Natural frequencies of rectangular plates using characteristic orthogonal polynomials in rayleigh-ritz method

Abstract

Natural frequencies of rectangular plates are obtained by employing a set of beam characteristic orthogonal polynomials in the Rayleigh-Ritz method. The orthogonal polynomials are generated by using a Gram-Schmidt process, after the first member is constructed so as to satisfy all the boundary conditions of the corresponding beam problems accompanying the plate problems. Natural frequencies obtained by using the orthogonal polynomial functions are compared with those obtained by other methods. The method yields superior results for lower modes, particularly when plates have some of the edges free. © 1985 Academic Press Inc.