Archives of Computational Methods in Engineering

, Volume 9, Issue 4, pp 291–370 | Cite as

Developments in structural-acoustic optimization for passive noise control

  • Steffen Marburg


Low noise constructions receive more and more attention in highly industrialized countries. Consequently, decrease of noise radiation challenges a growing community of engineers. One of the most efficient techniques for finding quiet structures consists in numerical optimization. Herein, we consider structural-acoustic optimization understood as an (iterative) minimum search of a specified objective (or cost) function by modifying certain design variables. Obviously, a coupled problem must be solved to evaluate the objective function. In this paper, we will start with a review of structural and acoustic analysis techniques using numerical methods like the finite- and/or the boundary-element method. This is followed by a survey of techniques for structural-acoustic coupling. We will then discuss objective functions. Often, the average sound pressure at one or a few points in a frequency interval accounts for the objective function for interior problems, wheareas the average sound power is mostly used for external problems. The analysis part will be completed by review of sensitivity analysis and special techniques. We will then discuss applications of structural-acoustic optimization. Starting with a review of related work in pure structural optimization and in pure acoustic optimization, we will categorize the problems of optimization in structural acoustics. A suitable distinction consists in academic and more applied examples. Academic examples iclude simple structures like beams, rectangular or circular plates and boxes; real industrial applications consider problems like that of a fuselage, bells, loudspeaker diaphragms and components of vehicle structures. Various different types of variables are used as design parameters. Quite often, locally defined plate or shell thickness or discrete point masses are chosen. Furthermore, all kinds of structural material parameters, beam cross sections, spring characteristics and shell geometry account for suitable design modifications. This is followed by a listing of constraints that have been applied. After that, we will discuss strategies of optimization. Starting with a formulation of the optimization problem we review aspects of multiobjective optimization, approximation concepts and optimization methods in general. In a final chapter, results are categorized and discussed. Very often, quite large decreases of noise radiation have been reported. However, even small gains should be highly appreciated in some cases of certain support conditions, complexity of simulation, model and large frequency ranges. Optimization outcomes are categorized with respect to objective functions, optimization methods, variables and groups of problems, the latter with particular focus on industrial applications. More specifically, a close-up look at vehicle panel shell geometry optimization is presented. Review of results is completed with a section on experimental validation of optimization gains. The conclusions bring together a number of open problems in the field.


Sound Pressure Sound Pressure Level Acoustical Society Sound Power Interior Noise 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    S. J. Abspoel, L. F. P. Etman, J. Vervoort, R. A. van Rooij, A. J. G. Schoofs, and J. E. Rooda (2001). Simulation based optimization of stochastic systems with integer design variables by sequential multipoint linear approximation,Structural and Multidisciplinary Optimization,22, 125–138.CrossRefGoogle Scholar
  2. 2.
    H. M. Adelman and R. T. Haftka (1986). Sensitivities for discrete structural systems,AIAA Journal,24, 823–832.CrossRefGoogle Scholar
  3. 3.
    R. A. Adey, S. M. Niku, J. Baynham, and P. Burns (1995). Predicting acoustic contributions and sensitivity, application to vehicle structures. In C. A. Brebbia (ed),Computational Acoustics and its Environmental Applications, pages 181–188. Computational Mechanics Publications.Google Scholar
  4. 4.
    S. Ahmad and P. K. Banerjee (1986). Free vibration analysis by BEM using particular integrals.ASCE Journal Engineering Mechanics,112, 682–695.CrossRefGoogle Scholar
  5. 5.
    A. Ali, C. Rajakumar, and S. M. Yunus (1995). Advances in acoustic eigenvalue analysis using boundary element method.Computers and Structures,56(5), 837–847.zbMATHCrossRefGoogle Scholar
  6. 6.
    S. Amini, C. Ke, and P. J. Harris (1990). Iterative solution of boundary element equations for the exterior helmholtz problem.Journal of Vibration and Acoustics,112, 257–262. April.CrossRefGoogle Scholar
  7. 7.
    S. Amini and N. D. Maines (1998). Preconditioned Krylov subspace methods for boundary element solution of the Helmholtz equation,International Journal for Numerical Methods in Engineering,41, 875–898.zbMATHMathSciNetCrossRefGoogle Scholar
  8. 8.
    M. A. Arslan and P. Hajela (2001). Use of counterpropagation neural networks to enhance the concurrent subspace optimization strategy.Engineering Optimization,33, 327–349.CrossRefGoogle Scholar
  9. 9.
    R. J. Astley (1987). A comparative note on the effects of local versus bulk reaction models for air moving ducts lined on all sides.Journal of Sound and Vibration,117(1), 191–197.CrossRefGoogle Scholar
  10. 10.
    R. J. Astley (1998). Finite elements in acoustics. InSound and Silence: Setting the Balance—Proceedings of the INTERNOISE 98, volume 1, pages 3–17, Christchurch. New Zealand Acoustical Society Inc.Google Scholar
  11. 11.
    R. J. Astley (1998). Mapped spheroidal elements for unbounded wave problems.International Journal for Numerical Methods in Engineering,41, 1235–1254.zbMATHMathSciNetCrossRefGoogle Scholar
  12. 12.
    R. J. Astley, J.-P. Coyette, and L. Cremes (1998). Three dimensional wave envelope elements of variable order for acoustical radiation and scattering. Part ii: Formulation in the time domain.Journal of the Acoustical Society of America,103, 64–72.CrossRefGoogle Scholar
  13. 13.
    R. J. Astley and A. Cummings (1987). A finite element scheme for attenuation in ducts lined with porous material: Comparison, with experiment,Journal of Sound and Vibration,116, 239–263.Google Scholar
  14. 14.
    R. J. Astley, G. J. Macaulay, and J.-P. Coyette (1994). Mapped wave envelope elements for acoustical radiation and scattering,Journal of Sound and Vibration,170, 97–118.zbMATHCrossRefGoogle Scholar
  15. 15.
    R. J. Astley, G. J. Macaulay, J.-P. Coyette, and L. Cremers (1998). Three dimensional wave envelope elements of variable order for acoustical radiation and scattering. Part i: Formulation in the frequency domain.Journal of the Acoustical Society of America,103, 49–63.CrossRefGoogle Scholar
  16. 16.
    T. W. Athan and P. Y. Papalambros (1996). A note on weighted criteria methods for compromise solutions in multi-objective optimization.Engineering Optimization,27, 155–176.CrossRefGoogle Scholar
  17. 17.
    K. E. Atkinson (1997).The Numerical Solution of Integral Equations of the Second Kind. Cambridge University Press, 1st edition.Google Scholar
  18. 18.
    T. Back (1996).Evolutionary algorithms in theory and practice. Oxford University Press.Google Scholar
  19. 19.
    R. S. Ballinger, E. L. Peterson, and D. L. Brown (1991). Design optimization of a vibration exciter head exapander.Sound and Vibration,25, 18–25.Google Scholar
  20. 20.
    P. K. Banerjee and D. P. Henry (1988). BEM formulations for body forces using particular integrals. In M. Tanaka and T. A. Cruse, editors,Boundary Element Methods in Applied Mechanics, Proceedings of the First Joint Japan/US Symposium on Boundary Element Methods, pages 25–34, Oxford, Pergamon Press.Google Scholar
  21. 21.
    J.-F. M. Barthelemy, and R. T. Haftka (1993). Approximation concepts for optimum structural design—a review.Structural Optimization,5(3), 129–144.CrossRefGoogle Scholar
  22. 22.
    M. Bassaou and P. Siarry (2001). A genetic algorithm with real-value coding to optimize multimodal continuous functions.Structural and Multidisciplinary Optimization,23, 63–74.CrossRefGoogle Scholar
  23. 23.
    K.-J. Bathe (1982).Finite Element Procedures in Engineering Analysis. Prentice Hall, Englewood Cliffs.Google Scholar
  24. 24.
    K.-J. Bathe, C. Nitikitpaiboon, and X. Wang (1995). A mixed displacement-based finite element formulation for acoustic fluid-structure interaction.Computers and Structures,56, 225–237.zbMATHMathSciNetCrossRefGoogle Scholar
  25. 25.
    R. Battiti and G. Tecchiolli (1996). The continuous reactive tabu search: Blending combinatorial optimization and stochastic search for global optimization.Annals of Operations Research,63, 153–188.zbMATHCrossRefGoogle Scholar
  26. 26.
