Free vibration analysis of plate assemblies using the dynamic stiffness method based on the higher order shear deformation theory

This paper deals with the free vibration analysis of isotropic plate assemblies using the dynamic stiffness method (DSM) based on the Reddy's higher-order shear deformation theory (HSDT). Using the proposed method, the isotropic rectangular plate assemblies of non-uniform thickness and material properties can be analyzed. The proposed model does not have any restrictions regarding the boundary conditions or the frequency limitations. It enables free vibration analysis of both thin and thick plates, making it advantageous in comparison with the conventional finite element method (FEM) regarding the computational cost and the accuracy of the results. Three coupled Euler-Lagrange equations of motion based on the HSDT have been transformed into two uncoupled equations of motion introducing a boundary layer function. The dynamic stiffness matrix for a completely free rectangular plate element has been derived using the superposition and the projection method. The proposed numerical model has been applied in the free vibration analysis of rectangular plate assemblies. Along with the convergence study, the results for natural frequencies have been validated against the existing data from the literature, the previous results from the authors as well as the results obtained by using the finite element software Abaqus. Excellent agreement has been obtained. Finally, a variety of new results is provided as a benchmark for future investigations