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Research Papers

Using a Dynamic Substructuring Approach to Model the Effects of Acoustic Damping in Coupled Acoustic–Structure Systems

[+] Author and Article Information
R. Benjamin Davis

College of Engineering,
University of Georgia,
Athens, GA 30602
e-mail: ben.davis@uga.edu

Ryan Schultz

Sandia National Laboratories,
Albuquerque, NM 87123
e-mail: rschult@sandia.gov

1Corresponding author.

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received July 11, 2018; final manuscript received November 20, 2018; published online January 16, 2019. Assoc. Editor: Izhak Bucher.

J. Vib. Acoust 141(2), 021019 (Jan 16, 2019) (11 pages) Paper No: VIB-18-1296; doi: 10.1115/1.4042103 History: Received July 11, 2018; Revised November 20, 2018

Acoustic–structure coupling can substantially alter the frequency response of air-filled structures. Coupling effects typically manifest as two resonance peaks at frequencies above and below the resonant frequency of the uncoupled structural system. Here, a dynamic substructuring approach is applied to a simple acoustic–structure system to expose how the system response depends on the damping in the acoustic subsystem. Parametric studies show that as acoustic damping is increased, the frequencies and amplitudes of the coupled resonances in the structural response undergo a sequence of changes. For low levels of acoustic damping, the two coupled resonances have amplitudes approximating the corresponding in vacuo resonance. As acoustic damping is increased, resonant amplitudes decrease dramatically while the frequency separation between the resonances tends to increase slightly. When acoustic damping is increased even further, the separation of the resonant frequencies decreases below their initial separation. Finally, at some critical value of acoustic damping, one of the resonances abruptly disappears, leaving just a single resonance. Counterintuitively, increasing acoustic damping beyond this point tends to increase the amplitude of the remaining resonance peak. These results have implications for analysts and experimentalists attempting to understand, mitigate, or otherwise compensate for the confounding effects of acoustic–structure coupling in fluid-filled test structures.

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Figures

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Fig. 1

Single degree-of-freedom piston coupled to one-dimensional closed waveguide

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Fig. 2

First three natural frequencies as calculated using three different types of bases (markers) compared to values calculated analytically using Eq. (32) (dashed lines)

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Fig. 3

(a) Structural FRF and (b) normalized mean-square cavity pressure averaged over the length of the waveguide (p¯av2=pav2/pav02) for σ = 10, η = 1, and no damping

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Fig. 4

Coupled mode shapes (solid) compared to corresponding closed–closed mode (dashed) for σ = 1, (a) η = 1, and (b) η = 2

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Fig. 5

(a) Structural FRF and (b) normalized mean-square cavity pressure averaged over the length of the waveguide for η = 1 and three different mass ratios

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Fig. 6

(a) Normalized coupled natural frequencies and (b) modal energy ratio versus uncoupled frequency ratio for three different mass ratios

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Fig. 7

(a) Structural FRF and (b) mean-square pressure averaged over the length of the waveguide for η = 1 and three different acoustic damping levels and ζs = 0.01. Vertical lines indicated resonant frequencies.

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Fig. 8

(Left) normalized resonant frequencies and amplitudes versus acoustic subsystem damping ratio and overlaid on the normalized imaginary parts of the system eigenvalues. (Right) Ratio of real to imaginary parts of first two system eigenvalues versus acoustic subsystem damping ratio. Subsystem damping level is indicated with dotted lines. ((a) and (b)) σ = 10, η = 0.95; ((c) and (d)) σ = 10, η = 1; ((e) and (f)) σ = 10, η = 1.05.

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Fig. 9

(Left) normalized resonant frequencies and amplitudes versus acoustic subsystem damping ratio and overlaid on the normalized imaginary parts of the system eigenvalues. (Right) Ratio of real to imaginary parts of first two system eigenvalues versus acoustic subsystem damping ratio. Subsystem damping level is indicated with dotted lines. ((a) and (b)) σ = 1, η = 1; ((c) and (d)) σ = 100, η = 1.

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Fig. 10

Acoustic damping ratio at which second resonance disappears versus uncoupled frequency ratio for four different mass ratios and ζs = 0.01

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Fig. 11

Normalized resonant amplitudes for versus subsystem damping ratio for four different mass ratios with ζs = 0.01 (solid) and ζs = 0.005 (dashed) (a) first system resonance (b) second system resonance

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Fig. 12

(a) Minimum (b) maximum resonant frequency separation, (ωr2−ωr1), normalized by the resonant frequency separation with ζa=0, (ωr2−ωr1)0. Results are shown versus uncoupled frequency ratio for four different mass ratios.

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