    T. Bauer and G. Henneberger (1999). Three-dimensional calculation and optimization of the acoustic field of the induction furnace caused by electromagnetic forces.IEEE Transactions on Magnetics,35(3), 1598–1601, May.CrossRefGoogle Scholar
  27. 27.
    A. D. Belegundu (1985). Lagrangian approach to design sensitivity analysis.Journal of Engineering Mechanics,111, 680–695.Google Scholar
  28. 28.
    A. D. Belegundu, R. R. Salagame, and G. H. Koopmann (1994). A general optimization strategy for sound power minimization.Structural Optimization,8(2–3), 113–119.CrossRefGoogle Scholar
  29. 29.
    M. P. Bendsoe (1995).Optimization of Structural Topology, Shape and material. Springer Verlag, Berlin Heidelberg New York.Google Scholar
  30. 30.
    G. W. Benthien and H. A. Schenck (1991). Structural-acoustic coupling. In R. D. Ciskowski and C. A. Brebbia, editors,Boundary Elements in Acoustics, chapter 6, pages 109–129. Computational Mechanics Publications and Elsevier Applied Science.Google Scholar
  31. 31.
    A. Bermudez, P. Gamallo, L. Hervella-Nieto, and R. Rodriguez (2002). Finite element analysis of pressure formulation of the elestoacoustic problem.Numerische Mathematik. In print.Google Scholar
  32. 32.
    A. Bermudez and R. Rodriguez (1994). Finite element computations of the vibration modes of a fluid-solid system.Computer Methods in Applied Mechanics and Engineering,119, 355–370.zbMATHMathSciNetCrossRefGoogle Scholar
  33. 33.
    A. Bermudez and R. Rodriguez (2001). Analysis of finite element method for pressure/potential formulation of elastoacoustic spectral problems.Mathematics of Computation,71(238), 537–552.MathSciNetCrossRefGoogle Scholar
  34. 34.
    R. J. Bernhard (1985). A finite element method for synthesis of acoustical, shapes,Journal of Sound and Vibration,98(1), 55–65.MathSciNetCrossRefGoogle Scholar
  35. 35.
    R. J. Bernhard (1986). Shape optimization of reactive mufflers,Noise Control Engineering Journal,27(1), 10–17.MathSciNetCrossRefGoogle Scholar
  36. 36.
    R. J. Bernhard and D. C. Smith (1991). Acoustic design sensitivity analysis. In R. D. Ciskowski and C. A. Brebbia, editors,Boundary Elements in Acoustics, chapter 4, pages 77–93. Computational Mechanics Publications and Elsevier Applied Science.Google Scholar
  37. 37.
    R. J. Bernhard and S. Takeo (1988). A finite element procedure for design of cavity acoustical treatments.Journal of the Acoustical Society of America,83, 2224–2230.CrossRefGoogle Scholar
  38. 38.
    A. N. Bespalov (1999). Cost-effective solution of the boundary integral equations for 3d Maxwell problems.Russian Journal of Numerical Analysis and Mathematical Modelling,14(5), 403–428.zbMATHMathSciNetGoogle Scholar
  39. 39.
    P. Bettess (1992).Infinite elements. Penshaw Press, Sunderland.Google Scholar
  40. 40.
    G. L. Bilbro and W. E. Snyder (1991). Optimization of functions with many minima.IEEE Transactions on Systems, Man, and Cybernetics,21 (4), 840–849.MathSciNetCrossRefGoogle Scholar
  41. 41.
    F. Bitsie and R. J. Bernhard (1998). Sensitivity calculations for structural-acoustic EFEM predictions.Noise Control Engineering Journal,46(3), 91–96.CrossRefGoogle Scholar
  42. 42.
    V. B. Bokil and U. S. Shirahatti (1994). A new modal technique for sound-structure interaction problems.Journal of Sound and Vibration,175, 23–41.CrossRefGoogle Scholar
  43. 43.
    G. V. Borgiotti (1990). The power radiated by a vibrating body in an acoustic fluid and its determination from acoustic measurements.Journal of the Acoustical Society of America,88(4), 1884–1893.CrossRefGoogle Scholar
  44. 44.
    M. J. Box (1965). A new method of constrained optimization and comparison with other methods.Computer Journal,8(1), 42–52.zbMATHMathSciNetGoogle Scholar
  45. 45.
    J. Branke, T. Kaußler and H. Schmeck (2001). Guidance in evolutionary multi-objective optimization.Advances in Engineering Software,32, 499–507.zbMATHCrossRefGoogle Scholar
  46. 46.
    C. A. Brebbia, J. J. d. Rego Silva, and P. W. Patridge (1991). Computational formulation. In R. D. Ciskowski and C. A. Brebbia, editors,Boundary Elements in Acoustics, chapter 2, pages 13–60. Computational Mechanics Publications and Elsevier Applied Science.Google Scholar
  47. 47.
    J. Bretl (1989). Prediction and reduction of in-vehicle noise due to road irregularity and other inputs.SAE-paper 890100, pages 207–212.Google Scholar
  48. 48.
    M. Bruyneel, P. Duysinx, and C. Fleury (2002). A family of mma approximations for structural optimization.Structural and Multidisciplinary Optimization,24, 263–276.CrossRefGoogle Scholar
  49. 49.
    R. T. Bührmann (2000). The minimization of noise diffraction over an irregularly shaped wall. InInternational Workshop on Multidisciplinary Design Optimization, pages 37–49, Pretoria, South Africa, August.Google Scholar
  50. 50.
    D. S. Burnett (1994). A three dimensional acoustic infinite element based on a prolate spheroidal multipole expansion.Journal of the Acoustical Society of America,96, 2798–2816.MathSciNetCrossRefGoogle Scholar
  51. 51.
    D. S. Burnett and R. L. Holford (1997). 3−d acoustic infinite element based on a oblate spheroidal multipole expansion. United States Patent 5604893.Google Scholar
  52. 52.
    D. S. Burnett and R. L. Holford (1997). 3−d acoustic infinite element based on a prolate spheroidal multipole expansion. United States Patent 5604891.Google Scholar
  53. 53.
    D. S. Burnett and R. L. Holford (1998). An ellipsoidal acoustic infinite element.Computer Methods in Applied Mechanical Engineering,164, 49–76.zbMATHMathSciNetCrossRefGoogle Scholar
  54. 54.
    D. S. Burnett and R. L. Holford (1998). Prolate and oblate spheroidal acoustic infinite elements.Computer Methods in Applied Mechancal Engineering,158, 117–141.zbMATHMathSciNetCrossRefGoogle Scholar
  55. 55.
    A. J. Burton and G. F. Miller (1971). The application of integral equation methods to the numerical solution of some exterior boundary-value problems.Proceedings of the Royal Society of London,323, 201–220.zbMATHMathSciNetCrossRefGoogle Scholar
  56. 56.
    C. Cabos and F. Ihlenburg (2002). Vibrational analysis of ships with coupled finite and boundary elements.Journal of Computational Acoustics. in print.Google Scholar
  57. 57.
    G. Chandler (1979).Superconvergence of numerical solutions to second kind integral equations. Phd-dissertation, Australian National University, Canberra.Google Scholar
  58. 58.
    F. Chatelin and R. Lebbar (1981). The iterated projection solution for the Fredholm integral equation of the second kind.Journal of the Australian Mathematical Society, Series B,22, 439–451.zbMATHMathSciNetCrossRefGoogle Scholar
  59. 59.
    R. Chelouah and P. Siarry (2000). A continuous genetic algorithm designed for the global optimization of multimodal functions.Journal of Heuristics,6(2), 191–213.zbMATHMathSciNetCrossRefGoogle Scholar
  60. 60.
    R. Chelouah and P. Siarry (2000). Tabu search applied to global optimization.European Journal of Operational Research,123(2), 256–270.zbMATHMathSciNetCrossRefGoogle Scholar
  61. 61.
    J. T. Chen, M. H. Chang, K. H. Chen and I. L. Chen (2002). Boundary collocation method for acoustic eigenanalysis of three-dimensional cavities using radial basis function.Computational Mechanics,29, 392–408.zbMATHCrossRefGoogle Scholar
  62. 62.
    P. T. Chen (1997). Vibrations of submerged structures in a heavy acoustic medium using radiation modes.Journal of Sound and Vibration,208(1), 55–71.CrossRefGoogle Scholar
  63. 63.
