In this paper a method for the parametric sensitivity of acoustic-structural coupled systems is presented. The symmetrical Eulerian formulation is applied in order to calculate the coupled frequencies and modes. From a state space formulation of the problem a sensitivity algorithm is developed to obtain the derivatives of the coupled frequencies and modes of the system versus a design parameter vector. The algorithm is based on the properties of the complex conjugate eigenvalues obtained from the solution of the state space equation. Numerical examples from an acoustic rectangular cavity backed by a simply supported plate are presented. The comparison reveals a good agreement between numerical and analytical results. [S0739-3717(00)00802-3]
Issue Section:
Technical Papers
1.
Lyon
, H.
, 1963
, “Noise Reduction in Rectangular Enclosures with One Flexible Wall
,” J. Acoust. Soc. Am.
, 35
, pp. 1791
–1797
.2.
Pretlove
, J.
, 1965
, “Free Vibration of a Rectangular Panel Backed by a Closed Cavity
,” J. Sound Vib.
, 2
, pp. 197
–209
.3.
Cura`
, F.
, Curti
, G.
, and Mantovani
, M.
, 1996
, “Study of the Forced Response of a Clamped Circular Plate Coupled to a Uni-dimensional Acoustic Cavity
,” J. Sound Vib.
, 190
, No. 4
, pp. 661
–676
.4.
Craggs
, A.
, 1971
, “The Transient Response of a Coupled Plate-acoustic System Using Plate and Acoustic Finite Elements
,” J. Sound Vib.
, 15
, pp. 509
–528
.5.
Petyt
, M.
, Lea
, J.
, and Koopman
, G. H.
, 1976
, “A Finite Element Method for Determining the Acoustic Modes of Irregular
,” J. Sound Vib.
, 45
, pp. 495
–502
.6.
Nefske
, D. J.
, Wolf
, Jr., 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
, No. 2
, pp. 247
–266
.7.
Wolf
, Jr., J. A.
, 1977
, “Modal Synthesis for Combined Structural-acoustic Systems
,” Am. Inst. Aeronaut. Astronaut.
, 15
, No. 5
, pp. 743
–745
.8.
Sung
, S. H.
, and Nefske
, D. J.
, 1986
, “Component Mode Synthesis of a Vehicle Structural-acoustic System Model
,” Am. Inst. Aeronaut. Astronaut.
, 24
, No. 8
, pp. 1021
–1026
.9.
Luo
, J.
, and Gea
, H. C.
, 1997
, “Modal Sensitivity Analysis of Coupled Acoustic-structural Systems
,” ASME J. Vibr. Acoust.
, 119
, pp. 545
–550
.10.
Dowell
, E. H.
, Gorman
, III, G. F.
, and Smith
, D. A.
, 1977
, “Acoustoelasticity: General Theory, Acoustic Natural Modes and Forced Response to Sinusoidal Excitation, Including Comparisons with Experiment
,” J. Sound Vib.
, 54
, No. 4
, pp. 519
–542
.11.
Guy
, R. W.
, and Bhattacharya
, M. C.
, 1973
, “The Transmission of Sound Through a Cavity-backed Finite Plate
,” J. Sound Vib.
, 27
, pp. 207
–223
.12.
Pan
, J.
, and Bies
, D. A.
, 1990
, “The Effect of Fluid-structural Coupling on Sound Waves in an Enclosure—Theoretical Part
,” J. Acoust. Soc. Am.
, 87
, No. 2
, pp. 691
–707
.13.
Everstine
, G. C.
, 1981
, “A Symmetric Potential Formulation for Fluid-structure Interaction
,” J. Sound Vib.
, 79
, No. 1
, pp. 157
–160
.14.
Bokil
, V. B.
, and Shirahatti
, U. S.
, 1994
, “A Technique for the Modal Analysis of Sound-structure Interaction Problems
,” J. Sound Vib.
, 173
, No. 1
, pp. 23
–41
.15.
Meirovitch
, L.
, 1974
, “A New Method of Solution of the Eigenvalue Problem for Gyroscopic Systems
,” Am. Inst. Aeronaut. Astronaut.
, 12
, pp. 1337
–1342
.16.
Fox
, R. L.
, and Kapoor
, M. P.
, 1968
, “Rates of Change of Eigenvalues and Eigenvectors
,” Am. Inst. Aeronaut. Astronaut.
, 6
, No. 12
, pp. 2426
–2429
.17.
Rogers
, L. C.
, 1970
, “Derivatives of Eigenvalues and Eigenvectors
,” Am. Inst. Aeronaut. Astronaut.
, 8
, pp. 943
–944
.18.
Nelson
, R. B.
, 1976
, “Simplified Calculations of Eigenvector Derivatives
,” Am. Inst. Aeronaut. Astronaut.
, 14
, No. 9
, pp. 1201
–1205
.19.
Wang
, B. P.
, and Caldwell
, S. P.
, 1993
, “An Improved Approximate Method for Computing Eigenvector Derivatives
,” Finite Elem. Anal. Design
, 14
, No. 4
, pp. 381
–392
.20.
Smith
, D. C.
, and Bernhard
, R. J.
, 1992
, “Computation of Acoustic Shape Design Sensitivity Using a Boundary Element Method
,” ASME J. Vibr. Acoust.
, 114
, No. 1
, pp. 127
–132
.21.
Salagame
, R. R.
, Belagundu
, A. D.
, and Koopman
, G. H.
, 1995
, “Analytical Sensitivity of Acoustic Power Radiated from Plates
,” ASME J. Vibr. Acoust.
, 114
, No. 2
, pp. 178
–186
.22.
Ma
, Z. D.
, and Hagiwara
, I.
, 1991
, “Sensitivity Analysis Methods for Coupled Acoustic-structural Systems, Part I: Modal Sensitivities
,” Am. Inst. Aeronaut. Astronaut.
, 29
, No. 11
, pp. 1787
–1795
.23.
Scarpa
, F.
, and Curti
, G.
, 1999
, “A Method for the Parametric Sensitivity of Interior Acousto-structural Coupled Systems
,” Appl. Acoust.
, 58
, No. 4
, pp. 451
–467
.24.
Seiranyan
, A.
, and Sharanyuk
, A. V.
, 1987
, “Sensitivity Analysis of Vibrational Frequencies of Mechanical Systems
,” Mechanics of Solids
, 22
, No. 2
, pp. 37
–41
.25.
Kim
, Y.
, Lee
, S.
, and Junkins
, J. L.
, 1995
, “Eigenvector Derivatives for Mechanical Second Order Systems
,” J. Guid. Control. Dyn.
, 18
, No. 4
, pp. 899
–906
.26.
Wilkinson, J. H., The Algebraic Eigenvalue Problem, Oxford University Press, New York, 1965, Chap. 2.
27.
Soedel, W., Vibration of Plates and Shells, Marcel Dekker, New York, 1981, Chap. 3.
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