In-plane vibration of rectangular plates with periodic inhomogeneity: Natural frequencies and their adjustment

We consider the in-plane free vibration of a rectangular plate with material properties varying periodically and rapidly in the plate plane. To this end, the two-scale asymptotic expansion method is employed to establish a homogenized model of the original heterogeneous plate, which is then analyzed by the state-space method. For a plate with each repetitive unit composed of two different materials at a fixed volume ratio, we compare the natural frequencies of the homogenized model with those of the original plate calculated by the finite element method, and good agreement is obtained. We also demonstrate that the plate can be designed to have particular frequencies through a proper selection of the material distribution law in each unit.