A general formulation to obtain the analytical expressions for the sensitivity of the acoustic power radiated by a vibrating structure to one of its design variables is described. The formulation, which is based on finite elements, is applied to both single frequency and broad band harmonic excitation of plates. The sensitivity coefficients indicate the effect of changing various design or modeling parameters on the acoustic power and can be used to optimize the structure for minimum sound radiation. Analytical sensitivity estimates are compared with finite difference values. Results show that analytical sensitivity analysis is important from both computational time and accuracy points of view.
Issue Section:
Research Papers
1.
Adelman
H. M.
Haftka
R. T.
1986
, “Sensitivity Analysis of Discrete Structural Systems
,” AIAA Journal
, Vol. 24
, No. 5
, pp. 823
–832
.2.
Belegundu, A. D., Salagame, R., Koopmann, G. H., and Naghshineh, K., 1993, “A General Optimization Approach for Minimizing Acoustic Power Using Finite Elements,” SAE International Congress, Detroit, MI.
3.
Bernhard
R. J.
1985
, “A Finite Element Method for Synthesis of Acoustical Shapes
,” Journal of Sound and Vibration
, Vol. 98
, No. 1
, pp. 55
–65
.4.
Cook, R. D., Malkus, D. S., and Plesha, M. E., 1989, Concepts and Applications of Finite Element Analysis, John Wiley and Sons, New York.
5.
Cunefare
K. A.
Koopmann
G. H.
1992
, “Acoustic Design Sensitivity for Structural Radiators
,” ASME JOURNAL OF VIBRATION AND ACOUSTICS
, Vol. 114
, No. 2
, pp. 178
–186
.6.
Ewins, D. J., 1984, Modal Testing Theory and Practice, Letchworth, Hertfordshire, England, Research studies Press, New York, Wiley.
7.
Fox
R. L.
Kapoor
1968
, “Rates of Change of Eigenvalues and Eigenvectors
,” AIAA Journal
, Vol. 6
, No. 12
, pp. 2426
–2429
.8.
Haftka
R. T.
Adelman
H. M.
1989
, “Recent Developments in Structural Sensitivity Analysis
,” Structural Optimization
, Vol. 1
, No. 3
, pp. 137
–151
.9.
Haftka, R. T., and Gurdal, Z., 1991, Elements of Structural Optimization, Kulwer Academic Publishers.
10.
Hughes, T. J. R., 1987, The Finite Element Method, Prentice-Hall Inc., Englewood Cliffs, NJ.
11.
Lamancusa
J. S.
1988
, “Geometric Optimization of Internal Combustion Engine Induction Systems for Minimum Noise Transmission
,” Journal of Sound and Vibration
, Vol. 127
, No. 2
, pp. 303
–318
.12.
Lamancusa, J. S., 1992, “Numerical Optimization Technical for Structural-Acoustic Design of Rectangular Panels,” Computers and Structures, in press.
13.
Naghshineh
K.
Koopmann
G. H.
Belegundu
A. D.
1992
, “Material Tailoring of Structures to Achieve a Minimum Radiation Conditions
,” Journal of Acoustical Society of America
, Vol. 92
, No. 2
, Pt. 1, pp. 841
–855
.14.
Nelson
R. B.
1976
, “Simplified Calculation of Eigenvalue Derivatives
,” AIAA Journal
, Vol. 14
, No. 9
, pp. 1201
–1205
.15.
Ojalvo
I. V.
1987
, “Efficient Computation of Mode Shape Derivatives for Large Dynamic Systems
,” AIAA Journal
, Vol. 25
, No. 10
, pp. 1386
–1390
.16.
Olhoff
N.
1974
, “Optimal Design of Vibrating Rectangular Plates
,” International Journal of Solids and Structures
, Vol. 10
, pp. 93
–109
.17.
Rayleigh, J. W. S., 1945, The Theory of Sound, reprinted by Dover, New York.
18.
Rudisill
C. S.
1974
, “Derivatives of Eigenvalues and Eigenvectors
,” AIAA Journal
, Vol. 12
, No. 5
, pp. 721
–722
.19.
Smith, D. C., and Bernhard, R. J., 1989, “Computing Acoustic Design Sensitivity Information Using Boundary Element Methods,” Proceedings of the Eleventh International Conference on Boundary Element Methods in Engineering, Cambridge, MA, Vol. 2 of 3, pp. 369–383.
20.
Smith, D. C., and Bernhard, R. J., 1989, “Computation of Acoustic Shape Design Sensitivity Using a Boundary Element Method,” Numerical Techniques in Acoustic Radiation, NCA-Vol. 6, R. J. Bernhard and R. F. Keltie, eds., The American Society of Mechanical Engineers, New York, pp. 109–116.
21.
Sutter
T. R.
Camarda
C. J.
Walsh
J. L.
Adelman
H. M.
1988
, “Comparison of Several Methods for Calculating Vibration Mode Shape Derivatives
,” AIAA Journal
, Vol. 26
, No. 12
, pp. 1506
–1511
.
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