An analytical method is applied to predict the acoustic attenuation performance of expansion chambers with continuously varying cross-sectional area. A feature of the present method is the use of spherical coordinates whose origin is at the top of the cone that is tangent to the wall of the expansion chamber. By this means, the characteristic functions can be analytically determined despite the non-uniform geometry of the expansion chamber. Using the Galerkin method, a variational principle is transformed into linear algebraic equations that are solved to determine the transmission coefficient of the expansion chamber. Numerical results are provided for the case where broadband noise attenuation is achieved.

1.
Miles
,
J.
,
1944
, “
The Reflection of Sound Due to a Change in Cross Section of a Circular Tube
,”
J. Acoust. Soc. Am.
,
16
, pp.
14
19
.
2.
Selamet
,
A.
, and
Radavich
,
P. M.
,
1997
, “
The Effect of Length on the Acoustic Attenuation Performance of Concentric Expansion Chambers: An Analytical, Computational and Experimental Investigation
,”
J. Sound Vib.
,
201
, pp.
407
426
.
3.
Selamet
,
A.
,
Dickey
,
N. S.
, and
Novak
,
J. M.
,
1995
, “
A Time-Domain Computational Simulation of Acoustic Silencers
,”
ASME J. Vibr. Acoust.
,
117
, pp.
323
331
.
4.
Selamet
,
A.
,
Dickey
,
N. S.
,
Kim
,
Y.
, and
Novak
,
J. M.
,
1998
, “
Venturi Tubes: Acoustic Attenuation With Flow Loss Considerations
,”
ASME J. Vibr. Acoust.
,
120
, pp.
607
613
.
5.
Astley
,
R. J.
, and
Eversman
,
W.
,
1978
, “
A Finite Element Method for Transmission in Non-Uniform Ducts Without Flow: Comparison With the Method of Weighted Residuals
,”
J. Sound Vib.
,
57
, pp.
367
388
.
6.
Astley
,
R. J.
, and
Eversman
,
W.
,
1981
, “
Acoustic Transmission in Non-Uniform Ducts With Mean Flow, Part II: The Finite Element Method
,”
J. Sound Vib.
,
74
, pp.
103
121
.
7.
Tam
,
C. K. W.
,
1971
, “
Transmission of Spinning Acoustic Modes in a Slightly Non-Uniform Duct
,”
J. Sound Vib.
,
18
, pp.
339
351
.
8.
Nayfeh
,
A. H.
,
Kaiser
,
J. E.
,
Marshall
,
R. L.
, and
Hurst
,
C. J.
,
1980
, “
A Comparison of Experiment and Theory for Sound Propagation in Variable Area Ducts
,”
J. Sound Vib.
,
71
, pp.
241
259
.
9.
Alfredson
,
R. J.
,
1972
, “
The Propagation of Sound in a Circular Duct of Continuously Varying Cross-Sectional Area
,”
J. Sound Vib.
,
23
, pp.
433
442
.
10.
Sadamoto
,
A.
,
Murakami
,
Y.
, and
Masuda
,
S.
,
1993
, “
Calculation for Reflection and Transmission of Higher-Order Mode Sound Waves at Sections of Varying Cross-Sectional Area in Circular Ducts (in Japanese)
,”
J. Acoust. Soc. Japan
,
49
, pp.
235
242
.
11.
Eversman
,
W.
,
Cook
,
E. L.
, and
Beckemeyer
,
R. J.
,
1975
, “
A Method of Weighted Residuals for the Investigation of Sound Transmission in Non-Uniform Ducts Without Flow
,”
J. Sound Vib.
,
38
, pp.
105
123
.
12.
Eversman
,
W.
, and
Astley
,
R. J.
,
1981
, “
Acoustic Transmission in Non-Uniform Ducts With Mean Flow, Part I: The Method of Weighted Residuals
,”
J. Sound Vib.
,
74
, pp.
89
101
.
