A Generalized kantorovich method and its application to free in-plane plate vibration problem

Abstract

In this paper, we develop a generalized Kantorovich method to construct a closed from solution for two coupled partial differential equations (PDEs) with mixed boundary conditions. One of the applications of this method is the study of i-plane vibration of rectangular plates. We obtain analytical expressions of plate mode shapes comprising a linear combination of progressive waves with unknow wave amplitudes. Using these mode shapes, we iteratively calculate the modal frequencies and wave amplitudes. We consider three cases: (1)a Plate with four edges clamped;(2)a plate with three edges clamped and one edge free; and(3)a plate with two parallel edges clamped and the remaining two edges free. Improvements in accuracy of the first six predicted natural frequencies were achieved by using our method, when compared with prior results from the literature.