Acta Mechanica Solida Sinica

, Volume 28, Issue 3, pp 294–304 | Cite as

Symplectic Analysis for Wave Propagation of Hierarchical Honeycomb Structures

  • Kai Zhang
  • Zichen Deng
  • Xiaojian Xu
  • Xiuhui Hou
  • Junmiao Meng
Article

Abstract

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.

Key Words

hierarchical honeycomb structures wave propagation band gap phase constant surface symplectic analysis 

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Copyright information

© The Chinese Society of Theoretical and Applied Mechanics and Technology 2015

Authors and Affiliations

  • Kai Zhang
    • 1
  • Zichen Deng
    • 1
  • Xiaojian Xu
    • 1
  • Xiuhui Hou
    • 2
  • Junmiao Meng
    • 1
  1. 1.School of Mechanics, Civil Engineering and ArchitectureNorthwestern Polytechnical UniversityXi’anChina
  2. 2.School of Civil EngineeringChang’an UniversityXi’anChina

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