    P. T. Chen and J. H. Ginsberg (1995). Complex power, reciprocity, and radiation modes for submerged bodies.Journal of the Acoustical Society of America,98(6), 3343–3351.CrossRefGoogle Scholar
  64. 64.
    Z. S. Chen, G. Hofstetter and H. A. Mang (1993). A 3d boundary element method for determination of acoustic eigenfrequencies considering admittance boundary conditions.Journal of Computational Acoustics,1(4), 455–468.CrossRefGoogle Scholar
  65. 65.
    Z. S. Chen, G. Hofstetter, and H. A. Mang (1997). A symmetric Galerkin formulation of the boundary element method for acoustic radiation and scattering.Journal of Computational Acoustics,5(2), 219–241.CrossRefGoogle Scholar
  66. 66.
    Z. S. Chen, G. Hofstetter, and H. A. Mang (1998). A Galerkin-type BE-FE formulation for elasto-acoustic coupling.Computer methods in applied mechanics and engineering,152, 147–155.zbMATHCrossRefGoogle Scholar
  67. 67.
    K. K. Choi, I. Shim, J. Lee, and H. T. Kulkarni (1993). Design sensitivity analysis of dynamic frequency responses of acousto-elastic built-up structures. In G. I. N. Rozvany, editor,Optimization of Large Structural Systems, volume 1, pages 329–343. Kluwer Academic Publishers.Google Scholar
  68. 68.
    K. K. Choi, I. Shim, and S. Wang (1997). Design sensitivity analysis of structure-induced noise and vibration.Journal of Vibration and Acoustics,119, 173–179, April.CrossRefGoogle Scholar
  69. 69.
    S. T. Christensen and N. Olhoff (1998). Shape optimization of a loudspeaker diaphragm with respect to sound directivity properties.Control and Cybernetics,27(2), 177–198.zbMATHMathSciNetGoogle Scholar
  70. 70.
    S. T. Christensen, S. V. Sorokin, and N. Olhoff (1998). On analysis and optimization in structural acoustics—Part i: Problem formulation and solution techniques.Structural Optimization,16, 83–95.Google Scholar
  71. 71.
    S. T. Christensen, S. V. Sorokin, and N. Olhoff (1998). On analysis and optimization in structural acoustics—Part ii: Exemplifications for axisymmetric structures.Structural Optimization,16, 96–107.Google Scholar
  72. 72.
    R. D. Ciskowski and C. A. Brebbia, editors (1991).Boundary Elements in Acoustics. Computational Mechanics Publications and Elsevier Applied Science, Southampton Boston.Google Scholar
  73. 73.
    L.-M. Cleon and A. Willaime (2000). Aero-acoustic optimization of the fans and cooling circuit on SNCF’s X 72500 railcar.Journal of Sound and Vibration,231 (3), 925–933.CrossRefGoogle Scholar
  74. 74.
    E. W. Constans, A. D. Belegundu, and G. H. Koopmann (1998). Design approach for minimizing sound power from vibrating shell structures.AIAA Journal,36(2), 134–139.zbMATHCrossRefGoogle Scholar
  75. 75.
    E. W. Constans, G. H. Koopmann, and A. D. Belegundu (1998). The use of modal tailoring to minimize the radiated sound power of vibrating shells: Theory and experiment.Journal of Sound and Vibration,217 (2), 335–350.CrossRefGoogle Scholar
  76. 76.
    A. Corana, M. Marchesi, C. Martini, and S. Ridella (1987). Minimizing multi-modal functions of continuous variables with the simulated annealing algorithm.ACM Transactions on Mathematical Software,13, 262–280.zbMATHMathSciNetCrossRefGoogle Scholar
  77. 77.
    J. P. Coyette and K. R. Fyfe (1990). An improved formulation for the acoustic eigenmode extraction from boundary element models.Journal of Vibration and Acoustics,112, 392–397.CrossRefGoogle Scholar
  78. 78.
    J.-P. Coyette, C. Lecomte, J.-L. Migeot, J. Blanche, M. Rochette, and G. Mirkovic (1999). Calculation of vibro-acoustic frequency response functions using a single frequency boundary element solution and a Padé expansion.Acustica,85(3), 371–377.Google Scholar
  79. 79.
    J.-P. Coyette, H. Wynendaele, and M. K. Chargin (1993). A global acoustic sensitivity tool for improving structural design.Proceedings-SPIE The International Society for Optical Engineering, Issue 1923, pages 1389–1394.Google Scholar
  80. 80.
    A. Craggs (1971). The transient response of a coupled plate-acoustic system using plate and acoustic finite elements.Journal of Sound and Vibration,15(4), 509–528.CrossRefGoogle Scholar
  81. 81.
    R. R. Craig and C. J. Chang (1976). Free-interface methods of substructre coupling for dynamic analysis.AIAA Journal,14(11), 1633–1635.CrossRefGoogle Scholar
  82. 82.
    S. P. Crane, K. A. Cunefare, S. P. Engelstad, and E. A. Powell (1997). Comparison of design optimization formulations for minimization of noise transmission in a cylinder.Journal of Aircraft,34(2), 236–243.CrossRefGoogle Scholar
  83. 83.
    L. Cremers, K. R. Fyfe and P. Sas (2000). A variable order infinite element for multi-domain boundary element modelling of acoustic radiation and scattering.Applied Acoustics,59, 185–220.CrossRefGoogle Scholar
  84. 84.
    L. Cremers, P. Guisset, L. Meulewaeter, and M. Tournour (2000). A computer-aided engineering method for predicting the acoustic signature of vibrating structures using discrete models. Great Britain Patent No. GB 2000-16259.Google Scholar
  85. 85.
    K. A. Cunefare (1991). The minimum multi-modal radiation efficiency of baffled finite beams.Journal of the Acoustical Society of America,90, 2521–2529.CrossRefGoogle Scholar
  86. 86.
    K. A. Cunefare, S. P. Crane, S. P. Engelstad, and E. A. Powell (1999). Design minimization of noise in stiffened cylinders due to tonal external excitation.Journal of Aircraft,36(3), 563–570.CrossRefGoogle Scholar
  87. 87.
    K. A. Cunefare and M. N. Currey (1994). On the exterior acoustic radiation modes of structures.Journal of the Acoustical Society of America,96(4), 2302–2312.CrossRefGoogle Scholar
  88. 88.
    K. A. Cunefare, M. N. Currey, M. E. Johnson, and S. J. Elliott (2001). The radiation efficiency grouping of free-space acoustic radiation modes.Journal of the Acoustical Society of America,109(1), 203–215.CrossRefGoogle Scholar
  89. 89.
    K. A. Cunefare and G. H. Koopmann (1992). Acoustic design sensitivities for structural radiators.Journal of Vibration and Acoustics,114, 178–186, April.CrossRefGoogle Scholar
  90. 90.
    M. N. Currey and K. A. Cunefare (1995). The radiation modes of baffled finite plates.Journal of the Acoustical Society of America,98(3), 1570–1580.CrossRefGoogle Scholar
  91. 91.
    D. Cvijovic and J. Klinowski (1995). Taboo search. An approach to the multiple minima problem.Science,667, 664–666.MathSciNetCrossRefGoogle Scholar
  92. 92.
    F. Dirschmid, H. Troidl, A. Kunert, S. Dillinger, O. von Estorff, E. Negele, and M. Stowasser (1996). Akustische Optimierung von Getriebegehäusen. InBerechnung und Simulation im Fahrzeugbau, pages 633–651. VDI-Report 1283.Google Scholar
  93. 93.
    S. J. Elliott, Book review of [180] (1998).Journal of Sound and Vibration,214(5), 987–989.CrossRefGoogle Scholar
  94. 94.
    S. P. Engelstad, K. A. Cunefare, E. A. Powell, and V. Biesel (2000). Stiffener shape design to minimize interior noise.Journal of Aircraft,37(1), 165–171.CrossRefGoogle Scholar
  95. 95.
    H. Eschenauer, J. Koski, and A. Oscycka (Eds) (1990).Multicriteria Design Optimization Procedures and Applications. Springer Verlag.Google Scholar
  96. 96.
    H. A. Eschenauer and N. Olhoff (2001). Topology optimization of continuum structures: A review.Applied Mechanics Reviews,54, 331–389.CrossRefGoogle Scholar
  97. 97.
    B. Esping (1995). Design optimization as an engineering tool.Structural Optimization,10, 137–152.CrossRefGoogle Scholar
  98. 98.
