S.I. Alvarez

TL;DR: In this article, the exact solution of the title problem was solved using the classical theory of vibrations of beams and a tabulation of eigenvalues was presented as a function of some of the governing mechanical parameters.

TL;DR: In this article, an approximate solution of the title problem is obtained by using the optimized Rayleigh-Ritz approach and it is shown that a simple polynomial co-ordinate function yields accurate fundamental frequency values.

TL;DR: In this paper, the Galerkin method and Rayleigh's optimization procedure were used to determine the fundamental frequency of vibration and buckling coefficient of clamped circular plates with geometric boundary perturbations.

TL;DR: In this article, the authors used the Ritz method and approximated the deflection function by means of polynomial co-ordinate functions which satisfy the essential boundary conditions, such as the presence of an axial force and concentrated masses.