四角点支承矩形板振动的Rayleigh—Ritz解

Rayleigh-Ritz Solution for the Vibrations of Rectangular Plates Supported at Four Corner Points

本文用Rayleigh—Ritz法计算四角点支承矩形板振动的最低固有频率。文中选用的振型函数满足位移边界条件,且在加权平均意义下满足全部内力边界条件,得到了较好的近似解。计算简单,便于实际应用。

In this paper, the lowest eigenfrequencies of rectangular plates supported at four corner points are calculated by the Rayleigh-Ritz method. The vibration shape functions given in this paper satisfy the displacement boundary conditions of the plate, and satisfy the inner force boundary conditions of the plate in the sense of weighted average. Consequently the better approximate solution is obtained. The calculation procedure is simple, so the present method is convenient to be used in engineering.