Dynamic modeling and characteristic analysis of the periodically coupled plate structure based on the dynamic stiffness method

In this paper, the dynamic model of periodically coupled plate structure is formulated by the dynamic stiffness method (DSM). Geometrical construction is assumed to vary periodically in the whole plate structure. According to the coupling condition, the whole periodic plate structure is divided into appropriate individual rectangular plates firstly. To the individual plate, the displacement fields both of in-plane and out-of-plane are derived from the governing equation with a strong-form methodology. The dynamic stiffness matrix is developed by the Projection method. Once the dynamic stiffness matrixes of the individual plates are obtained, the global dynamic stiffness matrix of the whole periodic structure can be assembled in the similar manner with the finite element method (FEM). Several examples are presented to validate the convergence and accuracy of the present formulation. From the harmonic responses, the band gap behaviors can be observed obviously. Furthermore, a parametric analysis is implemented to study the effects of geometrical distributions and plate dimensions on the vibration characteristics.