A New General Solution for the Bending and Vibration of Orthotropic Rectangular Thin Plates with Four Free Edges

Abstract

This paper firstly introduces a new general solution constructed by double trigonometric cosine series with supplementary terms for the bending and vibration analysis of orthotropic rectangular plates with four free edges on the Winkler foundation subjected to arbitrary vertical force. The general solution, which is fourth-order continuously differentiable with less undetermined coefficients, can be used to solve the bending and vibration problems of orthotropic rectangular plates on the Winkler foundation with various physical parameters requiring no classification and superposition. This makes the bending and vibration analysis of orthotropic rectangular plates with four free edges on the Winkler foundation more unified, simplified and regulated. This paper also gives a Series of analytical example to prove that the method is feasible.