A perturbation-based approach is implemented to study the sound attenuation in distorted cylindrical mufflers with various inlet/outlet orientations. Study of the transmission loss (TL) in mufflers requires solution of the Helmholtz equation. Exact solutions are available only for a limited class of problems where the method of separation of variables can be applied across the cross section of the muffler (e.g., circular, rectangular, elliptic sections). In many practical situations, departures from the regular geometry occur. The present work is aimed at formulating a general procedure for determining the TL in mufflers with small perturbations on the boundary. Distortions in the geometry have been approximated by Fourier series expansion, thereby, allowing for asymmetric perturbations. Using the method of strained parameters, eigensolutions for a distorted muffler are expressed as a series summation of eigensolutions of the unperturbed cylinder having similar dimensions. The resulting eigenvectors, being orthogonal up to the order of truncation, are used to define a Green's function for the Helmholtz equation in the perturbed domain. Assuming that inlet and outlet ports of the muffler are uniform-velocity piston sources, the Green's function is implemented to obtain the velocity potential inside the muffler cavity. The pressure field inside the muffler is obtained from the velocity potential by using conservation of linear momentum. Transmission loss in the muffler is derived from the averaged pressure field. In order to illustrate the method, TL of an elliptical muffler with different inlet/outlet orientations is considered. Comparisons between the perturbation results and the exact solutions show excellent agreement for moderate (0.4∼0.6) eccentricities.

References

References
1.
Kim
,
J.
, and
Soedel
,
W.
,
1989
, “
General Formulation of Four Pole Parameters for Three-Dimensional Cavities Utilizing Modal Expansion, With Special Attention to the Annular Cylinder
,”
J. Sound Vib.
,
129
, pp.
237
254
.10.1016/0022-460X(89)90580-4
2.
Kim
,
J.
, and
Soedel
,
W.
,
1990
, “
Development of a General Procedure to Formulate Four Pole Parameters by Modal Expansion and Its Application to Three-Dimensional Cavities
,”
ASME J. Vibr. Acoust.
,
112
, pp.
452
459
.10.1115/1.2930128
3.
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
.10.1121/1.392029
4.
Kim
,
Y. H.
, and
Kang
,
S. W.
,
1993
, “
Green's Solution of the Acoustic Wave Equation for a Circular Expansion Chamber With Arbitrary Locations of Inlet, Outlet Port, and Termination Impedance
,”
J. Acoust. Soc. Am.
,
94
, pp.
473
490
.10.1121/1.407060
5.
Venkatesham
,
B.
,
Tiwari
,
M.
, and
Munjal
,
M. L.
,
2009
, “
Transmission Loss Analysis of Rectangular Expansion Chamber Muffler With Arbitrary Location of Inlet/Outlet by Means of Green's Function
,”
J. Sound Vib.
,
323
, pp.
1032
1044
.10.1016/j.jsv.2009.01.035
6.
Ih
,
J. G.
, and
Lee
,
B. H.
,
1987
, “
Theoretical Prediction of the Transmission Loss of Circular Reversing Chamber Mufflers
,”
J. Sound Vib.
,
112
, pp.
261
272
.10.1016/S0022-460X(87)80194-3
7.
Ih
J. G.
,
1992
, “
The Reactive Attenuation of Rectangular Plenum Chamber
,”
J. Sound Vib.
,
157
, pp.
93
122
.10.1016/0022-460X(92)90569-J
8.
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
.10.1006/jsvi.1996.0720
9.
Selamet
,
A.
, and
Ji
,
Z. L.
,
1998
, “
Acoustic Attenuation Performance of Circular Expansion Chambers With Offset Inlet/Outlet: I. Analytical Approach
,”
J. Sound Vib.
,
213
, pp.
601
617
.10.1006/jsvi.1998.1514
10.
Munjal
,
M. L.
,
1997
, “
Plane Wave Analysis of Side Inlet/Outlet Chamber Mufflers With Mean Flow
,”
Appl. Acoust.
,
52
, pp.
165
175
.10.1016/S0003-682X(96)00053-9
11.
Sewall
,
J. L.
,
Thompson
,
W. M.
, Jr.
, and
Pusey
,
C. G.
,
1971
, “
An Experimental and Analytical Vibration Study of Elliptical Cylindrical Shells
,” NASA Report No. TN D-6089
.
12.
Nayfeh
,
A. H.
,
Mook
,
D. T.
,
Lobitz
,
D. W.
, and
Sridhar
,
S.
