A modal decomposition technique to analyze individual modal contributions to the sound power radiated from an externally excited structure submerged in a heavy fluid is presented. The fluid-loaded structural modes are calculated by means of a polynomial approximation and symmetric linearization of the underlying nonlinear eigenvalue problem. The eigenvalues and eigenfunctions of a fluid loaded sphere with and without internal structures are presented. The modal sound power contributions using both fluid-loaded structural modes and acoustic radiation modes are presented. The results for the resistive and reactive sound power obtained from the superposition of the individual modal sound power contributions are compared to the harmonic solution of the forced problem.

1.
Templates for the Solution of Algebraic Eigenvalue Problems: A Practical Guide
, edited by
Z.
Bai
,
J.
Demmel
,
J.
Dongarra
,
A.
Ruhe
, and
H.
van der Vorst
(
SIAM
,
Philadelphia, PA
,
2000
), pp.
1
410
.
2.
B.
Cazzolato
, “
Sensing systems for active control of sound transmission into cavities
,” Ph.D. thesis,
The University of Adelaide
, Adelaide, SA, Australia,
1999
.
3.
S.
Marburg
, “
Normal modes in external acoustics. Part III: Sound power evaluation based on superposition of frequency-independent modes
,”
Acta Acust. Acust.
92
(2
),
296
311
(
2006
).
4.
M.
Petyt
,
J.
Lea
, and
G.
Koopmann
, “
A finite element method for determining the acoustic modes of irregular shaped cavities
,”
J. Sound Vib.
45
(
4
),
495
502
(
1976
).
5.
D.
Nefske
,
A.
Wolf
, Jr.
, and
L.
Howell
, “
Structural-acoustic finite element analysis of the automobile passenger compartment: A review of current practice
,”
J. Sound Vib.
80
(
2
),
247
266
(
1982
).
6.
P.
Banerjee
,
S.
Ahmad
, and
H.
Wang
, “
A new BEM formulation for the acoustic eigenfrequency analysis
,”
Int. J. Numer. Methods Eng.
26
(
2
),
1299
1309
(
1988
).
7.
E.
de Mesquita Neto
,
E. R.
Carvalho
,
J.
de Franca Arruda
, and
R.
Pavanello
, “
Acoustic eigenvalue analysis by boundary element methods
,” in
Boundary Element Acoustics
(
WIT
,
Southampton, UK
,
2000
), pp.
117
158
.
8.
S.
Hein
,
T.
Hohage
, and
W.
Koch
, “
On resonances in open systems
,”
J. Fluid Mech.
506
,
255
284
(
2004
).
9.
W.
Koch
, “
Acoustic resonances in rectangular open cavities
,”
AIAA J.
43
(
11
),
2342
2349
(
2005
).
10.
S.
Kirkup
and
S.
Amini
, “
Solution of the Helmholtz eigenvalue problem via the boundary element method
,”
Int. J. Numer. Methods Eng.
36
(
2
),
321
330
(
1993
).
11.
A.
Ali
,
C.
Rajakumar
, and
S.
Yunus
, “
Advances in acoustic eigenvalue analysis using boundary element method
,”
Comput. Struct.
56
(
5
),
837
847
(
1995
).
12.
L.
Thompson
, “
A review of finite-element methods for time-harmonic acoustics
,”
J. Acoust. Soc. Am.
119
,
1315
1330
(
2006
).
13.
Computational Acoustics of Noise Propagation in Fluids
, edited by
S.
Marburg
and
B.
Nolte
(
Springer
,
Berlin
,
2008
), pp.
1
578
.
14.
J.
Giordano
and
G.
Koopmann
, “
State-space boundary element-finite element coupling for fluid-structure interaction analysis
,”
J. Acoust. Soc. Am.
98
(
1
),
363
372
(
1995
).
15.
K.
Cunefare
and
S.
de Rosa
, “
An improved state-space method for coupled fluid-structure interaction analysis
,”
J. Acoust. Soc. Am.
105
,
206
210
(
1999
).
16.
S.
Li
, “
A state-space coupling method for fluid-structure interaction analysis of plates
,”
J. Acoust. Soc. Am.
118
(
2
),
800
805
(
2005
).
17.
D.
Mackey
,
N.
Mackey
,
C.
Mehl
, and
V.
