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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Lyon, R. H., 1963, “Noise Reduction of Rectangular Enclosure With One Flexible Wall,” J. Acoust. Soc. Am., 35(11), pp. 1791–1797. [CrossRef]
Pretlove, A. J., 1966, “Forced Vibrations of a Rectangular Panel Backed by a Closed Rectangular Cavity,” J. Sound Vib., 3(3), pp. 252–261. [CrossRef]
Bhattacharya, M. C., and CrockerM. J., 1969, “Forced Vibration of a Panel and Radiation of Sound Into a Room,” Acustica, 22(5), pp. 275–294.
Dowell, E. H., Gorman, G. F., and SmithD. A., 1977, “Acoustoelasticity: General Theory, Acoustic Natural Modes and Forced Response to Sinusoidal Excitation, Including Comparisons With Experiment,” J. Sound Vib., 52(4), pp. 519–541. [CrossRef]
Guy, R. W., 1979, “The Steady State Transmission of Sound at Normal and Oblique Incidence Through a Thin Panel Backed by a Rectangular Room, a Multimodal Analysis,” Acustica, 43(5), pp. 295–304.
Guy, R. W., 1980, “Pressure Developed Within a Cavity Backing a Finite Panel When Subjected to External Transient Excitation,” J. Acoust. Soc. Am., 68(6), pp. 1736–1747. [CrossRef]
Qaisi, M., 1988, “Free Vibrations of a Rectangular Plate-Cavity System,” Appl. Acoust., 24(1), pp. 49–61. [CrossRef]
Fahy, F. J., 1985, Sound and Structural Vibration: Radiation, Transmission and Response, Academic, New York, pp. 241–269.
Pan, J., and Bies, D. A., 1990, “The Effect of Fluid-Structural Coupling on Sound Waves in an Enclosure—Theoretical Part,” J. Acoust. Soc. Am., 87(2), pp. 691–707. [CrossRef]
Rajalingham, C., Bhat, R. B., and Xistris, G. D., 1995, “Natural Vibration of a Cavity Backed Rectangular Plate Using a Receptor-Rejector System,” ASME J. Vib. Acoust., 117(4), pp. 416–423. [CrossRef]
Kim, S. M., and Brennan, M. J., 1999, “A Compact Matrix Formulation Using the Impedance and Mobility Approach for the Analysis of Structural-Acoustic Systems,” J. Sound Vib., 223(1), pp. 97–113. [CrossRef]
Al-Bassyiouni, M., and Balachandran, B., 2005, “Sound Transmission Through a Flexible Panel Into an Enclosure: Structural-Acoustics Model,” J. Sound Vib., 284(1–2), pp. 467–486. [CrossRef]
Li, Y. Y., and Cheng, L., 2004, “Modifications of Acoustic Modes and Coupling Due to a Leaning Wall in a Rectangular Cavity,” J. Acoust. Soc. Am., 116(6), pp. 3312–3318. [CrossRef] [PubMed]
Li, Y. Y., and Cheng, L., 2007, “Vibro-Acoustic Analysis of a Rectangular-Like Cavity With a Tilted Wall,” Appl. Acoust., 68(7), pp. 739–751. [CrossRef]
Tanaka, N., Takara, Y., and IwamotoH., 2012, “Eigenpairs of a Coupled Rectangular Cavity and Its Fundamental Properties,” J. Acoust. Soc. Am., 131(3), pp. 1910–1921. [CrossRef] [PubMed]
Pan, J., Hansen, C. H., and Bies, D. A., 1990, “Active Control of Noise Transmission Through a Panel Into a Cavity: I. Analytical Study,” J. Acoust. Soc. Am., 87(5), pp. 2098–2108. [CrossRef]
Pan, J., Hansen, C. H., and Bies, D. A., 1991, “Active Control of Noise Transmission Through a Panel Into a Cavity: II. Experimental Study,” J. Acoust. Soc. Am., 90(3), pp. 1488–1492. [CrossRef]
Koshigoe, S., Gillis, J. T., and Falangas, E. T., 1993, “A New Approach for Active Control of Sound Transmission Through an Elastic Plate Backed by a Rectangular Cavity,” J. Acoust. Soc. Am., 94(2), pp. 900–907. [CrossRef]
Snyder, S. D., and Hansen, C. H., 1994, “The Design of Systems to Actively Control Periodic Sound Transmission Into Enclosed Spaces, Part 1. Analytical Models,” J. Sound Vib., 170(4), pp. 433–449. [CrossRef]
Kim, S. M., and Brennan, M. J., 2000, “Active Control of Harmonic Sound Transmission Into an Acoustic Enclosure Using Both Structural and Acoustic Actuators,” J. Acoust. Soc. Am., 107(5), pp. 2523–2534. [CrossRef] [PubMed]
