Frecuencias Arbitrariamente Precisas de Placas Rectangulares Apoyadas en sus Vértices

Abstract

The vibrational problem of thin plates is analysed within the Germain-Lagrange theory. The case of rectangular plates
with rigid point supports is dealt with two methodologies. One of them, named WEM (Whole Element Method), is a direct variational method previously developed by the authors for boundary value and/or initial problems, in one, two and three dimensional domains, conservative or not, linear or not. A minimizing sequence is stated which is a linear combination of functions belonging to a complete set in L2. The essential boundary conditions, in case they exist, are imposed to the complete sequence and not —in general— to each coordinate function. If they are not identically satisfied, the Lagrange multiplier method is employed. The sequence generation is systematic, ensures the completeness and a previous study of the modal shapes is not required. The exactness of the eigenvalues and uniform convergence of the essential functions of the problem has been demonstrated. The second methodology, which is herein included for the sake of comparison, is the FEM (Finite Element Method). The title problem is addressed by means of two alternatives: a) with the plate element developed by Bogner, Fox and Schmit and, b) using the code ALGOR with the plate element Veuvecke. Numerical examples are solved. The modal shapes are also shown.