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中文摘要：
推导了板的有限元运动方程,构造了单元刚度矩阵和考虑转动惯量的单元质量矩阵,并采用子空间迭代法计算了板的前几阶频率,分析了广义协调厚薄通用板单元ATF-PQ4a的动力特性,并讨论了转动惯量和剪切变形对固有频率的影响.结果表明：ATF-PQ4a单元计算结果和理论解及有限元软件ABAQUS的结果比较吻合,说明在动力学范围内ATF-PQ4a单元能做到厚薄通用,满足工程需要.
英文摘要：
The finite element motion equation of plate is deduced, the stiffness and mass matrixes with consideration of the moment of inertia are constructed and the first several natural frequencies are calculated by using the sub-space iteration method. The vibration property of generalized conforming thick/thin element ATF-PQ4a is studied. The influence of moment of inertia and shearing distortion on the natural frequencies are discussed. The results obtained by using this element agree well with those obtained by ABAQUS and the theoretical solution. It can be concluded that the element ATF-PQ4a can be used for both thick and thin plates in the dynamics range for engineering purposes.
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