Vibraciones Naturales de Placas Rectangulares con Apoyos Parciales: Solución Exacta

Abstract

A methodology to find natural frequencies with arbitrary precision of thin rectangular plates on lineal supports and varied boundary conditions is presented. This means that
the edges are total or partially supported, clamped, free and any combination of these.
The layout, number and place of lineal intermediate supports are arbitrary, which allows for the analysis of a wide range of cases that include intermediate supports of different kinds: simple and multiple, straight and curved, complete (the ends coincide with the plate edges) and partial (at least one of the ends does not coincide with the plate edges). In the case of curved lineal supports, the curve can be open or closed.
The general solution is obtained using the Whole Element Method. A discrete model of equidistant points both for intermediate supports and clamped edges is adopted. In all cases, both a systematic approach to the solution and the theoretical basis should be emphasized as they ensure an arbitrary precision (accuracy) of the results.