    L. F. P. Etman (1997).Optimization of Multibody Systems using Approximation Concepts. Dissertation, Technische Universiteit Eindhoven.Google Scholar
  99. 99.
    G. C. Everstine (1981). A symmetric potential formulation for fluid-structure interaction.Journal of Sound and Vibration,79, 157–160.CrossRefGoogle Scholar
  100. 100.
    G. C. Everstine and F. M. Henderson (1990). Coupled finite element/boundary element approach for fluid structure interaction.Journal of the Acoustical Society of America,87(5), 1938–1947.CrossRefGoogle Scholar
  101. 101.
    G. M. Fadel, M. F. Riley, and J. M. Barthelemy (1990). Two-point exponential approximation method for structural optimization.Structural Optimization,2, 117–124.CrossRefGoogle Scholar
  102. 102.
    J. B. Fahnline and G. H. Koopmann (1995). Design for a high-efficiency sound source based on constrained optimization procedures.Acoustical Physics,41(5), 700–706.Google Scholar
  103. 103.
    J. B. Fahnline and G. H. Koopmann (1996). A lumped parameter model for the acoustic power output from a vibrating structure.Journal of the Acoustical Society of America,100(6), 3539–3547.CrossRefGoogle Scholar
  104. 104.
    J. B. Fahnline and G. H. Koopmann (1997). Numerical implementation of the lumped parameter model for the acoustic power output from a vibrating structure.Journal of the Acoustical Society of America,102(1), 179–192.CrossRefGoogle Scholar
  105. 105.
    G. R. Feijoo, M. Malhotra, A. A. Oberai, and P. M. Pinsky (2001). Shape sensitivity calculations for exterior acoustics problems.Engineering computations,18(3/4), 376–391.zbMATHCrossRefGoogle Scholar
  106. 106.
    K. A. Fisher (1995). The application of genetic algorithms to optimising the design of an engine block for low noise. InGenetic Algorithms in Engineering Systems: Innovations and Applications, pages 18–22. IEEE Conference Publication No. 414.Google Scholar
  107. 107.
    D. L. Flanigan and S. G. Borders (1984). Application of acoustic modeling methods for vehicle boom analysis.SAE-paper 840744, pages 207–217.Google Scholar
  108. 108.
    J. W. Free, A. R. Parkinson, G. R. Bryce, and R. J. Balling (1987). Approximation of computationally expensive and noisy functions for constrained nonlinear optimization.Journal of Mechanisms, Transmissions, and Automation in Design,109, 528–532.CrossRefGoogle Scholar
  109. 109.
    R. Freymann (1999). Sounddesign und Akustikentwicklung im Automobilbau. InMaschinenakustik ’99—Entwicklung lärm- und schwingungsarmer Produkte, pages 47–64 VDI-Report 1491.Google Scholar
  110. 110.
    R. Freymann, R. Stryczek, and H. Spannheimer (1995). Dynamic response of coupled structural-acoustic systems.Journal of Low Frequency Noise and Vibration,14(1), 11–32.Google Scholar
  111. 111.
    M. I. Frishwell and J. E. Mottershead (1995).Finite element model updating in Structural Dynamics. Kluwer Academic Publishers, Dordrecht Boston London.Google Scholar
  112. 112.
    D. Fritze, S. Marburg, and H.-J. Hardtke (2002). Reducing radiated sound power of plates and shallow shells by local modification of geometry.Acustica/Acta Acustica. in print.Google Scholar
  113. 113.
    A. A. Gates and M. L. Accorsi (1993). Automatic shape optimization of three-dimensional shell structures with large shape changes.Computers and Structures,49(1), 167–178.zbMATHCrossRefGoogle Scholar
  114. 114.
    L. Gaul, M. Wagner, and W. Wenzel (1998). Efficient field point evaluation by combined direct and hybrid boundary element methods.Engineering Analysis with Boundary Elements,21(3), 215–222.zbMATHCrossRefGoogle Scholar
  115. 115.
    L. Gaul, M. Wagner, W. Wenzel, and N. A. Dumont (2001). Numerical treatment of acoustical problems with the hybrid boundary element method.International Journal of Solids and Structures,38, 1871–1888.zbMATHCrossRefGoogle Scholar
  116. 116.
    L. Gaul and W. Wenzel (2002). A coupled symmetric BE-FE method for acoustic fluid-structure interaction.Engineering Analysis with Boundary Elements,26(7), 629–636.zbMATHCrossRefGoogle Scholar
  117. 117.
    K. Gerdes (1998). The conjugated versus the unconjugated infinite element method for the Helmholtz equation in exterior domains.Computer Methods in Applied Mechanical Engineering,152, 125–145.zbMATHMathSciNetCrossRefGoogle Scholar
  118. 118.
    K. Giebermann (2001). Multilevel representations of boundary integral operators.Computing,67, 183–207.zbMATHMathSciNetCrossRefGoogle Scholar
  119. 119.
    M. Ginsberg (2001). Influences on the solution process for large, numeric-intensive automotive simulations.Lecture Notes in Computer Science,2073, 1189–1198.CrossRefGoogle Scholar
  120. 120.
    D. Givoli (1992).Numerical methods for problems in infinite domains. Elsevier Science, Amsterdam.zbMATHGoogle Scholar
  121. 121.
    D. Givoli (1999). Recent advances in the DtN FE-method.Archives of Computational Methods in Engineering,6(2), 71–116.MathSciNetCrossRefGoogle Scholar
  122. 122.
    D. Givoli and T. Demchenko (2000). A boundary-perturbation finite element approach for shape optimization.International Journal for Numerical Methods in Engineering,47, 801–819.zbMATHCrossRefGoogle Scholar
  123. 123.
    W. L. Goffe, G. D. Ferrier, and J. Rogers (1994). Global optimization of statistical functions with simulated annealing.Journal of Econometrics,60, 65–99.zbMATHCrossRefGoogle Scholar
  124. 124.
    R. V. Grandhi (1993). Structural optimization with frequency constraints.AIAA Journal,31(12), 2296–2303.zbMATHCrossRefGoogle Scholar
  125. 125.
    L. Greengard, J. Huang, V. Rokhlin, and S. Wandzura (1998). Accelerating fast multipole methods for the Helmholtz equation at low frequencies.IEEE Computational Science and Engineering,5(3), 32–38.CrossRefGoogle Scholar
  126. 126.
    M. Gustafsson and S. He (2000). An optimization approach to multi-dimensional time domain acoustic inverse problems.Journal of the Acoustical Society of America,108(4), 1548–1556.MathSciNetCrossRefGoogle Scholar
  127. 127.
    A. Habbal (1998). Nonsmooth shape optimization applied to linear acoustics.SIAM Journal for Optimization,8(4), 989–1006.zbMATHMathSciNetCrossRefGoogle Scholar
  128. 128.
    D. Hackenbroich (1988). Reduktion des Innengeräusches bei Nutzfahrzeugen durch rechnerische Optimierung des Mündungsgeräusches von Motoransauganlagen. InBerechnung und Simulation im Fahrzeugbau, pages 631–654, VDI-Report 669.Google Scholar
  129. 129.
    R. Haftka and Z. Gürdal (1992).Elements of Structural Optimization. Kluwer Academic Publishers, Dortrecht.zbMATHGoogle Scholar
  130. 130.
    R. T. Haftka and H. M. Adelman (1989). Recent developments in structural sensitivity analysis.Structural Optimization 1, 137–151.CrossRefGoogle Scholar
  131. 131.
    R. T. Haftka and R. V. Grandhi (1986). Structural shape optimization—a survey.Computer Methods in Applied Mechanical Engineering,57, 91–106.zbMATHMathSciNetCrossRefGoogle Scholar
  132. 132.
    R. T. Haftka, J. Nachlas, L. Watson, T. Rizzo, and R. Desai (1987). Two-point constraint approximation in structural optimization.Computer Methods in Applied Mechanical Engineering,60, 289–301.zbMATHCrossRefGoogle Scholar
  133. 133.
    I. Hagiwara, Z.-D. Ma, A. Arai, and K. Nagabuchi (1991). Reduction of vehicle interior noise using structural-acoustic sensitivity analysis methods.SAE Technical Paper Series No. 910208. 10 pages.Google Scholar
  134. 134.
    S. R. Hahn and A. A. Ferri (1997). Sensitivity analysis of coupled structural-acoustic problems using perturbation techniques.Journal of the Acoustical Society of America,101(2), 918–924.CrossRefGoogle Scholar
  135. 135.
