Shear deformable dynamic stiffness elements for free vibration analysis of rectangular isotropic multilayer plates with arbitrary boundary conditions

Abstract

In this paper, two shear deformable dynamic stiffness elements for the free vibration analysis of rectangular, transversely isotropic, single- and multi-layer plates having arbitrary boundary conditions are presented. Dynamic stifness matrices are developed for the Reddy’s higher-order shear deformation theory (HSDT) and the Mindlin-Reissner’s first-order shear deformation theory (FSDT). The dynamic stiffness matrices contain both the stiffness and mass properties of the plate and can be assembled similarly as in the conventional finite element method. The influence of faceto-core thickness ratio and face-to-core module ratio of sandwich plate, as well as the influence of the shear deformation on the free vibration characteristics of sandwich plates have been analysed. The results obtained by proposed HSDT and FSDT dynamic stiffness element are validated against the results obtained using the conventional finite element analysis (ABAQUS), as well as the results obtained by 4-node layered rectangular finite element. The proposed model allows accurate prediction of free vibration response of rectangular layered plate assemblies with arbitrary boundary conditions.