Free vibration of line supported rectangular plates using a set of static beam functions

Abstract

The free vibration of thin orthotropic rectangular plates, which may be continuous over a number of intermediate line supports in one or two directions, is analyzed by the Rayleigh-Ritz method. A new set of admissible functions which are the static solutions of a point supported beam under a series of sine loads is developed. The eigenfrequency equation for the plate is derived by minimizing the potential energy. A very simple and general computer programme has been compiled. The basic concept to form the set of static beam functions is very clear and requires no complicated mathematical knowledge. Some numerical results presented are compared with those obtained by other numerical methods in the literature. It is shown that this set of static beam functions has some advantages in terms of computational cost, application versatility and numerical accuracy, especially for the plate problem with a large number of intermediate line supports and/or when higher vibrating modes need to be calculated. © 1999 Academic Press.