13.
Vo
,
P. T.
, and
Eversman
,
W.
,
1978
, “
Acoustic Transmission in Non-Uniform Ducts With Mean Flow, Part I: The Method of Weighted Residuals
,”
J. Sound Vib.
,
74
, pp.
89
101
.
14.
Pagneux
,
V.
,
Amir
,
N.
, and
Kergomard
,
J.
,
1996
, “
A Study of Wave Propagation in Varying Cross-Section Waveguides by Modal Decomposition. Part I. Theory and Validation
,”
J. Acoust. Soc. Am.
,
100
, pp.
2034
2048
.
15.
Stevenson
,
A. F.
,
1951
, “
Exact and Approximate Equations for Wave Propagation in Acoustic Horns
,”
J. Appl. Phys.
,
22
, pp.
1461
1463
.
16.
Utsumi
,
M.
,
1999
, “
An Efficient Method for Sound Transmission in Non-Uniform Circular Ducts
,”
J. Sound Vib.
,
227
, pp.
735
748
.
17.
Utsumi
,
M.
,
2001
, “
Sound Transmission in Circular Ducts of Continuously Varying Cross-Sectional Area
,”
J. Sound Vib.
,
242
, pp.
369
376
.
18.
Eriksson
,
L. J.
,
1980
, “
Higher Order Mode Effects in Circular Ducts and Expansion Chambers
,”
J. Acoust. Soc. Am.
,
68
, pp.
545
550
.
19.
Sadamoto
,
A.
, and
Murakami
,
Y.
,
2002
, “
Resonant Properties of Short Expansion Chambers in a Circular Duct: Including Extremely Short Cases and Asymmetric Mode Wave Incidence Cases
,”
J. Sound Vib.
,
249
, pp.
165
187
.
20.
Ih
,
J. G.
, and
Lee
,
B. H.
,
1985
, “
Analysis of Higher-Order Mode Effects in the Circular Expansion Chamber With Mean Flow
,”
J. Acoust. Soc. Am.
,
77
, pp.
1377
1388
.
21.
El-Sharkawy
,
A. I.
, and
Nayfeh
,
A. H.
,
1978
, “
Effect of an Expansion Chamber on the Propagation of Sound in Circular Ducts
,”
J. Acoust. Soc. Am.
,
63
, pp.
667
674
.
22.
Abom
,
M.
,
1990
, “
Derivation of Four-Pole Parameters Including Higher Order Mode Effects for Expansion Chamber Mufflers With Extended Inlet and Outlet
,”
J. Sound Vib.
,
137
, pp.
403
418
.
23.
Craggs
,
A.
,
1976
, “
A Finite Element Method for Damped Acoustic Systems: An Application to Evaluate the Performance of Reactive Mufflers
,”
J. Sound Vib.
,
48
, pp.
377
392
.
24.
Bernhard
,
R. J.
,
1986
, “
Shape Optimization of Reactive Mufflers
,”
Noise Control Eng. J.
,
27
, pp.
10
17
.
25.
Sahasrabudhe
,
A. D.
,
Munjal
,
M. L.
, and
Anantha Ramu
,
S.
,
1992
, “
Design of Expansion Chamber Mufflers Incorporating 3-D Effects
,”
Noise Control Eng. J.
,
38
, pp.
27
38
.
26.
Seybert
,
A. F.
, and
Cheng
,
C. Y. R.
,
1987
, “
Application of the Boundary Element Method to Acoustic Cavity Response and Muffler Analysis
,”
ASME J. Vibr. Acoust.
,
109
, pp.
15
21
.
27.
Wang
,
C. N.
,
1999
, “
A Numerical Analysis for Perforated Muffler Components With Mean Flow
,”
ASME J. Vibr. Acoust.
,
121
, pp.
231
236
.
28.
Lamb, H., 1879, Hydrodynamics, Cambridge University Press, seventh edition, 1975, London, p. 113.
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