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Abstract and Applied Analysis
Volume 2012, Article ID 391584, 13 pages
Research Article

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

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

Received 13 August 2012; Accepted 9 November 2012

Academic Editor: Lan Xu

Copyright © 2012 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.


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.