In the proposed approach, an acoustic domain is split into two parts by an arbitrary artificial boundary. The surrounding medium around the vibrating surface is discretized with finite elements up to the artificial boundary. The constraint equation specified on the artificial boundary is formulated with the Helmholtz integral equation straightforwardly, in which the source surface coincides with the vibrating surface discretized with boundary elements. To ensure the uniqueness of the numerical solution, the composite Helmholtz integral equation proposed by Burton and Miller was adopted. Due to the avoidance of singularity problems inherent in the boundary element formulation, this method is very efficient and easy to implement in an isoparametric element environment. It should be noted that the present method also can be applied to thin-body problems by using quarter-point elements.

Issue Section:
Research Papers
Topics:
Boundary-value problems, Finite element analysis, Integral equations, Boundary element methods, Acoustics, Composite materials
1.
Astley
R. J.
,
1983
, “
Wave Envelope and Infinite Element Schemes for Acoustical Radiation
,”
Int. J. Num. Methods Fluids
, Vol.
3
, pp.
507
–
526
.
2.
Astley
R. J.
, and
Eversman
W.
,
1983
, “
Finite Element Formulations for Acoustical Radiation
,”
J. Sound Vib.
, Vol.
88
, pp.
47
–
64
.
3.
Bernhard
R. J.
, and
Takeo
S.
,
1988
, “
A Finite Element Procedure for Design of Cavity Acoustical Treatments
,”
J. Acoust. Soc. Am.
, Vol.
83
, pp.
2224
–
2232
.
4.
Burton, A. J., and Miller, G. F., 1971, “The Application of Integral Equation Methods to the Numerical Solution of Some Exterior Boundary-Value Problems,” Proc. Roy. Soc. London, A232, pp. 201–210.
5.
Chen
L. H.
, and
Schweikert
D. G.
,
1963
, “
Sound Radiation from an Arbitrary Body
,”
J. Acoust. Soc. Am.
, Vol.
35
, pp.
1626
–
1632
.
6.
Chertock
G.
,
1964
, “
Sound Radiation from Vibrating Surfaces
,”
J. Acoust. Soc. Am.
, Vol.
36
, pp.
1305
–
1313
.
7.
Copley
L. G.
,
1967
, “
Integral Equation Method for Radiation from Vibrating Bodies
,”
J. Acoust. Soc. Am.
, Vol.
41
, pp.
807
–
816
.
8.
Givoli
D.
,
1991
, “
Nonreflecting Boundary Conditions
,”
J. Comput. Phys.
, Vol.
94
, pp.
1
–
29
.
9.
Givoli
D.
, and
Cohen
D.
,
1995
, “
Nonreflecting Boundary Conditions Based on Kirchhoff-Type Formulae
,”
J. Comput. Phys.
, Vol.
117
, pp.
102
–
113
.
10.
Givoli
D.
,
Patlashenko
I.
, and
Keller
J. B.
,
1997
, “
High-Order Boundary Conditions and Finite Elements for Infinite Domains
,”
Comput. Meth. App. Mech. Eng.
, Vol.
143
, pp.
13
–
39
.
11.
Gladwell
G. M. L.
, and
Zimmermann
G.
,
1966
, “
On Energy and Complementary Energy Formulations of the Acoustic and Structure Vibration Problems
,”
J. Sound Vib.
, Vol.
3
, pp.
233
–
241
.
12.
Henshell
D.
,
1975
, “
Crack Tip Finite Elements Are Unnecessary
,”
Int. J. Num. Methods Eng.
, Vol.
9
, pp.
495
–
507
.
13.
Ih
K. D.
, and
Lee
D. J.
,
1997
, “
Development of the Direct Boundary Element Method for Thin Bodies with General Boundary Conditions
,”
J. Sound Vib.
, Vol.
202
, pp.
361
–
373
.
14.
Joppa
P. D.
, and
Fyfe
I. M.
,
1978
, “
A Finite Element Analysis of the Impedance Properties of Irregular Shaped Cavities with Absorptive Boundaries
,”
J. Sound Vib.
, Vol.
56
, pp.
61
–
69
.
15.
Kagawa
Y.
,
Yamabuchi
T.
, and
Mori
A.
,
1977
, “
Finite Element Simulation of an Axisymmetric Acoustic Transmission System with a Sound Absorbing Wall
,”
J. Sound Vib.
, Vol.
53
, pp.
357
–
374
.
16.
Krishnasamy
G.
,
Rizzo
F. J.
, and
Liu
Y.
