Dynamic stiffness formulation is proposed in this paper for both transverse and in-plane vibration of rectangular plates that account for arbitrary boundary conditions. A generalized superposition method is developed to obtain the homogeneous solutions for the governing equations of both transverse and in-plane vibration. Consequently, the dynamic stiffness matrices are formed in a more straightforward way by projection method, the dimensions of which are greatly reduced in comparison with those from the conventional Gorman’s superposition method. The finite element technique is utilized to assemble local stiffness matrix into global coordinates so as to address the dynamics of plate assemblies. Various types of plate-like structures are investigated by the proposed method, through which excellent agreement is found between our results and those from finite element method. The effectiveness, accuracy and convergence of the proposed DSM for both transverse and in-plane vibration are proved in several numerical examples, which demonstrates the proposed DSM is an excellent alternative to the existing DSM.

本文提出了考虑到任意边界条件的矩形板的横向和平面振动的动态刚度公式。开发了一种通用的叠加方法来获得横向振动和平面振动控制方程的齐次解。因此，动态刚度矩阵通过投影方法以更直接的方式形成，与传统的戈尔曼叠加法相比，其尺寸大大减小。利用有限元技术将局部刚度矩阵组装成整体坐标，从而解决板组件的动力学问题。通过提出的方法研究了各种类型的板状结构，通过这些结果，我们的结果与有限元方法的结果之间找到了极好的一致性。在几个数值示例中证明了所提出的DSM对于横向和平面振动的有效性，准确性和收敛性，这表明所提出的DSM是现有DSM的绝佳替代品。