中国物理B ›› 2015, Vol. 24 ›› Issue (2): 24303-024303.doi: 10.1088/1674-1056/24/2/024303

• ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID DYNAMICS • 上一篇    下一篇

Homogenization theory for designing graded viscoelastic sonic crystals

曲兆亮, 任春雨, 裴永茂, 方岱宁   

  1. State Key Laboratory for Turbulence and Complex Systems, College of Engineering, Peking University, Beijing 100871, China
  • 收稿日期:2014-05-18 修回日期:2014-08-22 出版日期:2015-02-05 发布日期:2015-02-05
  • 基金资助:
    Project supported by the National Basic Research Program of China (Grant No. 2011CB610301).

Homogenization theory for designing graded viscoelastic sonic crystals

Qu Zhao-Liang (曲兆亮), Ren Chun-Yu (任春雨), Pei Yong-Mao (裴永茂), Fang Dai-Ning (方岱宁)   

  1. State Key Laboratory for Turbulence and Complex Systems, College of Engineering, Peking University, Beijing 100871, China
  • Received:2014-05-18 Revised:2014-08-22 Online:2015-02-05 Published:2015-02-05
  • Contact: Pei Yong-Mao, Fang Dai-Ning E-mail:peiym@pku.edu.cn;fangdn@pku.edu.cn
  • Supported by:
    Project supported by the National Basic Research Program of China (Grant No. 2011CB610301).

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摘要： In this paper, we propose a homogenization theory for designing graded viscoelastic sonic crystals (VSCs) which consist of periodic arrays of elastic scatterers embedded in a viscoelastic host material. We extend an elastic homogenization theory to VSC by using the elastic-viscoelastic correspondence principle and propose an analytical effective loss factor of VSC. The results of VSC and the equivalent structure calculated by using the finite element method are in good agreement. According to the relation of the effective loss factor to the filling fraction, a graded VSC plate is easily and quickly designed. Then, the graded VSC may have potential applications in the vibration absorption and noise reduction fields.

关键词: graded sonic crystals, homogenization theory, viscoelasticity

Abstract: In this paper, we propose a homogenization theory for designing graded viscoelastic sonic crystals (VSCs) which consist of periodic arrays of elastic scatterers embedded in a viscoelastic host material. We extend an elastic homogenization theory to VSC by using the elastic-viscoelastic correspondence principle and propose an analytical effective loss factor of VSC. The results of VSC and the equivalent structure calculated by using the finite element method are in good agreement. According to the relation of the effective loss factor to the filling fraction, a graded VSC plate is easily and quickly designed. Then, the graded VSC may have potential applications in the vibration absorption and noise reduction fields.

Key words: graded sonic crystals, homogenization theory, viscoelasticity

中图分类号:  (Phonons in crystal lattices, quantum acoustics)

  • 43.35.Gk
83.60.Bc (Linear viscoelasticity)