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本文把Przemieniecki动态有限元的概念推广应用于弯曲矩形板的固有振动分析。文中构造了满足控制微分方程的静态形状函数阵,并对二阶修正形状函数阵加以某种限制。使得所建立之弯曲板的运动方程,在不计频率高阶项时,能退化到常规分析的形式。从而,克服了Gupta所建立之薄膜及平面应变板动态有限元不能与常规分析相协调的缺点。最后,利用所建立之矩形板元的动态刚度及质量矩阵,计算了悬臂板的固有频率,得到合理的结果,证明了方法的有效性。
In this paper, the concept of Przemieniecki dynamic finite element is generalized to the natural vibration analysis of curved rectangular plates. In this paper, we construct a static shape function matrix that satisfies the control differential equation and imposes some restrictions on the second order shape function correction matrix. The equations of motion of the established curved plate degenerate into the form of routine analysis, regardless of the higher-order term of the frequency. Thus, the shortcoming that the dynamic finite element of the film and the plane strain plate established by Gupta can not be coordinated with the conventional analysis is overcome. Finally, by using the dynamic stiffness and mass matrix of the rectangular plate element, the natural frequencies of the cantilever plate are calculated and the reasonable results are obtained. The effectiveness of the method is proved.