受弹性点支的任意形状的膜的振动

Vibration of Arbitrarily Shaped Membranes with Elastical Supports at Points

本文提供了一个求解受弹性点支的任意形状的膜的振动的新方法.将弹性点支反力看作是作用于膜上的未知外力,求出了包含有未知反力的运动方程的精确解,利用弹性点支处位移和反力的线性关系导出频率方程.最后以受弹性点支的圆膜为例给出了其频率方程的具体计算公式,并数值计算了受两个对称弹性点支的圆膜的固有振动频率,

This paper presents a new method for solving the vibration of arbitrarily shaped memebranes with elastical supports at points. The reaction forces of elastical supports at points are regarded as unknown external forces acting on the membranes. The exact solution of the equation of motion is given which includes terms representing the unknown reaction forces The frequency equation is derived by the use of the linear relationship of the displacements with the-reaction forces of elastical supports at points. Finally the calculating formulae of the frequency equation of circular membranes are analytically performed as examples and the inherent frequencies of circular membranes with symmetric elastical supports at two points are numerically calculated.