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Journal of Vibration Testing and System Dynamics

C. Steve Suh (editor), Pawel Olejnik (editor),

Xianguo Tuo (editor)

Pawel Olejnik (editor)

Lodz University of Technology, Poland

Email: pawel.olejnik@p.lodz.pl

C. Steve Suh (editor)

Texas A&M University, USA

Email: ssuh@tamu.edu

Xiangguo Tuo (editor)

Sichuan University of Science and Engineering, China

Email: tuoxianguo@suse.edu.cn


Design and Dynamic Analysis of Bending Waves Waveguide Based on Coordinate Transformation Theory

Journal of Vibration Testing and System Dynamics 1(2) (2017) 167--175 | DOI:10.5890/JVTSD.2017.06.005

Xing Chen; Li Cai; Ji-Hong Wen

Laboratory of Science and Technology on Integrated Logistics Support, National University of Defense Technology, Changsha 410073, China

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Abstract

The finite embedded coordinate transformation theory is introduced into the elastic dynamic equation of bending waves, a design of bend waveguide to control bending waves to bend at arbitrary angel is proposed. The formula to describe the transformed materials properties in an elastic thin plate is obtained, which contains anisotropic heterogeneous Young modulus and a radially dependent mass density. Through homogenization of layered periodic composite materials, the anisotropic materials are dispersed into discrete layered isotropic materials. The simulation model of the waveguide is built, and full-wave dynamic simulations of the model are analyst with finite element method. Numerical analysis results show that the waveguide consisting of 10 layers alternating two types of isotropic elastic materials can achieve effective control of the bending wave propagation in thin plates, it works over the frequency range [1500, 10000] hertz with ultra-wideband characteristics. The study can provide technological approaches to bending waves control in thin plates, and it is expected to provide potential applications in isolating structures from vibrations.

References

  1. [1]  Pendry, J,B, Schurig, D, and Smith, D.R. (2006), Science, 312, 1780.
  2. [2]  Milton, G.W., Briane, M., Willis, J.R. (2006), New J. Phys., 8, 248.
  3. [3]  Cummer, S. A., Schurig, D. (2007), New J. Phys., 9, 45.
  4. [4]  Cummer, S.A., Popa, B.I., Schurig, D., Smith, D.R., Pendry, J., Rahm, M., and Starr, A. (2008), Phys. Rev. Lett., 100, 024301.
  5. [5]  Chen, H.Y. (2008),Waves in anisotropic materials:invisibility cloaking,rotation cloaking and phononic crystal Ph. D. Dissertation (Shanghai:Shanghai Jiao Tong University)
  6. [6]  Cai, L, Wen, J.H., Yu, D.L., Lu, Z.M., Wen, X.S. (2014), Chin. Phys. Lett., 31, 094303(in Chinese).
  7. [7]  Lu, Z.M., Cai, L., Wen, J.H., and Wen, X.S. (2016), Acta Phys. Sin., 65, 174301.
  8. [8]  Farhat, M, Guenneau, S, Enoch, S, and Movchan, A. B. (2009), Phys. Rev. B, 79, 033102.
  9. [9]  Rahm, M, Roberts, D.A., Pendry, J.B., and Smith, D.R. (2008), Opt. Express, 16, 11556.
  10. [10]  Timoshenko, S, Woinowsky-Krieger, S. (1959), Theory of Plates and Shells (New York: McGraw-Hill Book Company), 79-83.
  11. [11]  Farhat, M., Guenneau, S., and Enoch, S. (2009), Phys. Rev. Lett., 103, 024301
  12. [12]  Torrent, D. and S├ínchez-Dehesa, J. (2008), New J. Phys., 10, 063015.
  13. [13]  Chen, H.Y. and Chan, C.T. (2007), Appl. Phys. Lett., 91, 183518.