    P. Hajela (1992). Genetic search strategies in multicriterion optimal design.Structural Optimization,4, 99–107.CrossRefGoogle Scholar
  136. 136.
    P. Hajela (1999). Nongradient methods in multidisciplinary design optimization—status and potential.Journal of Aircraft,36(1), 255–265.CrossRefGoogle Scholar
  137. 137.
    P. Hajela and J. Yoo (1996). Constraint handling in genetic search using expression strategies.AIAA Journal,34(12), 2414–2420.zbMATHCrossRefGoogle Scholar
  138. 138.
    R. A. Hall (1994). Noise optimization of engine structures using response surface methods.Institution of Mechanical Engineers Conference Publications,3, 79–87.Google Scholar
  139. 139.
    S. A. Hambric (1995). Approximation techniques for broad-band acoustic radiated noise design optimization problems.Journal of Vibration and Acoustics,117(1), 136–144, January.CrossRefGoogle Scholar
  140. 140.
    S. A. Hambric (1996). Sensitivity calculations for broad-band acoustic radiated noise design optimization problems.Journal of Vibration and Acoustics,118(7), 529–532, July.CrossRefGoogle Scholar
  141. 141.
    M. Hamdi, Y. Ousset, and G. Verchery (1978). A displacement method for the analysis of vibrations of coupled fluid-structure systems.International Journal for Numerical Methods in Engineering,13, 139–150.zbMATHCrossRefGoogle Scholar
  142. 142.
    U. Hänle and J. Sielaff (1998). Eine Berechnungstrategie zur Auslegung des komfortrelevanten Karosserie-Strukturverhaltens. InBerechnung und Simulation im Fahrzeugbau, pages 733–750. VDI-Report, 1411.Google Scholar
  143. 143.
    I. Harari, K. Grosh, T. J. R. Hughes, M. Malhotra, P. M. Pinsky, J. R. Stewart, and L. L. Thompson (1996) Recent development in finite element methods for structural acoustics.Archives of Computational Methods in Engineering,3(2–3), 131–309.MathSciNetCrossRefGoogle Scholar
  144. 144.
    I. Harari and T. J. R. Hughes (1992). A cost comparison of boundary element and finite element methods for problems of time-harmonic acoustics.Computer Methods in Applied Mechanics and Engineering,97, 77–102.zbMATHMathSciNetCrossRefGoogle Scholar
  145. 145.
    L. Hermans and M. Brughmans (2000). Enabling vibro-acoustic optimization in a superelement environment: A case study.Proceedings-SPIE The International Society for Optical Engineering, Issue 4062//PT2, pages 1146–1152.Google Scholar
  146. 146.
    F. Hibinger (1998).Numerische Strukturoptimierung in der Maschinenakustik Dissertation, Technische Universität Darmstadt.Google Scholar
  147. 147.
    E. Hinton, M. Özakca, and V. R. Rao (1995). Free vibration analysis and shape optimization of variable thickness plates, prismatic folded plates and curved shells, Part ii: Shape optimization.Journal of Sound and Vibration,181(4), 567–581.CrossRefGoogle Scholar
  148. 148.
    R. Hooke and T. A. Jeeves (1961). Direct search solution of numerical and statistical problems.Journal of the Association of Computing Machinery,8, 212–229.zbMATHGoogle Scholar
  149. 149.
    Y.-L. Hsu (1994). A review of structural shape optimization.Computers in Industry,26, 3–13.CrossRefGoogle Scholar
  150. 150.
    G. Hübner (1991). Eine Betrachtung zur Physik der Schallabstrahlung.Acustica,75, 130–144.Google Scholar
  151. 151.
    G. Hübner and A. Gerlach (1999).Schalleistungsbestimmung mit der DFEM, volume FB 846 ofSchriftenreihe der Bundesanstalt für Arbeitsmedizin (Forschung). Bundesanstalt für Arbeitsschutz und Arbeitsmedizin, Dortmund Berlin.Google Scholar
  152. 152.
    G. Hübner, J. Messner, and E. Meynerts (1986),Schalleistungsbestimmung mit der Direkten Finite Elemente Methode, volume Fb 479 ofSchriftenreihe der Bundesanstalt für Arbeitsmedizin (Forschung). Bundesanstalt für Arbeitsschutz und Arbeitsmedizin, Dortmund Berlin.Google Scholar
  153. 153.
    F. Ihlenburg (1998).Finite Element Analysis of Acoustic Scattering, volume 132 ofApplied Mathematical Sciences. Springer Verlag, Berlin Heidelberg New York.Google Scholar
  154. 154.
    M. Imregun and W. J. Visser (1991). A review of model updating technique.The Shock and Vibration Digest,23, 9–20.CrossRefGoogle Scholar
  155. 155.
    S.-I. Ishiyama, M. Imai, S.-I. Maruyama, H. Ido, N. Sugiura, and S. Suzuki (1988). The application of ACOUST/BOOM—A noise level prediction and reduction code.SAE-paper 880910, pages 195–205.Google Scholar
  156. 156.
    A. H. Jawed and A. J. Morris (1984). Approximate higher-order sensitivities in structural design.Engineering Optimization,7, 121–142.CrossRefGoogle Scholar
  157. 157.
    A. H. Jawed and A. J. Morris (1985). Higher-order updates for dynamic responses in structural optimization.Computer Methods in Applied Mechanical Engineering,49, 175–201.zbMATHCrossRefGoogle Scholar
  158. 158.
    R. Jeans and I. C. Mathews (1991). Use of Lanczoz vectors in structural acoustic problems.ASME Applied Mechanics Division (AMD),128, 101–112. also:NCA Vol. 12.Google Scholar
  159. 159.
    R. A. Jeans and I. C. Mathews (1990). Solution of fluid-structure interaction problems using a coupled finite element and variational boundary element technique.Journal of the Acoustical Society of America,88(5), 2459–2466.CrossRefGoogle Scholar
  160. 160.
    C. S. Jog (2002). Reducing radiated sound power by minimizing the dynamic compliance. In[238], pages 215–236.Google Scholar
  161. 161.
    C. S. Jog (2002). Topology design of structures subjected to periodic load.Journal of Sound and Vibration,253(3), 687–709.CrossRefGoogle Scholar
  162. 162.
    C. S. Jog, R. B. Haber, and M. P. Bendsœ (1994). Topology design with optimized self-adaptive materials.International Journal for Numerical Methods in Engineering,37, 1323–1350.zbMATHMathSciNetCrossRefGoogle Scholar
  163. 163.
    D. S. Jones (1974). Integral equations for the exterior acoustic problem.Quarterly Journal of Mechanics and Applied Mathematics,27, 129–142.zbMATHMathSciNetCrossRefGoogle Scholar
  164. 164.
    P. Juhl (2000). Iterative solution of the direct collocation BEM equations. InProceedings of the 7th International Congress on Sound and Vibration., volume IV, pages 2077–2084, Garmisch-Partenkirchen, Germany.Google Scholar
  165. 165.
    J. H. Kane, S. Mao, and G. C. Everstine (1991). A boundary element formulation for acoustic shape sensitivity analysis.Journal of the Acoustical Society of America,90(1), 561–573, July.CrossRefGoogle Scholar
  166. 166.
    S. W. Kang and J. M. Lee (2000). Free vibration analysis of arbitrarily shaped two-dimensional cavities by the method of point matching.Journal of the Acoustical Society of America,107(3), 1153–1160.MathSciNetCrossRefGoogle Scholar
  167. 167.
    E. M. Kasprzak and K. E. Lewis (2001). Pareto analysis in multiobjective optimization using the collinearity theorem and scaling method.Structural and Multidisciplinary Optimization,22, 208–218.CrossRefGoogle Scholar
  168. 168.
    A. J. Keane (1995). Passive vibration control via unusual geometries: The application of genetic algorithm optimization to structural design.Journal of Sound and Vibration,185(3), 441–453.zbMATHMathSciNetCrossRefGoogle Scholar
  169. 169.
    J. B. Keller and D. Givoli (1989). Exact nonreflecting boundary conditions.Journal of Computational Physics,82, 172–192.zbMATHMathSciNetCrossRefGoogle Scholar
  170. 170.
    P. H. L. Kessels (2001).Engineering toolbox for structural-acoustic design. Applied to MRI-scanners. Dissertation, Technische Universiteit Eindhoven.Google Scholar
  171. 171.
