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Symplectic Analysis for Wave Propagation of Hierarchical Honeycomb Structures

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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.

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Authors and Affiliations

  1. School of Mechanics, Civil Engineering and Architecture, Northwestern Polytechnical University, 710072, Xi’an, China

    Kai Zhang, Zichen Deng, Xiaojian Xu & Junmiao Meng

  2. School of Civil Engineering, Chang’an University, 710064, Xi’an, China

    Xiuhui Hou

Authors
  1. Kai Zhang
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  2. Zichen Deng
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  3. Xiaojian Xu
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  4. Xiuhui Hou
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  5. Junmiao Meng
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Corresponding author

Correspondence to Zichen Deng.

Additional information

Project supported by the National Basic Research Program of China (No. 2011CB610300), the National Natural Science Foundation of China (Nos. 11172239 and 11372252), the Doctoral Program Foundation of Education Ministry of China (No. 20126102110023), the Fundamental Research Funds for the Central Universities (Nos. 310201401JCQ01001 and 3102015ZY036) and China Postdoctoral Science Foundation (No. 2013M540724) and Shaanxi postdoctoral research projects.

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Zhang, K., Deng, Z., Xu, X. et al. Symplectic Analysis for Wave Propagation of Hierarchical Honeycomb Structures. Acta Mech. Solida Sin. 28, 294–304 (2015). https://doi.org/10.1016/S0894-9166(15)30016-1

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  • DOI: https://doi.org/10.1016/S0894-9166(15)30016-1

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