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Analysis of the Nonlinear Structural‐Acoustic Resonant Frequencies of a Rectangular Tube with a Flexible End Using Harmonic Balance and Homotopy Perturbation Methods

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  • Y. Y. Lee

Abstract

The structural acoustic problem considered in this study is the nonlinear resonant frequencies of a rectangular tube with one open end, one flexible end, and four rigid side walls A multiacoustic single structural modal formulation is derived from two coupled partial differential equations which represent the large amplitude structural vibration of the flexible end and acoustic pressure induced within the tube. The results obtained from the harmonic balance and homotopy perturbation approaches verified each other. The effects of vibration amplitude, aspect ratio, the numbers of acoustic modes and harmonic terms, and so forth, on the first two resonant natural frequencies, are examined.

Suggested Citation

  • Y. Y. Lee, 2012. "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, John Wiley & Sons, vol. 2012(1).
    • Handle: RePEc:wly:jnlaaa:v:2012:y:2012:i:1:n:391584
    DOI: 10.1155/2012/391584
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    References listed on IDEAS

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    6. Ji-Huan He, 2012. "Homotopy Perturbation Method with an Auxiliary Term," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    7. M. L. Santos & J. Ferreira & C. A. Raposo, 2005. "Existence and uniform decay for a nonlinear beam equation with nonlinearity of Kirchhoff type in domains with moving boundary," Abstract and Applied Analysis, Hindawi, vol. 2005, pages 1-19, January.
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    1. Y. Y. Lee, 2014. "Analytic Formulation for the Sound Absorption of a Panel Absorber under the Effects of Microperforation, Air Pumping, Linear Vibration and Nonlinear Vibration," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).

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