A hybrid symplectic and high-frequency homogenization analysis for the dispersion property of periodic micro-structured thin plate structures

A hybrid homogenization analysis approach is developed for the dispersion of one- and two-dimensional periodic micro-structured thin plate structures by combining the high-frequency homogenization method and the symplectic method. In the present method, the displacement field of the unit cell which is needed in the high frequency homogenization method is expressed in terms of wave components which are obtained by solving an eigenvalue problem which is first proposed. The eigenproblem developed based on the symplectic method allows the displacement function of the unit cell with arbitrary simple boundary conditions to be obtained rationally, so that the high-frequency homogenization analysis can be more conveniently applied to the dispersion analysis of the periodic micro-structured plate structures. Numerical examples of one-dimensional and two-dimensional periodic structures with various boundary conditions for the unit cell are provided to confirm the utility of the proposed method.