,
1994
, “
Boundary Integral Equations for Thin Bodies
,”
Int. J. Num. Methods Eng.
, Vol.
37
, pp.
107
–
121
.
17.
Leitner
A.
,
1949
, “
Diffraction of Sound by a Circular Disk
,”
J. Acoust. Soc. Am.
, Vol.
21
, pp.
331
–
334
.
18.
Lenoir
M.
, and
Jami
A.
,
1978
, “
A Variational Formulation for Exterior Problems in Linear Hydrodynamics
,”
Comp. Meth. App. Mech. Eng.
, Vol.
16
, pp.
341
–
359
.
19.
Li
H. B.
,
Han
G. M.
,
Mang
H. A.
, and
Torzicky
P.
,
1986
, “
A New Method for the Coupling of Finite Element and Boundary Element Discretized Subdomains of Elastic Bodies
,”
Comp. Meth. App. Mech. Eng.
, Vol.
54
, pp.
161
–
185
.
20.
Liu
Y.
, and
Rizzo
F. J.
,
1992
, “
A Weakly Singular Form of the Hypersingular Boundary Integral Equation Applied to 3-D Acoustic Wave Problems
,”
Comp. Meth. App. Mech. Eng.
, Vol.
96
, pp.
271
–
287
.
21.
Martinez
R.
,
1991
, “
The Thin-Shape Breakdown (TSB) of the Helmholtz Integral Equation
,”
J. Acoust. Soc. Am.
, Vol.
90
, pp.
2728
–
2738
.
22.
Melvyn
S. M.
,
1965
, “
A Finite Element Method Applied to the Vibration of Submerged Structures
,”
J. Ship Res.
, Vol.
9
, pp.
11
–
22
.
23.
Meyer
W. L.
,
Bell
W. A.
,
Zinn
B. T.
, and
Stallybrass
M. P.
,
1978
, “
Boundary Integral Solutions of Three Dimensional Acoustic Radiation Problems
,”
J. Sound Vib.
, Vol.
59
, pp.
245
–
262
.
24.
Norton, M. P., 1989, Fundamentals of Noise and Vibration Analysis for Engineers, Cambridge University Press, Cambridge.
25.
Petyt
M.
, and
Lim
S. P.
,
1978
, “
Finite Element Analysis of the Noise Inside a Mechanically Excited Cylinder
,”
Int. J. Num. Methods Eng.
, Vol.
13
, pp.
109
–
122
.
26.
Schenck
H. A.
,
1968
, “
Improved Integral Formulation for Acoustic Radiation Problems
,”
J. Acoust. Soc. Am.
, Vol.
44
, pp.
41
–
58
.
27.
Seybert
A. F.
,
Soenarko
B.
,
Rizzo
F. J.
, and
Shippy
D. J.
,
1985
“
An Advanced Computational Method for Radiation and Scattering of Acoustic Waves in Three Dimensions
,”
J. Acoust. Soc. Am.
, Vol.
77
, pp.
362
–
368
.
28.
Seybert
A. F.
,
Soenarko
B.
,
Rizzo
F. J.
, and
Shippy
D. J.
,
1986
, “
A Special Integral Equation Formulation for Acoustic Radiation and Scattering for Axisymmetric Bodies and Boundary Conditions
,”
J. Acoust. Soc. Am.
, Vol.
80
, pp.
1241
–
1247
.
29.
Spence
R. D.
, and
Granger
S.
,
1951
, “
The Scattering of Sound from a Prolate Spheroid
,”
J. Acoust. Soc. Am.
, Vol.
23
, pp.
701
–
706
.
30.
Terai
T.
,
1980
, “
On Calculation of Sound Field around Three Dimensional Objects by Integral Equation Methods
,”
J. Sound Vib.
, Vol.
69
, pp.
71
–
100
.
31.
Ting
L.
, and
Miksis
M. J.
,
1986
, “
Exact Boundary Conditions for Scattering Problems
,”
J. Acoust. Soc. Am.
, Vol.
80
, pp.
1825
–
1827
.
32.
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
.
33.
Wu
T. W.
, and
Wan
G. C.
,
1992
, “
Numerical Modeling of Acoustic Radiation and Scattering from Thin Bodies Using a Cauchy Principle Integral Equation
,”
J. Acoust. Soc. Am.
, Vol.
92
, pp.
2900
–
2906
.
This content is only available via PDF.
Copyright © 1999
 by The American Society of Mechanical Engineers
You do not currently have access to this content.