两对边简支中间有任意多个单向弹性线支矩形板横向振动的一个解析解法

An Analytical Solution of Transverse Vibration of Rectangular Plates Simply Supported at Two opposite Edges withArbitrary Number of Elastic Line Supports in one Way

本文给出了两对边简支另两对边任意支承的中间有任意多个单向弹性线支矩形板横向振动的一个新的解析解法、将弹性线支反力看作是作用于板上的待求外力，求得了含有来知的弹性线支反力的两对边简支矩形板的运动方程的解析解；利用弹性线支反力与板横向位移之间的线性关系导出频率方程；频率方程及振型函数的表述均与已有方法不同．

This paper presents a new analytical solution of transverse vibration of rectangular plates simply supported at two opposite edges with arbitrary number of elastic line supports in one way. The reaction forces of the elastic line supports are regarded as the unknown external forces acted on the plate. The analytical solution of the differential equation of motion of the rectangular plate,which includes the unknown reaction forces, is gained. The frequency equationis derived by using the linear relationships between the reacion forces of the elastic line supports and the transverse displacements of the plate along the elastic line supports. The representations of the frequency equation and the mode shape functions are different from those obtained by other methods.