Effective Inertia Coefficients Prediction and Cell Size Effects in Thickness Direction of Periodic Composite Plates

Abstract

This paper develops a new homogenization method for free vibration problems of periodic composite plates. In this new method, three-dimensional (3D) periodic plates are equivalent to Reissner–Mindlin plates with both effective stiffnesses and effective inertia coefficients. The effective stiffnesses for the dynamic problems are the same as those for the static problems, and they can be achieved by the equivalence principle of macro- and microscopic internal virtual work. To fully take the inertia effects into account, the effective inertia coefficients including the effective translational, translational–rotational and rotational inertias are determined by the two-scale equivalence principle of kinetic energies under three rigid modes. In addition, cell size effects in the thickness direction of composite plates are investigated by using the proposed method and the asymptotic homogenization method (AHM). Numerical experiments validate the effectiveness of the proposed equivalent method for different scale factors, and show that the rotational inertia cannot be ignored for out-of-plane deformations, especially for higher-order modes. Besides, numerical comparisons show that the cell size effects are not negligible when using the AHM to analyze the out-of-plane deformations, and three or more repeated unit cells in the thickness direction are required to ensure accuracy.