Modal analysis of coupled acoustic-structural systems leads to unsymmetric eigenproblem of special form which introduce different left and right eigenvectors. In this paper, the relation between left and right eigenvectors is first established by symmetrization of the unsymmetric eigensystem, and then Nelson’s method is extended to coupled acoustic-structural systems for calculating the sensitivities of the eigenvalues and eigenvectors. The method only needs to calculate the sensitivities of the right eigenvectors and can treat the Helmholtz resonance mode naturally. Numerical examples of an acoustic box model solved by the proposed approach are compared with finite difference approach and good agreement is noted.

1.
Gladwell
G. M. L.
, and
Zimmermann
G.
,
1966
, “
On Energy and Complementary Energy Formulations of Acoustic and Structural Vibration Problems
,”
Journal of Sound and Vibration
, Vol.
3
, No.
3
, pp.
233
241
.
2.
Craggs
A.
,
1971
, “
The Transient Response of a Coupled Plate-Acoustic System Using Plate and Acoustic Finite Elements
,”
Journal of Sound and Vibration
, Vol.
15
, No.
4
, pp.
509
528
.
3.
Petyt
M.
,
Lea
J.
, and
Koopmann
G. H.
,
1976
, “
A Finite Element Method for Determining Acoustic Modes of Irregular Shape Cavities
,”
Journal of Sound and Vibration
, Vol.
45
, pp.
495
502
.
4.
Nefske
D. J.
,
Wolf
J. A.
, and
Howell
L. J.
,
1982
, “
Structural-Acoustic Finite Element Analysis of the Automobile Passenger Compartment: A Review of Current Practice
,”
Journal of Sound and Vibration
, Vol.
80
, No.
2
, pp.
247
266
.
5.
Goswami
P.
,
Rizzo
F. J.
, and
Shippy
D. J.
,
1987
, “
Acoustic Scattering by Elastic Solids Using the Boundary Element Method
,”
Review Quantitative Non-destruct, Eval
, Vol.
7
, pp.
95
102
.
6.
Smith
D. C.
, and
Bernhard
R. J.
,
1992
, “
Computation of Acoustic Shape Design Sensitivity Using a Boundary Element Method
,”
ASME JOURNAL OF VIBRATION AND ACOUSTICS
, Vol.
114
, No.
1
, pp.
127
132
.
7.
Cunefare
K. A.
, and
Koopmann
G. H.
,
1992
, “
Acoustic Design Sensitivity for Structural Radiators
,”
ASME JOURNAL OF VIBRATION AND ACOUSTICS
, Vol.
114
, No.
2
, pp.
178
186
.
8.
Salagame
R. R.
,
Belagundu
A. D.
, and
Koopmann
G. H.
,
1995
, “
Analytical Sensitivity of Acoustic Power Radiated from Plates
,”
ASME JOURNAL OF VIBRATION AND ACOUSTICS
, Vol.
117
, No.
1
, pp.
43
48
.
9.
Sutter
T. R.
,
Camarda
C. J.
,
Walsh
J. L.
, and
Adelman
H. M.
,
1988
, “
Comparison of Several Methods for Calculating Vibration Mode Shape Derivatives
,”
American Institute of Aeronautics and Astronautics Journal
, Vol.
26
, No.
12
, pp.
1506
1511
.
10.
Fox
R. L.
, and
Kapoor
M. P.
,
1978
, “
Rates of Change of Eigenvalues and Eigenvectors
,”
American Institute of Aeronautics and Astronautics Journal
, Vol.
6
, No.
12
, pp.
2426
2429
.
11.
Wang
B. P.
, and
Caldwell
S. P.
1993
, “
An Improved Approximate Method for Computing Eigenvector Derivatives
,”
Finite Elements in Analysis and Design
, Vol.
14
, No.
4
, pp.
381
392
.
12.
Nelson
R. B.
,
1976
, “
Simplified Calculation of Eigenvector Derivatives
,”
American Institute of Aeronautics and Astronautics Journal
, Vol.
14
, No.
9
, pp.
1201
1205
.
13.
Aria, A., Hagiwara, I., and Nagabuchi, T., 1988, “Sensitivity Analysis of Vehicle Interior Vibration and Noise,” Proceedings of Symposium on Computational Methods in Structural Engineering and Related Fields, Vol. 12, pp. 545–550.
14.
Ma
Z. D.
, and
Hagiwara
I.
,
1991
, “
Sensitivity Analysis Methods for Coupled Acoustic-Structural Systems, Part I: Modal Sensitivities
,”
American Institute of Aeronautics and Astronautics Journal
, Vol.
29
, No.
11
, pp.
1787
1795
.
15.
Wolf
J. A.
,
1977
, “
Modal Synthesis for Combined Structural-Acoustic Systems
,”
American Institute of Aeronautics and Astronautics Journal
, Vol.
15
, No.
5
, pp.
743
745
.
This content is only available via PDF.
You do not currently have access to this content.