Análisis de Vibraciones Naturales de Placas Rectangulares Consideradas como Sólidos Tridimensionales

Abstract

A variational method developed by the authors for boundary value problems in both one and two dimensions is herein extended to three dimensions. The method consists in extemizing an appropiate functional after using certain sequences that fulfil essential boundary conditions. The exactness of the proposed solution is founded by means of theorems. A comparison is carried out with an available classical solution in the sense of Saint-Venant's inverse method. A brief discussion of the latter is included in an Appendix. Finally the numerical values of the natural frequencies allow to measure the aproximation involved in the Mindlin theory of thick plates.