Jin, G. Y., Liu, Z. G., and Yang, T. J., 2009, “Active Control of Sound Transmission Into an Acoustic Cavity Surrounded by More Than One Flexible Plate,” Noise Control Eng. J., 57(3), pp. 210–220. [CrossRef]
Lau, S. K., and Tang, S. K., 2003, “Active Control on Sound Transmission Into an Enclosure Through a Flexible Boundary With Edges Elastically Restrained Against Translation and Rotation,” J. Sound Vib., 259(3), pp. 701–710. [CrossRef]
Qiu, X. J., Sha, J. Z., and Yang, J., 1995, “Mechanisms of Active Control of Noise Transmission Through a Panel Into a Cavity Using a Point Force Actuator on the Panel,” J. Sound Vib., 182(1), pp. 167–170. [CrossRef]
Hill, S. G., Tanaka, N., and Iwamoto, H., 2012, “A Generalised Approach for Active Control of Structural—Interior Global Noise: Practical Implementation,” J. Sound Vib., 331(14), pp. 3227–3239. [CrossRef]
Snyder, S. D., and Tanaka, N., 1993, “On Feedforward Active Control of Sound and Vibration Using Vibration Error Signals,” J. Acoust. Soc. Am., 94(4), pp. 2181–2193. [CrossRef]
Sampath, A., and Balachandran, B., 1999, “Active Control of Multiple Tones in an Enclosure,” J. Acoust. Soc. Am., 106(1), pp. 211–225. [CrossRef]
Tanaka, N., and Kobayashi, K., 2006, “Cluster Control of Acoustic Potential Energy in a Structural/Acoustic Cavity,” J. Acoust. Soc. Am., 119(5), pp. 2758–2771. [CrossRef]
Berry, A., Guyader, J.-L., and Nicolas, J., 1990, “A General Formulation for the Sound Radiation From Rectangular Baffled Plates With Arbitrary Boundary Conditions,” J. Acoust. Soc. Am., 88(6), pp. 2792–2802. [CrossRef]
Atalla, N., Nicolas, J., and Gauthier, C., 1996, “Acoustic Radiation of an Unbaffled Vibrating Plate With General Elastic Boundary Conditions,” J. Acoust. Soc. Am., 99(3), pp. 1484–1494. [CrossRef]
Cheng, L., and Nicolas, J., 1992, “Free Vibration Analysis of a Cylindrical Shell—Circular Plate System With General Coupling and Various Boundary Conditions,” J. Sound Vib., 155(2), pp. 231–247. [CrossRef]
Cheng, L., and Nicolas, J., 1992, “Radiation of Sound Into a Cylindrical Enclosure From a Point-Driven End Plate With General Boundary Conditions,” J. Acoust. Soc. Am., 91(3), pp. 1504–1513. [CrossRef]
Yuan, J., and Dickson, S. M., 1992, “The Flexural Vibration of Rectangular Plate Systems Approached by Using Artificial Springs in the Rayleigh–Ritz Method,” J. Sound Vib., 159(1), pp. 39–55. [CrossRef]
Jin, G. Y., Ye, T. G., Ma, X. L., Chen, Y. H., Su, Z., and XieX., 2013, A Unified Approach for the Vibration Analysis of Moderately Thick Composite Laminated Cylindrical Shells With Arbitrary Boundary Conditions,” Int. J. Mech. Sci., 75, pp. 357–376. [CrossRef]
Jin, G. Y., Chen, Y. H., and Liu, Z. G., 2014, “A Chebyshev–Lagrangian Method for Acoustic Analysis of a Rectangular Cavity With Arbitrary Impedance Walls,” Appl. Acoust., 78, pp. 33–42. [CrossRef]
Pan, J., 1999, “A Third Note on the Prediction of Sound Intensity,” J. Acoust. Soc. Am., 105(1), pp. 560–562. [CrossRef]
Zhou, D., Cheung, Y. K., Au, F. T. K., and Lo, S. H., 2002, “Three-Dimensional Vibration Analysis of Thick Rectangular Plates Using Chebyshev Polynomial and Ritz Method,” Int. J. Solids Struct., 39(26), pp. 6339–6353. [CrossRef]
Zhou, D., Au, F. T. K., Cheung, Y. K., and Lo, S. H., 2003, “Three-Dimensional Vibration Analysis of Circular and Annular Plates Via the Chebyshev–Ritz Method,” Int. J. Solids Struct., 40(12), pp. 3089–3105. [CrossRef]
Fox, L., and Parker, I. B.1968, Chebyshev Polynomials in Numerical Analysis, Oxford University Press, London, pp. 1–205.


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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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