Dynamic stiffness formulation for transverse and in-plane vibration of rectangular plates with arbitrary boundary conditions based on a generalized superposition method

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.

Automated summary

This paper proposes a new dynamic stiffness formulation for transverse and in-plane vibration of rectangular plates, utilizing a generalized superposition method to obtain homogeneous solutions and forming dynamic stiffness matrices through projection method. The finite element technique is used to address the dynamics of plate assemblies in global coordinates, with numerical examples demonstrating the effectiveness and accuracy of the proposed method.