Mehrmann
, “
Vector spaces of linearizations for matrix polynomials
,”
SIAM J. Matrix Anal. Appl.
28
(
4
),
971
1004
(
2006
).
18.
N.
Higham
,
D.
Mackey
, and
F.
Tisseur
, “
The conditioning of linearizations of matrix polynomials
,”
SIAM J. Matrix Anal. Appl.
28
(
4
),
1005
1028
(
2006
).
19.
E.
Antoniou
and
S.
Vologiannidis
, “
A new family of companion forms of polynomial matrices
,”
Electron. J. Linear Algebra
11
,
78
87
(
2004
).
20.
N.
Higham
,
D.
Mackey
,
N.
Mackey
, and
F.
Tisseur
, “
Symmetric linearizations for matrix polynomials
,”
SIAM J. Matrix Anal. Appl.
29
,
143
159
(
2006
).
21.
D.
Mackey
,
N.
Mackey
,
C.
Mehl
, and
V.
Mehrmann
, “
Structured polynomial eigenvalue problems: Good vibrations from good linearizations
,”
SIAM J. Matrix Anal. Appl.
28
(
4
),
1029
1051
(
2006
).
22.
V.
Mehrmann
and
H.
Voss
, “
Nonlinear eigenvalue problems: A challenge for modern eigenvalue methods
,”
GAMM Mitt.
27
,
121
152
(
2004
).
23.
H.
Voss
, “
A Jacobi-Davidson method for nonlinear and nonsymmetric eigenproblems
,”
Comput. Struct.
85
(
17–18
),
1284
1292
(
2007
).
24.
K. A.
Cunefare
and
M. N.
Currey
, “
On the exterior acoustic radiation modes of structures
,”
J. Acoust. Soc. Am.
96
,
2302
2312
(
1994
).
25.
P. T.
Chen
and
J. H.
Ginsberg
, “
Complex power, reciprocity, and radiation modes for submerged bodies
.”
J. Acoust. Soc. Am.
98
,
3343
3351
(
1995
).
26.
B.
Flemisch
,
M.
Kaltenbacher
, and
B.
Wohlmuth
, “
Elasto-acoustic and acoustic-acoustic coupling on nonmatching grids
,”
Int. J. Numer. Methods Eng.
67
,
1791
1810
(
2006
).
27.
H.
Peters
,
S.
Marburg
, and
N.
Kessissoglou
, “
Structural-acoustic coupling on non-conforming meshes with quadratic shape functions
,”
Int. J. Numer. Methods Eng.
91
(
1
),
27
38
(
2012
).
28.
K. A.
Cunefare
,
M. N.
Currey
,
M. E.
Johnson
, and
S. J.
Elliot
, “
The radiation efficiency grouping of free-space acoustic radiation modes
,”
J. Acoust. Soc. Am.
109
,
203
215
(
2001
).
29.
E.
Antoniou
and
S.
Vologiannidis
, “
Linearizations of polynomial matrices with symmetries and their applications
,”
Electron. J. Linear Algebra
15
,
107
114
(
2006
).
30.
F.
Tisseur
and
K.
Meerbergen
, “
The quadratic eigenvalue problem
,”
SIAM Rev.
43
(
2
),
235
286
(
2001
).
31.
N.
Karampetakis
, “
Matrix pencil equivalents of symmetric polynomial matrices
,”
Asian J. Control
12
(
2
),
177
186
(
2010
).
32.
R.
Lehoucq
,
D.
Sorensen
, and
C.
Yang
,
ARPACK Users' Guide: Solution of Large Scale Eigenvalue Problems with Implicitly Restarted Arnoldi Methods
(
SIAM
,
Philadelphia, PA
,
1998
), pp.
1
142
.
33.
M.
Baruch
and
I.
Bar-Itzhack
, “
Optimal weighted orthogonalization of measured modes
,”
AIAA J.
16
,
345
351
(
1978
).
34.
H.
Peters
,
S.
Marburg
, and
N.
Kessissoglou
, “
Enforcing reciprocity in numerical analysis of acoustic radiation modes and sound power evaluation
,”
J. Comput. Acoust.
20
,
1250005
(
2012
).
35.
M.
Junger
and
D.
Feit
,
Sound, Structures, and Their Interaction
, 2nd ed. (
MIT Press
,
Cambridge, MA
,
1986
), pp.
279
312
.
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