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Technical Brief

Transmission Loss of Variable Cross Section Apertures

[+] Author and Article Information
J. Li

Institute of Sound and Vibration Research,
School of Mechanical and Automotive Engineering,
Hefei University of Technology,
193 Tunxi Road,
Hefei, Anhui 230009, China
e-mail: 13856086466@163.com

L. Zhou

Department of Mechanical Engineering,
University of Kentucky,
151 RGAN Building,
Lexington, KY 40506-0503
e-mail: unilmzh@gmail.com

X. Hua

Department of Mechanical Engineering,
University of Kentucky,
151 RGAN Building,
Lexington, KY 40506-0503
e-mail: huaxin0210@gmail.com

D. W. Herrin

Department of Mechanical Engineering,
University of Kentucky,
151 RGAN Building,
Lexington, KY 40506-0503
e-mail: dherrin@engr.uky.edu

1Corresponding author.

Contributed by the Noise Control and Acoustics Division of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received November 5, 2013; final manuscript received April 3, 2014; published online April 25, 2014. Assoc. Editor: Theodore Farabee.

J. Vib. Acoust 136(4), 044501 (Apr 25, 2014) (5 pages) Paper No: VIB-13-1390; doi: 10.1115/1.4027402 History: Received November 05, 2013; Revised April 03, 2014; Accepted April 05, 2014

Openings in enclosures or walls are frequently the dominant path for sound propagation. In the current work, a transfer matrix method is used to predict the transmission loss of apertures assuming that the cross-sectional dimensions are small compared with an acoustic wavelength. Results are compared with good agreement to an acoustic finite element approach in which the loading on the source side of the finite element model (FEM) is a diffuse acoustic field applied by determining the cross-spectral force matrix of the excitation. The radiation impedance for both the source and termination is determined using a wavelet algorithm. Both approaches can be applied to leaks of any shape and special consideration is given to apertures with varying cross section. Specifically, cones and abrupt area changes are considered, and it is shown that the transmission loss can be increased by greater than 10 dB at many frequencies.

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References

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Figures

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Fig. 1

Schematic identifying variables for an aperture with the entry on the left and exit on the right

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Fig. 2

Acoustic finite element model of a uniform cross-sectional area aperture with diffuse acoustic field excitation at the entry and radiation impedance at the aperture entry and exit

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Fig. 3

Transmission loss of a circular aperture with radius of 5.64 mm and length of 10 cm. For the acoustic FEM, the element length is 0.7 mm with 257,474 nodes (quadratic tetrahedral elements). Fifty four acoustic modes were included in the forced response analysis.

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Fig. 4

Transmission loss for uniform cross section apertures having the same cross-sectional area but different shape

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Fig. 8

Schematic showing an aperture with abrupt contraction. l1 and l2 are each 50 mm and r is 5.64 mm.

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Fig. 9

Effect of radius ratio (R/r) on the transmission loss for an aperture with abrupt cross-sectional area change

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Fig. 10

Transmission loss determined by acoustic finite element analysis and compared with measured results [23] for aperture with 6 cm × 13 cm cross section and length of 30 cm. The cutoff frequency is approximately 1310 Hz. For the acoustic FEM, the element length is 5 mm with 186,819 nodes (quadratic tetrahedral elements). Four hundred and eighty two acoustic modes were included in the forced response analysis.

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Fig. 5

Schematic showing a conical aperture and variables. r2 and L are held constant at 5.64 mm and 100 mm, respectively.

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Fig. 6

Transmission loss for converging and diverging cones. For the converging case, r1 and r2 are 22.56 mm and 5.64 mm, respectively. For the diverging case, r1 and r2 are 5.64 mm and 22.56 mm, respectively. For the acoustic FEM, the element length is 1 mm with 527,924 nodes (quadratic tetrahedral elements). Two hundred and sixty eight acoustic modes were included in the forced response analysis.

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Fig. 7

Effect of radius ratio on the transmission loss of a conical aperture; r = 5.64 mm

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