In this paper, a single-domain boundary element method is presented for muffler analysis. This method is based on a direct mixed-body boundary integral formulation recently developed for acoustic radiation and scattering from a mix of regular and thin bodies. The main feature of the mixed-body integral formulation is that it can handle all kinds of complex internal geometries, such as thin baffles, extended inlet/outlet tubes, and perforated tubes, without using the tedious multi-domain approach. The variables used in the direct integral formulation are the velocity potential (or sound pressure) on the regular wall surfaces, and the velocity potential jump (or pressure jump) on any thin-body or perforated surfaces. The linear impedance boundary condition proposed by Sullivan and Crocker (1978) for perforated tubes is incorporated into the mixed-body integral formulation. The transmission loss is evaluated by a new method called “the three-point method.” Unlike the conventional four-pole transfer-matrix approach that requires two separate computer runs for each frequency, the three-point method can directly evaluate the transmission loss in one single boundary-element run. Numerical results are compared to existing experimental data for three different muffler configurations.

Issue Section:
Research Papers
Topics:
Boundary element methods, Silencers, Acoustics, Boundary-value problems, Computers, Electromagnetic scattering, Poles (Building), Pressure, Radiation (Physics), Radiation scattering, Scattering (Physics), Sound pressure
1.
Cheng
C. Y. R.
,
Seybert
A. F.
, and
Wu
T. W.
,
1991
, “
A Multidomain Boundary Element Solution for Silencer and Muffler Performance Prediction
,”
J. Sound Vib.
, Vol.
151
, pp.
119
–
129
.
2.
Hadamard, J., 1923, Lectures on Cauchy’s Problem in Linear Partial Differential Equations, Yale Univ. Press, New Haven, Conn.
3.
Igarashi, J., and Toyama, M., 1959, “Fundamentals of Acoustical Silencers (I)—Theory and Experiments of Acoustic Low-Pass Filters,” Aeronautical Research Institute, University of Tokyo, Report No. 339.
4.
Ji
Z.
,
Ma
Q.
, and
Zhang
Z.
,
1994
, “
Application of the Boundary Element Method to Predicting Acoustic Performance of Expansion Chamber Mufflers with Mean Flow
,”
J. Sound Vib.
, Vol.
173
, pp.
57
–
71
.
5.
Jia, Z. H., Mohanty, A. R., and Seybert, A. F., 1992, “Numerical Modeling of Reactive Perforated Mufflers,” Proceedings of the Second International Congress on Recent Developments in Air- and Structure-Borne Sound and Vibration, M. J. Crocker and P. K. Raju, eds., pp. 957–964.
6.
Krishnasamy
G.
,
Schmerr
L. W.
,
Rudolphi
T. J.
, and
Rizzo
F. J.
,
1990
, “
Hypersingular Boundary Integral Equations: Some Applications in Acoustic and Elastic Wave Scattering
,”
ASME Journal of Applied Mechanics
, Vol.
57
, pp.
404
–
414
.
7.
Mariem
J. B.
, and
Hamdi
M. A.
,
1987
, “
A New Boundary Finite Element Method for Fluid-Structure Interaction Problems
,”
Int. J. Num. Methods Eng.
, Vol.
24
, pp.
1251
–
1267
.
8.
Martinez
R.
,
1991
, “
The Thin-Shape Breakdown (TSB) of the Helmholtz Integral Equation
,”
J. Acoust. Soc. Am.
, Vol.
90
, pp.
2728
–
2738
.
9.
Munjal, M. L., 1987, Acoustics of Ducts and Mufflers, Wiley-Interscience, New York.
10.
Seybert
A. F.
, and
Ross
D. F.
,
1977
, “
Experimental Determination of Acoustic Properties Using a Two-Microphone Random-Excitation Technique
,”
J. Acoust. Soc. Am.
, Vol.
61
, pp.
1362
–
1370
.
11.
Sullivan
J. W.
,
1979
, “
A Method for Modeling Perforated Tube Muffler Components. II. Applications
,”
J. Acoust. Soc. Am.
, Vol.
66
, pp.
779
–
788
.
12.
Sullivan
J. W.
, and
Crocker
M. J.
,
1978
, “
Analysis of Concentric-Tube Resonators Having Unpartitioned Cavities
,”
J. Acoust. Soc. Am.
, Vol.
64
, pp.
207
–
215
.
13.
Terai
T.
,
1980
, “
On Calculation of Sound Fields Around Three Dimensional Objects by Integral Equation Methods
,”
J. Sound Vib.
, Vol.
69
, pp.
71
–
100
.
14.
Wan, G. C, 1995, “Prediction and Measurement of the Acoustic Performance of Mufflers,” Proceedings of Inter-Noise 95, Newport Beach, CA, July 10–12, 1995.
15.
Wang
C. N.
,
Tse
C. C.
, and
Chen
Y. N.
,
1993
, “
A Boundary Element Analysis of a Concentric-Tube Resonator
,”
Engineering Analysis with Boundary Elements
, Vol.
12
, pp.
21
–
27
.
16.
Wu
T. W.
,
1995
, “
A Direct Boundary Element Method for Acoustic Radiation and Scattering from Mixed Regular and Thin Bodies
,”
J. Acoust. Soc. Am.
, Vol.
97
, pp.
84
–
91
.
17.
Wu
T. W.
, and
Wan
G. C.
,
1992
, “
Numerical Modeling of Acoustic Radiation and Scattering from Thin Bodies Using a Cauchy Principal Integral Equation
,”
J. Acoust. Soc. Am.
, Vol.
92
, pp.
2900
–
2906
.
18.
Wu, X. F., Pierce, A. D., and Ginsberg, J. H., 1987, “Variational Method for Computing Surface Acoustic Pressure on Vibrating Bodies, Applied to Transversely Oscillating Disks,” IEEE J. Oceanic Eng., OE-12, pp. 412–418.
This content is only available via PDF.
Copyright © 1996
 by The American Society of Mechanical Engineers
You do not currently have access to this content.