    S. Kibsgaard (1992). Sensitivity analysis—the basis for optimization.International Journal for Numerical Methods in Engineering,34, 901–932.CrossRefGoogle Scholar
  172. 172.
    L. Kiefling and G. C. Feng (1976). Fluid-structure finite element vibration analysis.AIAA Journal,14(2), 199–203.zbMATHMathSciNetCrossRefGoogle Scholar
  173. 173.
    R. K. Kincaid, M. Weber, and J. Sobieszczanski-Sobieski (2001). Performance of a bell-curve based evolutionary optimization algorithm.Structural and Multidisciplinary Optimization,21, 261–271.CrossRefGoogle Scholar
  174. 174.
    S. Kirkpatrick, C. D. Gellat, Jr., and M. P. Vecchi (1983). Optimization by simulated annealing.Science, 220(4598), 671–680.MathSciNetCrossRefGoogle Scholar
  175. 175.
    S. M. Kirkup (1998).The boundary element method in acoustics. Integrated Sound Software, Heptonstall.Google Scholar
  176. 176.
    R. E. Kleinmann, G. F. Roach, L. S. Schuetz, and J. Shirron (1988). An iterative solution to acoustic scatterin by rigid objects.Journal of the Acoustical Society of America,84(1) 385–391.CrossRefGoogle Scholar
  177. 177.
    F. G. Kollmann (1999).Maschinenakustik. Grundlagen, Meßtechnik, Berechnung, Beeinflussung. Springer Verlag, Berlin Heidelberg.Google Scholar
  178. 178.
    B. U. Koo (1997). Shape design sensitivity analysis of acoustic problems using a boundary element method.Computers and Structures,65(5), 713–719.zbMATHCrossRefGoogle Scholar
  179. 179.
    B.-U. Koo, J.-G. Ih, and B.-C. Lee (1998). Acoustic shape sensitivity analysis using the boundary integral equation.Journal of the Acoustical Society of America,104(5), 2851–2860.CrossRefGoogle Scholar
  180. 180.
    G. H. Koopmann and J. B. Fahnline (1997).Designing Quiet Structures: A Sound Power Minimization Approach. Academic Press, San Diego, London.Google Scholar
  181. 181.
    W. Kozukue, C. Pal, and I. Hagiwara (1992). Optimization of noise level reduction by truncated model coupled structural-acoustic sensitivity analysis.Computers in Engineering (ASME),2, 15–22.Google Scholar
  182. 182.
    A. H. W. M. Kuijpers, G. Verbeek, and J. W. Verheij (1997). An improved acoustic Fourier boundary element formulation using fast Fourier transform integration.Journal of the Acoustical Society of America,102(3), 1394–1401.CrossRefGoogle Scholar
  183. 183.
    B. M. Kwak, J. S. Arora, and E. J. Haug, Jr (1975). Optimum design of damped vibration absorbers over a finite frequency range.AIAA Journal,13(4), 540–542.CrossRefGoogle Scholar
  184. 184.
    M. la Civita and A. Sestieri (1999). Optimization of an engine mounting system for vibroacoustic comfort improvement.Proceedings- SPIE The International Society for Optical Engineering, Issue 3727//PT2, pages 1998–2004.Google Scholar
  185. 185.
    C. Lage and C. Schwab (1999). Advanced boundary element algorithms. In J. R. Whiteman, editor,The Mathematics of Finite Elements and Applications X—MAFELAP 1999, pages 283–306. Elsevier, Amsterdam.Google Scholar
  186. 186.
    C. Lage and C. Schwab (1999). Wavelet Galerkin algorithms for boundary integral equations.SIAM Journal for Scientific Computing,20(6), 2195–2222.zbMATHMathSciNetCrossRefGoogle Scholar
  187. 187.
    O. Laghrouche and P. Bettess (2000). Short wave modelling using special finite elements.Journal of Computational Acoustics,8(1), 189–210.MathSciNetGoogle Scholar
  188. 188.
    J. S. Lamancusa (1988). Geometric optimization of internal combustion engine induction systems for minimum noise transmission.Journal of Sound and Vibration,127(2), 303–318.CrossRefGoogle Scholar
  189. 189.
    J. S. Lamancusa (1993). Numerical optimization techniques for structural-acoustic design of rectangular panels.Computers and Structures,48(4), 661–675.zbMATHCrossRefGoogle Scholar
  190. 190.
    J. S. Lamancusa and H. A. Eschenauer (1994). Design optimization methods for rectangular panels with minimal sound radiation.AIAA Journal,32(3), 472–479.zbMATHCrossRefGoogle Scholar
  191. 191.
    M. A. Lang and C. L. Dym (1975). Optimal acoustic design of sandwich panels.Journal of the Acoustical Society of America,57(6), 1481–1487.CrossRefGoogle Scholar
  192. 192.
    J. Lee and P. Hajela (1996). Parallel genetic algorithm implementation in multidisciplinary rotor blade design.Journal of Aircraft,33(5), 962–969.CrossRefGoogle Scholar
  193. 193.
    A. Lehr (1987). A carillon of major-third bells. Part iii: From theory to practice.Music Perception,4(3), 267–280.Google Scholar
  194. 194.
    K. E. Lewis and F. Mistree (1998). The other side of multidisciplinary design optimization: Accomodating a multiobjective, uncertain and non-deterministic world.Engineering Optimization,31, 161–189.CrossRefGoogle Scholar
  195. 195.
    Q. Q. Liang and G. P. Steven (2002). A performance-based optimization method for topology design of continuum structures with mean compliance constraints.Computer Methods in Applied Mechanical Engineering,191, 1471–1489.zbMATHCrossRefGoogle Scholar
  196. 196.
    LMS Numerical Technologies, Leuven (2000).SYSNOISE User’s Manual, Rev. 5.5. Google Scholar
  197. 197.
    Y. Lü, Q. Wang, Z. Hu, and J. Cui (1996). Optimization of acoustic impedance, geometric structure and operating condition of liners mounted in engine duct.Chinese Journal of Aeronautics,9(3), 193–203.Google Scholar
  198. 198.
    J. Luo and H. C. Gea (1997). Modal sensitivity analysis of coupled acoustic-structural systems.Journal of Vibration and Acoustics,119, 545–550, October.CrossRefGoogle Scholar
  199. 199.
    Z.-D. Ma and I. Hagiwara (1991). Sensitivity analysis methods for coupled acoustic-structural systems. Part ii: Direct frequency response and its sensitivities.AIAA Journal,29(11), 1796–1801.zbMATHCrossRefGoogle Scholar
  200. 200.
    Z.-D. Ma and I. Hagiwara (1991). Sensitivity analysis methods for coupled acoustic-structural systems. Part i: Modal sensitivities.AIAA Journal,29(11), 1787–1795.zbMATHCrossRefGoogle Scholar
  201. 201.
    Z.-D. Ma and I. Hagiwara (1994). Development of new mode-superposition technique for truncating lower and/or higher-frequency modes (Application of eigenmode sensitivity analysis for systems with repeated eigenvalues).JSME International Journal, Series C,37(1), 7–13.Google Scholar
  202. 202.
    Z. D. Ma, N. Kikuchi, and H. C. Cheng (1995). Topological design for vibrating structures.Computer Methods in Applied Mechanical Engineering,121, 259–280.zbMATHMathSciNetCrossRefGoogle Scholar
  203. 203.
    The MacNeal-Swendler Corporation (1998).MSC/Nastran manual, V70.5. Google Scholar
  204. 204.
    S. N. Makarov and M. Ochmann (1998). An iterative solver for the Helmholtz integral equation for high frequency scattering.Journal of the Acoustical Society of America,103(2), 742–750.CrossRefGoogle Scholar
  205. 205.
    S. E. Makris, C. L. Dym, and J. MacGregor Smith (1986). Transmission loss optimization in acoustic sandwich panels.Journal of the Acoustical Society of America,92(6), 1833–1843.CrossRefGoogle Scholar
  206. 206.
    M. Malhotra and P. M. Pinsky (1996). A matrix-free interpretation of the non-local Dirichlet-to-Neumann radiation boundary condition.International Journal of Numerical Methods in Engineering,39, 3705–3713.zbMATHCrossRefGoogle Scholar
  207. 207.
