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Research Papers

A General Analytical Method for Vibroacoustic Analysis of an Arbitrarily Restrained Rectangular Plate Backed by a Cavity With General Wall Impedance

[+] Author and Article Information
Yuehua Chen, Shuangxia Shi, Zhigang Liu

College of Power and Energy Engineering,
Harbin Engineering University,
Harbin 150001, China

Guoyong Jin

College of Power and Energy Engineering,
Harbin Engineering University,
Harbin 150001, China
e-mail: guoyongjin@hrbeu.edu.cn

1Corresponding author.

Contributed by the Noise Control and Acoustics Division of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received May 20, 2013; final manuscript received February 5, 2014; published online April 15, 2014. Assoc. Editor: Theodore Farabee.

J. Vib. Acoust 136(3), 031015 (Apr 15, 2014) (11 pages) Paper No: VIB-13-1172; doi: 10.1115/1.4027136 History: Received May 20, 2013; Revised February 05, 2014

A general modeling method is developed for the vibroacoustic analysis of an arbitrarily restrained rectangular plate backed by a cavity with general wall impedance. The present method provides a uniform way to obtain the solution of the coupled structure-cavity system, making changes of both boundary conditions of the plate and impedance of the cavity walls as simple as the modifications of geometrical or material parameters without requiring any altering of the whole solution procedure. With the displacement of the plate and acoustic pressure in the cavity expanded as double and triple Chebyshev polynomial series, respectively, a simple yet efficient solution to the problem of the modal and vibroacoustic behavior of the coupled system is obtained under the Rayleigh–Ritz frame. The current method can be applied to handle strong structural-acoustic coupling cases and this is illustrated explicitly by considering one case with a shallow cavity and very thin plate while the other with a water-filled cavity. The spatial matching of velocity at the interface is checked by numerical examples. The excellent orthogonal and complete properties of the Chebyshev series representations enable excellent accuracy and numerical stability. An experiment is conducted to validate the present method. In addition, the accuracy and reliability of the current method are also extensively validated by numerical examples and comparisons with theoretical solutions, finite element results, and results available in the literature. The effects of several key parameters are analyzed, including structural boundary conditions, plate thickness, cavity depth, and wall impedance.

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Figures

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Fig. 1

Schematic of plate-cavity coupling model with general impedance surfaces

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Fig. 2

Comparisons of velocity and sound pressure responses: (a) velocity responses and (b) sound pressure responses

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Fig. 3

Spatial matching of velocity continuity at the interface and frequency responses: spatial matching of velocity continuity at the resonant frequency, (a) first order (111.49 Hz); (b) second order (141.03 Hz); (c) velocity responses at (13Lx/30, Ly/2); and (d) sound pressure responses at (2 Lx/5, Ly/2, Lz/2)

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Fig. 4

Velocity responses of a cavity with impedance walls at (a) (13Lx/30, Ly/2) and (b) (16Lx/30, Ly/3)

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Fig. 5

Comparisons of frequency responses between the experimental results and the present method. (a) Velocity responses and (b) sound pressure responses.

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Fig. 6

Curves of coupling parameters versus different variables: (a) thickness of plate and (b) depth of cavity

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Fig. 7

Sound pressure responses of the plate-cavity system with one impedance wall at y = 0 (a) contour plot and (b) curve plot

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Fig. 8

Effects of wall impedance on vibroacoustic responses: (a) velocity response and (b) sound pressure response

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