Wave propagation in infinitely long hollow sandwich cylinders with prismatic cores is analyzed by the extended Wittriek-Williams （W-W） algorithm and the precise integration method （PIM）. The effective elastic constants of prismatic cellular materials are obtained by the homogenization method. By applying the variational principle and introducing the dual variables the canonical equations of Hamiltonian system are constructed. Thereafter, the wave propagation problem is converted to an eigenvalue problem. In numerical examples, the effects of the prismatic cellular topology, the relative density, and the boundary conditions on dispersion relations, respectively, are investigated.
Wave propagation in two-dimensional hierarchical honeycomb structures with two- order hierarchy is investigated by using the symplectic algorithm. By applying the variational prin- ciple to the dual variables, the wave propagation problem is transformed into a two-dimensional symplectie eigenvalue problem. The band gaps and spatial filtering phenomena are examined to find the stop bands and directional stop bands. Special attention is directed to the effects of the relative density and the length ratio on the band gaps and phase constant surfaces. This work provides new opportunities for designing hierarchical honeycomb structures in sound insulation applications.
Kai ZhangZichen DengXiaojian XuXiuhui HouJunmiao Meng
