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Abstract and Applied Analysis
Volume 2014, Article ID 906506, 12 pages
http://dx.doi.org/10.1155/2014/906506
Research Article

Analytic Formulation for the Sound Absorption of a Panel Absorber under the Effects of Microperforation, Air Pumping, Linear Vibration and Nonlinear Vibration

Department of Civil and Architectural Engineering, City University of Hong Kong, Kowloon Tong, Kowloon, Hong Kong

Received 27 March 2014; Revised 24 June 2014; Accepted 1 July 2014; Published 23 July 2014

Academic Editor: Rehana Naz

Copyright © 2014 Y. Y. Lee. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. Y. Y. Lee and C. F. Ng, “Sound insertion loss of stiffened enclosure plates using the finite element method and the classical approach,” Journal of Sound and Vibration, vol. 217, no. 2, pp. 239–260, 1998. View at Publisher · View at Google Scholar · View at Scopus
  2. Y. Y. Lee, “The response frequency conversion characteristic of a nonlinear curved panel with a centre mass and the sound radiations,” Mathematical Problems in Engineering, vol. 2012, Article ID 298413, 11 pages, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  3. S. Y. Hsia and Y. T. Chou, “Traffic noise propagating from vibration of railway wagon,” Mathematical Problems in Engineering, vol. 2013, Article ID 651797, 7 pages, 2013. View at Publisher · View at Google Scholar
  4. J. Feng, X. P. Zheng, H. T. Wang, Y. J. Zou, Y. H. Liu, and Z. H. Yao, “Low-frequency acoustic-structure analysis using coupled FEM-BEM method,” Mathematical Problems in Engineering, vol. 2013, Article ID 583079, 8 pages, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  5. S. M. Chen, D. F. Wang, and J. M. Zan, “Interior noise prediction of the automobile based on hybrid FE-SEA method,” Mathematical Problems in Engineering, vol. 2011, Article ID 327170, 20 pages, 2011. View at Publisher · View at Google Scholar · View at Scopus
  6. R. V. Craster and S. G. L. Smith, “A class of expansion functions for finite elastic plates in structural acoustics,” Journal of the Acoustical Society of America, vol. 106, no. 6, pp. 3128–3134, 1999. View at Publisher · View at Google Scholar · View at Scopus
  7. K. A. Mulholland and H. D. Parbrook, “Transmission of sound through apertures of negligible thickness,” Journal of Sound and Vibration, vol. 5, no. 3, pp. 499–508, 1967. View at Publisher · View at Google Scholar · View at Scopus
  8. R. D. Ford and M. A. McCormick, “Panel sound absorbers,” Journal of Sound and Vibration, vol. 10, no. 3, pp. 411–423, 1969. View at Publisher · View at Google Scholar · View at Scopus
  9. D. Maa, “Microperforated-panel wideband absorbers,” Noise Control Engineering Journal, vol. 29, no. 3, pp. 77–84, 1987. View at Publisher · View at Google Scholar · View at Scopus
  10. D. Maa, “Potential of microperforated panel absorber,” Journal of the Acoustical Society of America, vol. 104, no. 5, pp. 2861–2866, 1998. View at Publisher · View at Google Scholar · View at Scopus
  11. Y. Wu and G. Han, “Infinitely many sign-changing solutions for some nonlinear fourth-order beam equations,” Abstract and Applied Analysis, vol. 2013, Article ID 635265, 11 pages, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  12. X. Liu, B. Huo, and S. Zhang, “Nonlinear dynamic analysis on the rain-wind-induced vibration of cable considering the equilibrium position of rivulet,” Abstract and Applied Analysis, vol. 2013, Article ID 927632, 10 pages, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  13. X. Lin and F. Li, “Asymptotic energy estimates for nonlinear Petrovsky plate model subject to viscoelastic damping,” Abstract and Applied Analysis, vol. 2012, Article ID 419717, 25 pages, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  14. J. A. Esquivel-Avila, “Dynamic analysis of a nonlinear Timoshenko equation,” Abstract and Applied Analysis, vol. 2011, Article ID 724815, 36 pages, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  15. M. L. Santos, J. Ferreira, and C. A. Raposo, “Existence and uniform decay for a nonlinear beam equation with nonlinearity of Kirchhoff type in domains with moving boundary,” Abstract and Applied Analysis, no. 8, pp. 901–919, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  16. X. He, “Modal decoupling using the method of weighted residuals for the nonlinear elastic dynamics of a clamped laminated composite,” Mathematical Problems in Engineering, vol. 2009, Article ID 972930, 19 pages, 2009. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  17. D. Wang, J. Zhang, and Y. Wang, “Strong attractor of beam equation with structural damping and nonlinear damping,” Mathematical Problems in Engineering, vol. 2013, Article ID 769514, 8 pages, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  18. Y. Y. Lee, “Structural-acoustic coupling effect on the nonlinear natural frequency of a rectangular box with one flexible plate,” Applied Acoustics, vol. 63, no. 11, pp. 1157–1175, 2002. View at Publisher · View at Google Scholar · View at Scopus
