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Research Papers

A Dimensionless Quotient for Determining Coupling Strength in Modal Energy Analysis

[+] Author and Article Information
Peng Zhang, Shaoqing Wu, Yanbin Li

Department of Engineering Mechanics,
Southeast University,
Nanjing, Jiangsu 210096, China

Qingguo Fei

Department of Engineering Mechanics,
Southeast University,
Nanjing, Jiangsu 210096, China
e-mail: QGFei@seu.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 March 29, 2016; final manuscript received July 27, 2016; published online September 21, 2016. Assoc. Editor: Nicole Kessissoglou.

J. Vib. Acoust 138(6), 061014 (Sep 21, 2016) (7 pages) Paper No: VIB-16-1150; doi: 10.1115/1.4034377 History: Received March 29, 2016; Revised July 27, 2016

Modal energy analysis (MODENA) is an energy-based method recently proposed to estimate the dynamic response of a coupled structure/acoustic cavity system. The accuracy of MODENA is affected by the coupling strength between structural and acoustic modes. A dimensionless coupling quotient which is equal to the ratio of the gyroscopic coupling coefficient and the critical coefficient at modal frequencies is defined to determine the coupling strength in MODENA. The coupling strength of the system is classified as weak, moderate, or strong, according to the coupling quotient with a proposed criterion. When computing the modal input power in MODENA, the mobility of the uncoupled mode can be used if the modes are weakly coupled, but the mobility of the coupled mode should be adopted to obtain accurate results if many modes are moderately coupled. The effectiveness of the proposed criterion is validated via a numerical example where a plate is coupled with an acoustic cavity. Results show that many low-order structural and acoustic modes are moderately coupled while almost all high-order modes are weakly coupled. Errors of the energy responses appear in a low-frequency band, but accurate results are acquired in a mid- to high-frequency band when the mobility of uncoupled mode is used.

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Topics: Acoustics , Cavities , Errors
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Figures

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Fig. 1

Schematic diagram of a multimodal coupling system

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Fig. 2

The energy responses Ea and the errors ea near the eigenfrequencies of (a) the structural mode and (b) the acoustic mode

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Fig. 3

The critical quotient κam as a function of the structural modal damping ηs

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Fig. 4

The critical quotient as a function of the modal frequencies when ηs = ηa = 0.01. White dashed lines—contour lines; blue solid lines—boundary of the octave frequency band.

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Fig. 5

The critical quotient κam as a function of the dimensionless factor T

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Fig. 6

Total energy responses Eat of the acoustic subsystem in (a) case I, (b) case II, and (c) case II

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Fig. 7

Sketch of the plate/cavity coupling case

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Fig. 8

The coupling quotients between the uncoupled structural modes and the uncoupled acoustic modes

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Fig. 9

The ratios of the coupling quotients to the critical quotients κa/ κam

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Fig. 10

Total energy responses Ecavity of the cavity

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