Analysis of the nonlinear structural-acoustic resonant frequencies of a rectangular tube with a flexible end using harmonic balance and homotopy perturbation methods. (English) Zbl 1257.35176

Lee, Y. Y.

Abstr. Appl. Anal. 2012, Article ID 391584, 13 p. (2012).

Summary: 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.

MSC:

35Q74	PDEs in connection with mechanics of deformable solids
74H45	Vibrations in dynamical problems in solid mechanics

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