Lord Rayleigh was the first to popularly adapt the variational principles for the search of eigenvalues and eigenvectors for the study of elasticity and classical waves in his 1877 Theory of Sound. The Rayleigh method allows approximation of the fundamental frequencies without full knowledge of the material composition and without the requirement of computational power. From 1903 to 1908, Walther Ritz introduced a series of improved methods for static and free vibration problems based on the optimization of an ansatz or trial function. Ritz demonstrated his use in the Euler–Bernoulli beam theory and the determination of Chladni figures.