    M. Malhotra and P. M. Pinsky (2000). Efficient computation of multi-frequency far-field solutions of the Helmholtz equation using Pade approximation.Journal of Computational Acoustics,8(1), 223–240.MathSciNetGoogle Scholar
  208. 208.
    S. Marburg (1996). Calculation and visualization of acoustic influence co-efficients in vehicle cabins using mode superposition techniques. In C. A. Brebbia, J. B. Martins,et al. (Eds),Boundary Elements XVIII Proceedings of the 18th International Conference on BEM in Braga (Portugal), pages 13–22, Southampton Boston. Computational Mechanics Publications.Google Scholar
  209. 209.
    S. Marburg (1998). Explicit frequency dependent matrices in the BE formulation. InSound and Silence: Setting the Balance—Proceedings of the INTERNOISE 98, volume 3, pages 1533–1536, Christchurch. New Zealand Acoustical Society Inc.Google Scholar
  210. 210.
    S. Marburg (2002). Efficient optimization of a noise transfer function by modification of a shell structure geometry. Part i: Theory.Structural and Multidisciplinary Optimization,24(1), 51–59.CrossRefGoogle Scholar
  211. 211.
    S. Marburg (2002). A general concept for design modification of shell meshes in structural—acoustic optimization. Part i: Formulation of the concept.Finite Elements in Analysis and Design,38(8), 725–735.zbMATHCrossRefGoogle Scholar
  212. 212.
    S. Marburg (2002). Six elements per wavelength. Is that enough?Journal of Computational Acoustics,10(1), 25–51.CrossRefGoogle Scholar
  213. 213.
    S. Marburg, H.-J. Beer, J. Gier, H.-J. Hardtke, R. Rennert, and F. Perret (2002). Experimental verification of structural-acoustic modeling and design optimization.Journal of Sound and Vibration,252(4), 591–615.CrossRefGoogle Scholar
  214. 214.
    S. Marburg and H.-J. Hardtke (2001). Shape optimization of a vehicle hat-shelf: Improving acoustic properties for different load-cases by maximizing first eigenfrequency.Computers and Structures,79, 1943–1957.CrossRefGoogle Scholar
  215. 215.
    S. Marburg and H.-J. Hardtke (2002). Efficient optimization of a noise transfer function by modification of a shell structure geometry. Part ii: Application to a vehicle dashboard.Structural and Multidisciplinary Optimization,24(1), 60–71.CrossRefGoogle Scholar
  216. 216.
    S. Marburg and H.-J. Hardtke (2002). A general concept for design modification of shell meshes in structural-acoustic optimization. Part ii: Application to a vehicle floor panel.Finite Elements in Analysis and Design,38(8), 737–754.zbMATHCrossRefGoogle Scholar
  217. 217.
    S. Marburg and H.-J. Hardtke (2002). Investigation and optimization of a spare wheel well to reduce vehicle interior noise.Journal of Computational Acoustics. In print.Google Scholar
  218. 218.
    S. Marburg, H.-J. Hardtke, R. Schmidt, and D. Pawandenat (1997). An application of the concept of acoustic influence coefficients for the optimization of a vehicle roof.Engineering Analysis with Boundary Elements,20(4), 305–310.CrossRefGoogle Scholar
  219. 219.
    S. Marburg, H.-J. Hardtke, R. Schmidt, and D. Pawandenat (1997). Design optimization of a vehicle panel with respect to cabin noise problems. InProceedings of the NAFEMS World-Congress, pages 885–896, Stuttgart.Google Scholar
  220. 220.
    S. Marburg and S. Schneider (2002). Influence of element types on numeric error for acoustic boundary elements.Journal of Computational Acoustics. in print.Google Scholar
  221. 221.
    S. Marburg and S. Schneider (2002). Performance of iterative solvers for acoustic problems. Part i: Solvers and effect of diagonal preconditioning.Engineering Analysis with Boundary Elements. in print.Google Scholar
  222. 222.
    J. B. Mariem and M. A. Hamdi (1987). A new boundary finite element method for fluid-structure interaction problems.International Journal of Numerical Methods in Engineering,24, 1251–1267.zbMATHCrossRefGoogle Scholar
  223. 223.
    A. F. Mastryukov (1999). Solution of an inverse problem for acoustic-wave equations by a multilevel optimization method.Russian Geology and Geophysics,40(5), 747–757.Google Scholar
  224. 224.
    T. Matsumoto, M. Tanaka, and Y. Yamada (1995). Design sensitivity analysis of steady-state acoustic problems using boundary integral equation formulation.JSME International Journal, Series C,38(1), 9–16.Google Scholar
  225. 225.
    A. J. McMillan and A. J. Keane (1996). Shifting resonances from a frequency band by applying concentrated masses to a thin rectangular plate.Journal of Sound and Vibration,192(2), 549–562.CrossRefGoogle Scholar
  226. 226.
    A. J. McMillan and A. J. Keane (1997). Vibration isolation in a thin rectangular plate using a large number of optimally positioned point masses.Journal of Sound and Vibration,202(2), 219–234.CrossRefGoogle Scholar
  227. 227.
    F. P. Mechel (2001). Computational optimization of absorbers.Acustica,87, 513–518.Google Scholar
  228. 228.
    J. M. Melenk and I. Babuska (1996). The partition of unity finite element method. Basic theory and applications.Computer Methods in Applied Mechanical Engineering,139, 289–314.zbMATHMathSciNetCrossRefGoogle Scholar
  229. 229.
    R. A. Meric (1996). Shape design sensitivities and optimization for the nonhomogeneous Helmholtz equation by BEM.Communications in Numerical Methods in Engineering,12(2), 95–105.zbMATHCrossRefGoogle Scholar
  230. 230.
    N. Metropolis, A. Rosenbluth, M. Rosenbluth, A. Teller, and E. Teller (1953). Equations of state calculations by fast computing machines.Journal of Chemical Physics,21(6), 1087–1092.CrossRefGoogle Scholar
  231. 231.
    G. Miccoli (1999). Vibro-acoustic optimization of earth-moving machine cab structural components. InProceedings of the Inter-Noise 99, volume 3, pages 1761–1766, Fort Lauderdale.Google Scholar
  232. 232.
    M. G. Milsted, T. Zhang, and R. A. Hall (1993). A numerical method for noise optimization of engine structures.Proceedings of the Institution of Mechanical Engineers/Part D: Journal of Automobile Engineering,207, 135–143.CrossRefGoogle Scholar
  233. 233.
    H. P. Mlejnek, U. Jehle, and R. Schirrmacher (1992). Second order approximations in structural genesis and shape finding.International Journal for Numerical Methods in Engineering, 34(3):853–872.zbMATHCrossRefGoogle Scholar
  234. 234.
    D. C. Montgomery (1991).Design and Analysis of Experiments. John Wiley, New York.zbMATHGoogle Scholar
  235. 235.
    H. Morand and R. Ohayon (1979). Substructure variational analysis of the vibrations of coupled fluid-structure systems. Finite element results.International Journal for Numerical Methods in Engineering, 14:741–755, 1979.zbMATHCrossRefGoogle Scholar
  236. 236.
    H. Morand and R. Ohayon (1995).Fluid Structure Interactions. J. Wiley & Sons, Chichester.Google Scholar
  237. 237.
    J. E. Mottershead and M. I. Frishwell (1993). Model updating in structural dynamics: A survey.Journal of Sound and Vibration,167, 347–375.zbMATHCrossRefGoogle Scholar
  238. 238.
    M. L. Munjal (Ed) (2002).IUTAM Symposium on Designing for Quietness. Kluwer Academic Publishers, Dortrecht/Boston/London.zbMATHGoogle Scholar
  239. 239.
    K. Nagaya and L. Li (1997). Control of sound noise radiated from a plate using dynamic absorbers under the optimization by neural network.Journal of Sound and Vibration,208(2), 289–298.CrossRefGoogle Scholar
  240. 240.
    K. Naghshineh, G. H. Koopmann, and A. D. Belegundu (1992). Material tailoring of structures to achieve a minimum radiation condition.Journal of the Acoustical Society of America,92(2), 841–855.CrossRefGoogle Scholar
  241. 241.
    D. Nardini and C. A. Brebbia (1982). A new approach to free-vibration analysis using boundary elements. In C. A. Brebbia, editor,Boundary Element Methods in Engineering, Proceedings of the 4th Conference on BEM, pages 313–326, Southampton. Springer-Verlag.Google Scholar
  242. 242.
