of displacement; written: (d2x/dt). Usually given in terms of g’s (See below, "G"). The time rate of change of velocity. Typical units are ft/sec/sec, meters/sec/sec, and G’s (1 G = 32.17 ft/sec/sec = 9.81 m/sec/sec). Acceleration measurements are usually made with accelerometers.

Amplitude, A

A measure of the wave height of a cyclic quantity at any particular point along the wave in either the positive or negative direction. (See Peak Amplitude, Peak to Peak Amplitude, RMS Amplitude.) The magnitude of dynamic motion or vibration. Amplitude is expressed in terms of peak-to-peak, zero-to-peak, or rms. For pure sine waves only, these are related as follows:
rms = 0.707 times zero-to-peak; peak-to-peak = 2 times zero-to-peak.

Background Noise

The total of all noise sources when no signal is input into the amplifier.

Baseline Spectrum

A vibration spectrum taken when a machine is in good operating condition; used as a reference for monitoring and analysis.


A measure of frequency in cycles per minute (1 CPM = 1 Hz x 60)


A condition which can occur in liquid-handling machinery (e.g., centrifugal pumps) where system pressure decrease in the suction line and pump inlet lowers fluid pressure and vaporization occurs. The result is mixed flow which may produce vibration.                  


The condition reached when the signal amplitude exceeds the limits imposed by the amplifier and/or supply voltage. The condition is marked by a rounding or flattening of the signal peaks; this may cause signal attenuation and distortion. Clipping is the term applied to the, generally undesirable, circumstance in which a signal excursion is limited in some sense by an amplifier, ADC, or other device when its full scale range is reached. Clipping may be “hard,” in which the signal excursion is strictly limited at some voltage; or, it may be “soft,” in which case the clipped signal continues to follow the input at some reduced gain above a certain output value.

Coherence Function

Coherence is a frequency domain function generally computed to show the degree to which a linear, noise-free relationship exists between a system input and the output. Values vary between one and zero, with one being total coherence and zero being no coherence between input and output.

Critical Speed

A machine speed, or integer multiple of machine speed, that is equal to a natural frequency. Often used interchangeably with natural frequency or resonance.


One complete sequence of values of a periodic quantity.


The dissipation of energy which tends to bring a system to rest when the driving stimulus is removed. The quality of a mechanical system that restrains the amplitude of motion with each successive cycle. Damping of shaft motion is provided by oil bearings, seals, etc. The damping process converts mechanical energy to other forms, usually heat.

Displacement, x.

The vector quantity denoting any change in position, in terms of the distance from a point of rest. Usually given in mm, inches, or mils (thousandths of an inch). The change in distance or position of an object relative to a reference.

Digital Spectrum Analyzer (DSA)

An instrument that converts an analog signal to a digital representation, and performs spectrum analysis of that signal.

Endurance Limit

The maximum alternating stress that may be repeated an indefinite number of times on a standard test specimen without causing failure. It is also referred to as the fatigue limit.

Endurance Strength

The strength of actual parts, based on the endurance limit, with consideration given for the stress concentrations, surface condition, size, and expected life of the part.

Engineering Units

In a Digital Spectrum Analyzer (DSA), refers to units that are calibrated by the user (e.g., in/sec., g’s).

FEA Finite Element Analysis

A method of analysis which can be used to calculate natural frequencies, displacements, and stresses of structures. This technique may be applied to other fields such as heat transfer, fluid flow, electrostatics, etc.

Frequency, ƒ

The reciprocal of the period of a cyclic quantity. This may be written in terms of cycles per second (cps or Hz), or cycles per minute (CPM), or revolutions per minute (RPM). The repetition rate of a periodic event, usually expressed in cycles per second (Hz), revolutions per minute (RPM), or multiples of rotational speed (orders). Orders are commonly referred to as 1 x for rotational speed, 2 x for twice rotational speed, etc.

Frequency Range 

The frequency range (bandwidth) over which a measurement is considered valid; i.e., within manufacturer’s specs. Typical analyzers have selectable ranges. Usually refers to upper frequency limit of analysis, considering zero as the lower analysis limit.


The lowest frequency periodic component present in a complex spectrum. At least one complete period of a signal must be present for it to qualify as the “fundamental”.


The value of acceleration produced by the force of gravity. A standard unit of acceleration equal to one earth’s gravity. The acceleration of free fall. One g equals 32.17 ft/s2 (FPS).

