Application of the Reciprocal Theorem for Calculating the Natural Frequencies of Rectangular Elastic Thin Plates

This paper further extends the applications of the reciprocal theorem to calculating the natural frequencies of rectangular elastic thin plates on the basis of [1]. Applying the presented method, there is no need to solve governing differential equations, it is only necessary to solve a simple integral equation after using the reciprocal theorem between the basic system, and the actual system.Using the idea of the generalized edge simply supported and introducing the frequency matrix, then all frequency equations of the rectangular plates with two opposite edges simply supported and other two opposite edges variously supported are obtained together.This is a simple, convenient and general method for calculating the frequency equations of the rectangular plates.