Solution methods of exact solutions for free vibration of rectangular orthotropic thin plates with classical boundary conditions

Abstract

The exact solutions for free vibrations of orthotropic rectangular thin plates are presented in an elegant way using separation of variables method. And the exact solutions of three configurations (G-G-C-C, SS-G-C-C and C-C-C-G) are solved for the first time. In separation of variables method, the general formulation of the natural mode function and the relations among two spatial eigenvalues and a temporal eigenvalue are directly obtained from the characteristic differential equation, and the coefficients of exact mode functions and two exact eigenvalue equations are determined by two pairs of opposite edge conditions. It was regarded before 2009 that there were not exact solutions for rectangular thin plates with at least two adjacent clamped edges, and the others to be arbitrary combinations of clamped (C), simply supported (SS) and guided (G) conditions. For these configurations, the exact eigensolutions are solved successfully and the first ten exact frequencies are tabulated for a few of aspect ratios.