边缘有弹性点支矩形板的横向振动

Transverse Vibration of Rectangular Plates Elastically Supported at Points on Edges

本文研究了两对边简支、另两对边任意支承的自由边有弹性点支的矩形板的横向振动问题,提供了一种求其固有频率和振型的高精度解法,自由边上弹性点支的个数及位置均可任意,本文用脉冲函数表示弹性点支的反力和力矩,利用Fourier级数将脉冲函数沿边缘展开,从而得到了满足全部边界条件的特征方程,可求得任意精度的任意阶固有频率及振型.

This paper studies transverse vibration of rectangular plates with two opposite edges simply supported, other two edges arbitrarily supported and free edges elastical-ly supported at points. A highly accurate solution is presented for calculating inherent frequencies and mode shape of rectangular plates elastically supported at points. The number and location of these points on free edges may be completely arbitrary. This paper uses impulse function to represent reaction and moment at points. Fourier series is used to expand the impulse function along the edges. Characteristic equations satisfying all boundary conditions are given. Inherent frequencies and mode shape with any accuracy can be gained.