  19. Y. Y. Lee, “Analysis of the nonlinear structural-acoustic resonant frequencies of a rectangular tube with a flexible end using harmonic balance and homotopy perturbation methods,” Abstract and Applied Analysis, vol. 2012, Article ID 391584, 13 pages, 2012. View at Publisher · View at Google Scholar · View at Scopus
  20. C. K. Hui, Y. Y. Lee, and J. N. Reddy, “Approximate elliptical integral solution for the large amplitude free vibration of a rectangular single mode plate backed by a multi-acoustic mode cavity,” Thin-Walled Structures, vol. 49, no. 9, pp. 1191–1194, 2011. View at Publisher · View at Google Scholar · View at Scopus
  21. Y. Y. Lee, Q. S. Li, A. Y. T. Leung, and R. K. L. Su, “The jump phenomenon effect on the sound absorption of a nonlinear panel absorber and sound transmission loss of a nonlinear panel backed by a cavity,” Nonlinear Dynamics, vol. 69, no. 1-2, pp. 99–116, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  22. Y. Y. Lee, R. K. L. Su, C. F. Ng, and C. K. Hui, “The effect of modal energy transfer on the sound radiation and vibration of a curved panel: theory and experiment,” Journal of Sound and Vibration, vol. 324, no. 3–5, pp. 1003–1015, 2009. View at Publisher · View at Google Scholar · View at Scopus
  23. A. Mamandi, M. H. Kargarnovin, and S. Farsi, “Dynamic analysis of a simply supported beam resting on a nonlinear elastic foundation under compressive axial load using nonlinear normal modes techniques under three-to-one internal resonance condition,” Nonlinear Dynamics, vol. 70, no. 2, pp. 1147–1172, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  24. A. H. Nayfeh, The Method of Normal Forms, Wiley-VCH, Weinheim, Germany, 2nd edition, 2011. View at Publisher · View at Google Scholar · View at MathSciNet
  25. M. H. Ghayesh and S. Balar, “Non-linear parametric vibration and stability of axially moving visco-elastic Rayleigh beams,” International Journal of Solids and Structures, vol. 45, no. 25-26, pp. 6451–6467, 2008. View at Publisher · View at Google Scholar · View at Scopus
  26. S. W. Shaw and C. Pierre, “Normal modes of vibration for nonlinear continuous systems,” Journal of Sound and Vibration, vol. 169, no. 3, pp. 319–347, 1994. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  27. M. E. King and A. F. Vakakis, “Energy-based formulation for computing nonlinear normal modes in undamped continuous systems,” Journal of Vibration and Acoustics, Transactions of the ASME, vol. 116, no. 3, pp. 332–340, 1994. View at Publisher · View at Google Scholar · View at Scopus
  28. J. Kang and H. V. Fuchs, “Predicting the absorption of open weave textiles and micro-perforated membranes backed by an air space,” Journal of Sound and Vibration, vol. 220, no. 5, pp. 905–920, 1999. View at Publisher · View at Google Scholar · View at Scopus
  29. L. E. Kinsler, A. R. Frey, A. B. Coppens, and J. V. Sanders, Fundamentals of Acoustics, John Wiley & Sons, 4th edition, 1999.
  30. H. N. Chu and G. Herrmann, “Influence of large amplitudes on free flexural vibrations of rectangular elastic plates,” Journal of Applied Mechanics, vol. 23, pp. 532–540, 1956. View at Google Scholar · View at MathSciNet
  31. W. Weisstein Eric, “Vieta's Substitution,” From MathWorld—A Wolfram Web Resource, http://mathworld.wolfram.com/VietasSubstitution.html.
  32. Y. Y. Lee, X. Guo, and E. W. M. Lee, “Effect of the large amplitude vibration of a finite flexible micro-perforated panel absorber on sound absorption,” International Journal of Nonlinear Sciences and Numerical Simulation, vol. 8, no. 1, pp. 41–44, 2007. View at Google Scholar · View at Scopus
  33. Y. Y. Lee, E. W. M. Lee, and C. F. Ng, “Sound absorption of a finite flexible micro-perforated panel backed by an air cavity,” Journal of Sound and Vibration, vol. 287, no. 1-2, pp. 227–243, 2005. View at Publisher · View at Google Scholar · View at Scopus
  34. Y. Y. Lee and E. W. M. Lee, “Widening the sound absorption bandwidths of flexible micro-perforated curved absorbers using structural and acoustic resonances,” International Journal of Mechanical Sciences, vol. 49, no. 8, pp. 925–934, 2007. View at Publisher · View at Google Scholar · View at Scopus