Goodman Diagram

A plot of the alternating stress versus the mean stress in a component compared with the endurance strength and ultimate strength of the material. The design limit is defined by a line joining the endurance strength and ultimate strength. Points on the diagram below the line are considered acceptable. The concept of a safety factor is used; however, since the material properties are based on a statistical average, the design limit should be considered a band rather than a line. Generally, a safety factor of 2 or more is considered to be an acceptable design.


Frequency component at a frequency that is an integer multiple of the fundamental frequency.

Hertz, (Hz)

A measure of frequency (1 Hz = 1 cycle per second).

Impact Test

Response test where the broad frequency range produced by an impact is used as the stimulus. Sometimes referred to as a bump test.

Impedance, Mechanical

The mechanical properties of a machine system (mass, stiffness, damping) that determine the response to periodic forcing functions.


Mechanical Natural Frequency. See Natural Frequency

Modal Analysis

The process of breaking complex vibration into its component modes of vibration, very much like frequency domain analysis breaks vibration down to component frequencies.

Mode Shape

The deflected shape of a structure that corresponds to a particular natural frequency.

First Mode

The mode shape at the first natural frequency, or the lowest natural frequency. There can be second, third, etc. modes.

Natural Frequency

The characteristic frequencies of vibration at which a system will respond with large amplitudes of vibration when excited by small forces.
In general, vibrations can refer to oscillations of mechanical systems, pressure, light, electricity, gravity, etc.

Operating Deflected Shape (ODS)

The resultant deflected shape of a structure at a specific frequency to an applied forcing function. May also be the overall deflected shape of the structure over time.

Peak Amplitude

The amplitude of a cyclic quantity as measured from the rest value to the extreme maximum of the wave height, usually in the positive direction.

Peak-to-Peak Amplitude

The amplitude of a cyclic quantity as measured from the extreme minimum to the extreme maximum of the wave height.

Peak Channel Hold (Peak Hold)

A frequency domain “averaging” method which saves the highest response measured in each quantized increment during a specified time interval or number of spectral averages. The resultant spectrum is a composite of the highest spectral values measured during the averaging process.

Peak Reading, (pk)

For a given vibration pulsation, the peak reading is the amplitude measured from the neutral position to the maximum positive or negative amplitude. Similarly, a peak-to-peak reading is the amplitude measured from the maximum positive to the maximum negative amplitude. (1 peak-to-peak = 1 peak x 2 assuming a sinusoidal function)

Peak Spectra

A frequency domain measurement where, in a series of spectral measurements, the one spectrum with the highest magnitude at a specified frequency is retained.


A measurement of the timing relationship between two signals, between a specific vibration event and a keyphasor pulse, or between two frequency components of a spectrum.


A measure of shaft speed in revolutions per minute. (1 RPM = 1 Hz x 60)


Occurs when the frequency of an exciting force coincides with the natural frequency of a system. The system can be mechanical (translational or torsional), acoustical (pulsations, or flow), electrical (voltage or current), etc.

Roll-off Frequency Cutoff frequency

The frequency at which a filter attenuates a pass band gain by 3dB.


A distribution of amplitude components as a function of frequency. The distribution of the amplitude of the components of a time domain signal as a function of frequency.


The ratio of the force on an elastic body to the resulting change in deflection. The spring-like quality of mechanical and hydraulic elements to elastically deform under load.


The physical deformation, deflection, or change in length resulting from stress (force per unit area).


The force per unit area or intensity of the loads distributed over a given area. By convention, tensile stresses are positive and compressive stresses are negative.

Alternating Stress, sigmaA Refers to the peak amplitude of a stress that varies with time. It is often referred to as a dynamic stress as it is the stress due to a dynamic (time varying) load.

Mean Stress, sigmam


Refers to the static or steady state stress in a component.

Normal Stress sigman


A stress that is perpendicular to a plane cut through a component (i.e., the stress produced by pulling on a rope).

Shear Stress


A stress that is parallel to a plane cut through a component (i.e., the stress produced in rivets of a riveted joint).

Test Point, (TP)

Refers to a location where a measurement or reading was recorded.

Transient Analysis

When the excitation of a system is of finite duration, the analysis of the data is a transient analysis. A transient analysis can also be used to study the change from one steady-state to a second steady-state condition.

Transient Vibration

Temporarily sustained vibration of a mechanical system. It may consist of forced or free vibration or both. Typically this is associated with changes in machine operating condition such as speed, load, etc.

Velocity, v.

The vector quantity denoting any change in displacement with respect to time; written: (dx/dt). Usually given in the vibration monitoring field in terms of in/sec or mm/sec.


Motion in a mechanical system, resulting in various reversals in velocity relative to a reference.