应用功的互等定理计算矩形弹性薄板的自然频率

在文[1]的基础上,本文进一步推广功的互等定理的应用于计算矩形弹性薄板的自然频率.应用本法无需求解控制微分方程,只需在基本系统与实际系统之间应用功的互等定理后求解一简单的积分方程即可.使用了广义简支边的概念并且引入了频率矩阵,从而一并得到了两对边简支、另两对边为各种支持的矩形板的所有频率方程.这是计算矩形板自然频率的一个简便通用的方法.

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.