用积分方程法解板的振动问题*

本文把带有集中质量、弹性支承和弹簧支撑着的质量块(振子)的薄板的振动微分方程化成为积分方程的特征值问题。然后利用广义函数理论和积分方程理论,得到了用一无穷阶矩阵的标准特征值形式给出的频率方程,从而方便地得到了固有频率和振型。并讨论了这种方法的收敛性。

Solving Vibration Problem of Thin Plates Using Integral Equation Method

This paper deals with reducing differential equations of vibration problem ofplates with concentrated masses, elastic supports and elastically mounted massesinto eigenvalue problem of integral equations. By applying the general functiontheory and the integral equation theory, the frequency equation is derived interms of standard eigenvalue problems of a matrix with infinite order. So that,the natural frequencies and mode shapes can be determined. Convergence of thismethod has also been discussed at the end of this paper.