Formulations are derived to analyze the relative panel acoustic contributions of a vibrating structure. The essence of this analysis is to correlate the acoustic power flow from each panel to the radiated acoustic pressure at any field point. The acoustic power is obtained by integrating the normal component of the surface acoustic intensity, which is the product of the surface acoustic pressure and normal surface velocity reconstructed by using the Helmholtz equation least squares based nearfield acoustical holography, over each panel. The significance of this methodology is that it enables one to analyze and rank relative acoustic contributions of individual panels of a complex vibrating structure to acoustic radiation anywhere in the field based on a single set of the acoustic pressures measured in the near field. Moreover, this approach is valid for both interior and exterior regions. Examples of using this method to analyze and rank the relative acoustic contributions of a scaled vehicle cabin are demonstrated.

1.
K.
Wyckaert
and
H.
van der Auweraer
, “
Operational analysis, transfer path analysis, modal analysis: Tools to understand road noise problems in cars
,” in
Proceedings of SAE Noise and Vibration Conference
(
1995
), pp.
139
143
.
2.
J.
Plunt
, “
Strategy for transfer path analysis (TPA) applied to vibro-acoustic systems at medium and high frequencies
,” paper presented at the International Seminar on Modal Analysis, Leuven, Belgium (September 16–18,
1999
).
3.
J.
Hald
,
C.
Blaabjerg
,
M.
Kimura
,
Y.
Ishii
,
M.
Tsuchiya
, and
H.
Ando
, “
Panel contribution analysis using a volume velocity source and a double layer array with the sonah algorithm
,”
Inter-Noise2006
, Honolulu, HI (December 3–6
,
2006
).
4.
O.
Wolff
, “
Fast panel noise contribution analysis using large PU sensor arrays
,”
Inter-Noise2007
, Istanbul, Turkey (August 28–31,
2007
).
5.
S. F.
Wu
, “
On reconstruction of acoustic pressure fields using the Helmholtz equation least squares method
,”
J. Acoust. Soc. Am.
107
,
2511
2522
(
2000
).
6.
E. G.
Williams
,
Fourier Acoustic: Sound Radiation and Nearfield Acoustical Holography
(
Academic Press
,
London
,
1999
), Chap. 3, pp.
89
93
.
7.
J. D.
Maynard
,
E. G.
Williams
, and
Y.
Lee
, “
Nearfield acoustic holography: I. Theory of generalized holography and the development of NAH
,”
J. Acoust. Soc. Am.
78
,
1395
1413
(
1985
).
8.
E. G.
Williams
,
B. H.
Houston
, and
P. C.
Herdic
, “
Fast Fourier transform and singular value decomposition formulations for patch nearfield acoustical holography
,”
J. Acoust. Soc. Am.
114
,
1322
1333
(
2003
).
9.
A.
Sarkissian
, “
Extension of measurement surface in near-field acoustic holography
,”
J. Acoust. Soc. Am.
115
,
1593
1596
(
2004
).
10.
M.
Lee
and
J. S.
Bolton
, “
Patch near-field acoustical holography in cylindrical geometry
,”
J. Acoust. Soc. Am.
118
,
3721
3732
(
2005
).
11.
M. R.
Bai
, “
Application of BEM (boundary element method)-based acoustic holography to radiation analysis of sound sources with arbitrary shaped geometries
,”
J. Acoust. Soc. Am.
92
,
533
549
(
1992
).
12.
B.-K.
Kim
and
J.-G.
Ih
, “
On the reconstruction of vibro-acoustic field over the surface enclosing an interior space using the boundary element method
,”
J. Acoust. Soc. Am.
100
,
3030
3016
(
1996
).
13.
Z.
Zhang
,
N.
Vlahopoulos
,
S. T.
Raveendra
,
T.
Allen
, and
K. Y.
Zhang
, “
A computational acoustic field reconstruction process based on an indirect boundary element formulation
,”
J. Acoust. Soc. Am.
108
,
2167
2178
(
2000
).
14.
S. F.
Wu
and
X.
Zhao
, “
Combined Helmholtz equation least squares (CHELS) method for reconstructing acoustic radiation
,”
J. Acoust. Soc. Am.
112
,
179
188
(
2002
).
15.
N.
Valdivia
and
E. G.
Williams
, “
Implicit methods of solution to integral formulations in boundary element method based nearfield acoustic holography
,”
J. Acoust. Soc. Am.
116
,
1559
1573
(
2004
).
16.
S. F.
Wu
, “
Methods for reconstructing acoustic quantities based on acoustic pressure measurements
,”
J. Acoust. Soc. Am.
124
,
2680
2697
(
2008
).
17.
V.
Isakov
and
S. F.
Wu
, “
On theory and applications of the HELS method in inverse acoustics
,”
Inverse Probl.
18
,
1147
1159
(
2002
).
18.
G. V.
Borgiotti
,
A.
Sarkissian
,
E. G.
Williams
, and
L.
Schuetz
, “
Conformal generalized near-field acoustic holography for axisymmetric geometries
,”
J. Acoust. Soc. Am.
88
,
199
209
(
1990
).
19.
A. N.
Tikhonov
and
V. Y.
Arsenin
,
Solutions of Ill-Posed Problems
(
Wiley
,
New York
,
1977
), pp.
71
73
.
20.
P. C.
Hansen
, “
Rank-deficient and discrete ill-posed problems
” [SIAM (Society for Industrial and Applied Mathematics), Philadelphia, PA,
1998
], Chap. 4, pp.
83
87
; Chap. 5, pp. 109–114.
21.
X.
Zhao
and
S. F.
Wu
, “
Reconstruction of the vibro-acoustic fields using hybrid nearfield acoustical holography
,”
J. Sound Vib.
282
,
1183
1199
(
2005
).
22.
E. G.
Williams
, “
Regularization methods for near-field acoustic holography
,”
J. Acoust. Soc. Am.
110
,
1976
1988
(
2001
).
23.
G. H.
Golub
,
M.
Heath
, and
G.
Wahba
, “
Generalized cross-validation as a method for choosing a good ridge parameter
,”
Technometrics
21
,
215
223
(
1979
).
24.
L. K.
Natarajan
and
S. F.
Wu
, “
Reconstruction of normal surface velocities on a baffled plate using Helmholtz equation least squares method
,”
J. Acoust. Soc. Am.
131
,
4570
4583
(
2012
).
25.
A.
Leissa
,
Vibration of Plates
(
Acoustical Society of America
,
New York
,
1973
), Chap. 4, pp.
41
45
.
26.
E. G.
Williams
,
B. H.
Houston
,
P. C.
Herdic
,
S. T.
Raveendra
, and
B.
Gardner
, “
Interior nearfield acoustical holography in flight
,”
J. Acoust. Soc. Am.
108
,
1451
1463
(
2000
).
You do not currently have access to this content.