,
1975
, “
Vibration of Nearly Annular and Circular Plates
,”
J. Sound Vib.
,
47
, pp.
75
84
.10.1016/0022-460X(76)90408-9
13.
Roberts
,
S. B.
,
1967
, “
The Eigenvalue Problem for Two Dimensional Regions With Irregular Boundaries
,”
ASME J. Appl. Mech.
,
34
, pp.
618
622
.10.1115/1.3607752
14.
DiPerna
,
D. T.
, and
Stanto
,
T. K.
,
1993
, “
Sound Scattering by Cylinders of Noncircular Cross Section: A Conformal Mapping Approach
,”
J. Acoust. Soc. Am.
,
96
, pp.
3064
3079
.10.1121/1.411243
15.
Parker
,
R. G.
, and
Mote
,
C. D.
, Jr.
,
1998
, “
Exact Boundary Condition Perturbation for Eigensolutions of the Wave Equation
,”
J. Sound Vib.
,
211
, pp.
389
407
.10.1006/jsvi.1997.1312
16.
Panda
,
S.
,
Chakraborty
,
S.
, and
Khastgir
,
S. P.
,
2011
, “
Eigenvalue Problem in Two Dimensions for an Irregular Boundary: Neumann Condition
,”
Eur. Phys. J. Plus
,
126
, pp.
62
–88.10.1140/epjp/i2011-11062-4
17.
Cummings
,
A.
,
Chang
,
I. J.
, and
Astley
,
R. J.
,
1984
, “
Sound Transmission at Low Frequencies Through the Walls of Distorted Circular Ducts
,”
J. Sound Vib.
,
97
, pp.
261
286
.10.1016/0022-460X(84)90322-5
18.
Pico
,
R.
, and
Gautier
,
F.
,
2007
, “
The Vibroacoustics of Slightly Distorted Cylindrical Shells: A Model of the Acoustic Input Impedance
,”
J. Sound Vib.
,
302
, pp.
18
38
.10.1016/j.jsv.2006.10.045
19.
Sarkar
,
A.
, and
Sonti
,
V.
,
2009
, “
Wave Equations and Solutions of In Vacuo and Fluid-Filled Elliptical Cylindrical Shells
,”
Int. J. Acoust. Vib.
,
14
, pp.
35
45
.
20.
Denia
,
F. D.
,
Albelda
,
J.
, and
Fuenmayor
,
F. J.
,
2001
, “
Acoustic Behavior of Elliptical Chamber Mufflers
,”
J. Sound Vib.
,
241
, pp.
401
421
.10.1006/jsvi.2000.3289
21.
Banerjee
,
S.
, and
Jacobi
,
A.
,
2011
, “
Analysis of Sound Attenuation in Elliptical Chamber Mufflers by Using Green's Function
,”
ASME 2011 International Mechanical Engineering Congress & Expositions
,
Denver, CO
, November 11–17,
ASME
Paper No. IMECE2011-65345.10.1115/IMECE2011-65345
22.
Mimani
,
A.
, and
Munjal
,
M. L.
,
2012
, “
3-D Acoustic Analysis of Elliptical Chamber Mufflers Having an End-Inlet and a Side-Outlet: An Impedance Matrix Approach
,”
Wave Motion
,
49
, pp.
271
295
.10.1016/j.wavemoti.2011.11.001
23.
Nayfeh
,
A. H.
,
1981
,
Introduction to Perturbation Techniques
,
Wiley
,
New York
.
24.
Morse
,
P. M.
, and
Ingard
,
K. U.
,
1968
,
Theoretical Acoustics
,
McGraw-Hill
,
New York
.
25.
Courant
,
R.
, and
Hilbert
,
D.
,
1953
,
Methods of Mathematical Physics
, Vol.
1
,
Interscience
,
New York
.
26.
Munjal
,
M. L.
,
1987
,
Acoustics of Ducts and Mufflers
,
Wiley
,
New York
.
27.
Hong
,
K.
, and
Kim
,
J.
,
1985
, “
Natural Mode Analysis of Hollow and Annular Elliptical Cylindrical Cavities
,”
J. Sound Vib.
,
183
, pp.
327
351
.10.1006/jsvi.1995.0257
28.
Parker
,
R. G.
, and
Mote
, Jr.,
C. D.
,
1996
, “
Exact Perturbation for the Vibration of Almost Annular or Circular Plates
,”
ASME J. Vib. Acoust.
,
118
, pp.
436
445
.10.1115/1.2888203
You do not currently have access to this content.