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.

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Isogeometric analysis (IGA) is based on a concept that uses the same base functions for description of displacement field and undeformed model geometry. The most common base functions used in the IGA are NURBS functions. In this paper, the IGA is applied in the free vibration analysis of beam element. The stiffness and mass matrices have been developed for rotation-free Bernoulli-Euler and Timoshenko beam using the Galerkin method. Natural frequencies of beam element with specific boundary conditions have been computed using the isogeometric approach. The results were compared with the exact analytical solutions obtained by using the dynamic stiffness method (DSM) and the conventional finite element method (FEM).