Symplectic analysis for wave propagation of hierarchical honeycomb structures

Wave propagation in two-dimensional hierarchical honeycomb structures with two-order hierarchy is investigated by using the symplectic algorithm. By applying the variational principle to the dual variables, the wave propagation problem is transformed into a two-dimensional symplectic 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.