A noise-vibration-harshness (NVH) design optimization of a complex vehicle structure is presented using finite element and boundary element analyses. The steady-state dynamic behavior of the vehicle is calculated from the frequency response finite element analysis, while the sound pressure level within the acoustic cavity is calculated from the boundary element analysis. A reverse solution process is employed for the design sensitivity calculation using the adjoint variable method. The adjoint load is obtained from the acoustic boundary element re-analysis, while the adjoint solution is calculated from the structural dynamic re-analysis. The evaluation of pressure sensitivity only involves a numerical integration process over the structural part where the design variable is defined. A design optimization problem is formulated and solved, where the structural weight is reduced while the noise level in the passenger compartment is lowered.

Issue Section:
Technical Papers
Keywords:
structural acoustics, road vehicles, integration, mechanical engineering computing, noise abatement, finite element analysis, boundary-elements methods, frequency response, design engineering
Topics:
Acoustics, Design, Finite element analysis, Optimization, Vehicles, Frequency response, Sound pressure, Boundary element methods
1.
Hughes, T. J. R., 1987, The Finite Element Method, Prentice-Hall, Englewood Cliffs, NJ.
2.
Kythe, P. K., 1995, Introduction to Boundary Element Methods, CRS Press, Florida.
3.
Lyon, R., 1975, Statistical Energy Analysis of Dynamical Systems: Theory and Application, The MIT Press, Cambridge, MA.
4.
Rybak
,
S. A.
,
1972
, “
Waves in Plate Containing Random Inhomogeneities
,”
Sov. Phys. Acoust.
,
17
(
3
), pp.
345
–
349
.
5.
Nefske
,
D. J.
, and
Sung
,
S. H.
,
1989
, “
Power Flow Finite-Element Analysis of Dynamic-Systems—Basic Theory and Application to Beams
,”
ASME J. Vibr., Acoust., Stress, Reliab. Des.
,
111
(
1
), pp.
94
–
100
.
6.
Bernhard
,
R. J.
, and
Huff
,
J. E.
,
1999
, “
Structural-Acoustic Design at High Frequency Using the Energy Finite Element Method
,”
ASME J. Vibr. Acoust.
,
121
(
3
), pp.
295
–
301
.
7.
Vlahopoulos
,
N.
,
Garza-Rios
,
L. O.
, and
Mollo
,
C.
,
1999
, “
Numerical Implementation, Validation, and Marine Applications of an Energy Finite Element Formulation
,”
J. Ship Res.
,
43
(
3
), pp.
143
–
156
.
8.
Gockel, M. A., 1983, MSC/NASTRAN Handbook for Dynamic Analysis, The MacNeal-Schwendler Corporation, 815 Colorado Blvd., Los Angeles, CA.
9.
COMET/ACOUSTICS User’s Manual, Automated Analysis Corporation.
10.
Ma
,
Z.-D.
, and
Hagiwara
,
I.
,
1991
, “
Sensitivity Analysis-Method for Coupled Acoustic-Structural Systems Part 2: Direct Frequency-Response and Its Sensitivities
,”
AIAA J.
,
29
, pp.
1796
–
1801
.
11.
Choi
,
K. K.
,
Shim
,
I.
, and
Wang
,
S.
,
1997
, “
Design Sensitivity Analysis of Structure-Induced Noise and Vibration
,”
ASME J. Vibr. Acoust.
,
119
, pp.
173
–
179
.
12.
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
,”
J. Sound Vib.
,
80
, pp.
247
–
266
.
13.
Salagame
,
R. R.
,
Belegundu
,
A. D.
, and
Koopman
,
G. H.
,
1995
, “
Analytical Sensitivity of Acoustic Power Radiated From Plates
,”
ASME J. Vibr. Acoust.
,
117
, pp.
43
–
48
.
14.
Scarpa
,
F.
,
2000
, “
Parametric Sensitivity Analysis of Coupled Acoustic-Structural Systems
,”
ASME J. Vibr. Acoust.
,
122
, pp.
109
–
115
.
15.
Smith
,
D. C.
, and
Bernhard
,
R. J.
,
1992
, “
Computation of Acoustic Shape Design Sensitivity Using a Boundary Element Method
,”
ASME J. Vibr. Acoust.
,
114
, pp.
127
–
132
.
16.
Cunefare
,
K. A.
, and
Koopman
,
G. H.
,
1992
, “
Acoustic Design Sensitivity for Structural Radiators
,”
ASME J. Vibr. Acoust.
,
114
, pp.
179
–
186
.
17.
Kane
,
J. H.
,
Mao
,
S.
, and
Everstine
,
G. C.
,
1991
, “
Boundary Element Formulation for Acoustic Shape Sensitivity Analysis
,”
J. Acoust. Soc. Am.
,
90
, pp.
561
–
573
.
18.
Matsumoto
,
T.
,
Tanaka
,
M.
, and
Yamada
,
Y.
,
1995
, “
Design Sensitivity Analysis of Steady-State Acoustic Problems Using Boundary Integral Equation Formulation
,”
JSME Int. J., Ser. C
,
38
, pp.
9
–
16
.
19.
Kim
,
N. H.
,
Dong
,
J.
,
Choi
,
K. K.
,
Vlahopoulos
,
N.
,
Ma
,
Z.-D.
,
Castanier
,
M. P.
, and
Pierre
,
C.
,
2003
, “
Design Sensitivity Analysis for Sequential Structural-Acoustic Problems
,”
J. Sound Vib.
,
26
(
33
), June, pp.
569
–
591
.
20.
Kim, N. H., Choi, K. K., Dong, J., Pierre, C., Vlahopoulos, N., Ma, Z.-D., and Castanier, M., 2001, “A Sequential Adjoint Variable Method in Design Sensitivity Analysis of NVH Problems,” ASME International Mechanical Engineering Congress and Exposition (IMECE’01), November 11–16, New York, NY.
21.
Chang
,
K. H.
,
Choi
,
K. K.
,
Tsai
,
C. S.
,
Chen
,
C. J.
,
Choi
,
B. S.
, and
Yu
,
X.
,
1995
, “
Design Sensitivity Analysis and Optimization Tool (DSO) for Shape Design Applications
,”
Computing Systems in Engineering
,
6
(
2
), pp.
151
–
175
.
22.
Vanderplaats, G. N., 1997, DOT User’s Manual, VMA Corp., Colorado Springs, CO.
23.
Horvath, J., 1966, Topological Vector Spaces and Distributions, Addison-Wesley, London.
24.
Dimarogonas, A. D., 1976, Vibration Engineering, West Publishing Co., St. Paul, MN.
Copyright © 2004
 by ASME
You do not currently have access to this content.