    D. J. Nefske, J. A. Wolf Jr., and L. J. Howell (1982). Structural-acoustic finite element analysis of the automobile passenger compartment: A review of current practice.Journal of Sound and Vibration,80(2), 247–266.CrossRefGoogle Scholar
  243. 243.
    J. C. O. Nielsen (2000). Acoustic optimization of railway sleepers.Journal of Sound and Vibration,231(3), 753–764.CrossRefGoogle Scholar
  244. 244.
    A. A. Oberai, M. Malhotra, and P. M. Pinsky (1998). On the implementation of the Dirichletto-Neumann radiation condition for iterative solution of the Helmholtz equation.Applied Numerical Mathematics,27, 443–464.zbMATHMathSciNetCrossRefGoogle Scholar
  245. 245.
    A. A. Oberai and P. M. Pinsky (1998). A multiscale finite element method for the Helmholtz equation.Computer Methods in Applied Mechanical Engineering,154(3/4), 281–298.zbMATHMathSciNetCrossRefGoogle Scholar
  246. 246.
    A. A. Oberai and P. M. Pinsky (2000). A numerical comparison of finite element methods for the Helmholtz equation.Journal of Computational Acoustics,8(1), 211–221.MathSciNetGoogle Scholar
  247. 247.
    M. Ochmann (1999). The full-field equations for acoustic radiation and scattering.Journal of the Acoustical Society of America,105(3), 2674–2584.Google Scholar
  248. 248.
    N. Olhoff (1974). Optimal design of vibrating rectangular panels.International Journal of Solid Structures,10, 93–109.zbMATHCrossRefGoogle Scholar
  249. 249.
    N. Olhoff (1976). A survey of the optimal design of vibrating structural elements. Part i: Theory.The Shock and Vibration Digest,8(8), 3–10.CrossRefGoogle Scholar
  250. 250.
    N. Olhoff (1976). A survey of the optimal design of vibrating structural elements. Part ii: Applications.The Shock and Vibration Digest,8(9), 3–10.CrossRefGoogle Scholar
  251. 251.
    L. G. Olson and K.-J. Bathe (1985). Analysis of fluid-structure interactions. A direct symmetric coupled formulation based on the fluid velocity potential.Computers and Structures,21, 21–32.zbMATHCrossRefGoogle Scholar
  252. 252.
    C. Pal and I. Hagiwara (1993). Dynamic analysis of a coupled structural-acoustic problem. Simultaneous multi-modal reduction of vehicle interior noise level by combined optimization.Finite Elements in Analysis and Design,14, 225–234.zbMATHCrossRefGoogle Scholar
  253. 253.
    C. Pal and I. Hagiwara (1994). Optimization of noise level reduction by truncated modal coupled structural-acoustic sensitivity analysis.JSME International Journal, Series C,37(2), 246–251.Google Scholar
  254. 254.
    O. I. Panič (1965). K voprosu o razrešimosti vnešnich kraevich zadač dlja volnovogo uravnenija i dlja sistemi uravnenij MAXWELLa.Uspechi Math. Nauk,20(1), 221–226.zbMATHGoogle Scholar
  255. 255.
    C. I. Papadopoulos (2001). Redistribution of the low frequency acoustic modes of a room: A finite element-based optimisation method.Applied Acoustics,62, 1267–1285.CrossRefGoogle Scholar
  256. 256.
    M. Papila and R. T. Haftka (2000). Response surface approximation: Noise, error repair, and modelling errors.AIAA Journal,38, 2336–2343.CrossRefGoogle Scholar
  257. 257.
    D. M. Photiadis (1990). The relationship of singular value decomposition to wave-vector filtering in sound radiation problems.Journal of the Acoustical Society of America,88(2), 1152–1159.MathSciNetCrossRefGoogle Scholar
  258. 258.
    P. M. Pinsky (2000). Personal communication.Google Scholar
  259. 259.
    D. Polyzos, G. Dassics, and D. E. Beskos (1994). On the equivalence of dual reciprocity and particular integral approaches in the bem.Boundary Element Communications,5(6), 285–288.Google Scholar
  260. 260.
    M. J. D. Powell (1978). A fast algorithm for nonlinearly constrained optimization calculations. In G. A. Watson, editor,Numerical Analysis. Lecture notes in mathematics, volume 630. Springer Verlag, Berlin.Google Scholar
  261. 261.
    O. M. Querin, G. P. Steven, and Y. M. Xie (1998). Evolutionary structural optimization ESO using bidirectional algorithm.Engineering Computations,15, 1031–1048.zbMATHCrossRefGoogle Scholar
  262. 262.
    C. Rajakumar, A. Ali, and S. M. Yunus (1992). A new acoustic interface element for fluid structure interaction problems.International Journal of Numerical Methods in Engineering,33, 369–386.zbMATHCrossRefGoogle Scholar
  263. 263.
    A. Ratle and A. Berry (1998). Use of genetic algorithms for the vibroacoustic optimization of a plate carrying point-masses.Journal of the Acoustical Society of America,104(6), 3385–3397.CrossRefGoogle Scholar
  264. 264.
    P. A. Raviart and J. M. Thomas (1977). A mixed finite element method for second order elliptic problems. InMathematical Aspects of Finite Element Methods. Lecture Notes in Mathematics, volume 606. Springer Verlag, Berlin, Heidelberg, New York.Google Scholar
  265. 265.
    J. J. d. Rego Silva (1993).Acoustic and Elastic Wave Scattering using Boundary Elements, volume 18 ofTopics in Engineering. Computational Mechanics Publications, Southampton Boston.Google Scholar
  266. 266.
    D. Roesems (1997). A new methodology to support an optimized NVH engineering process.Sound and Vibration,31(5) 36–45.Google Scholar
  267. 267.
    P. J. M. Roozen-Kroon (1992).Structural Optimization of Bells. Dissertation, Technische Universiteit Eidhoven.Google Scholar
  268. 268.
    H. H. Rosenbrock (1960). An automated method for finding the greatest or least value of a function.Computer Journal,3(4), 175–184.MathSciNetCrossRefGoogle Scholar
  269. 269.
    G. I. Rozvany (2001). Stress ratio and compliance based methods in topology optimization—a critical review.Structural and Multidisciplinary Optimization,21, 109–119.CrossRefGoogle Scholar
  270. 270.
    Y. Saad (1994). ILUT: A dual threshold incompleteLU factorization.Numerical linear algebra with applications,1(4), 387–402.zbMATHMathSciNetCrossRefGoogle Scholar
  271. 271.
    R. R. Salagame, A. D. Belegundu, and G. H. Koopmann (1995). Analytical sensitivity of acoustic power radiated from plates.Journal of Vibration and Acoustics,117, 43–48, January.CrossRefGoogle Scholar
  272. 272.
    G. Sandberg (1995). A new strategy for solving fluid-structure problems.International Journal of Numerical Methods in Engineering,38, 357–370.zbMATHMathSciNetCrossRefGoogle Scholar
  273. 273.
    G. Sandberg and P. A. Görasson (1988). A symmetric finite element formulation for acoustic fluid-structure interaction analysis.Journal of Sound and Vibration,123, 507–515.CrossRefGoogle Scholar
  274. 274.
    A. Sarkissian (1990). Acoustic radiation from finite structures.Journal of the Acoustical Society of America,90, 574–578.CrossRefGoogle Scholar
  275. 275.
    S. Sauter (2000). Variable order panel clustering.Computing-Wien,64(3), 223–262.zbMATHMathSciNetGoogle Scholar
  276. 276.
    F. Scarpa (2000). Parametric sensitivity analysis of coupled acoustic-structural systems.Journal of Vibration and Acoustics,122, 109–115, April.CrossRefGoogle Scholar
  277. 277.
    F. Scarpa and G. Curti (1999). A method for the parametric sensitivity of interior acoustostructural coupled systems.Applied Acoustics,58(4), 451–467.CrossRefGoogle Scholar
  278. 278.
    H. A. Schenck (1968). Improved integral formulation for acoustic radiation problems.Journal of the Acoustical Society of America,44, 41–58.CrossRefGoogle Scholar
  279. 279.
    S. Schneider (2002). Application of fast methods for acoustic scattering and radiation problems.Journal of Computational Acoustics. In print.Google Scholar
  280. 280.
    S. Schneider and S. Marburg (2002). Performance of iterative solvers for acoustic problems. Part ii: Acceleration by ilu-type preconditioner.Engineering Analysis with Boundary Elements. In print.Google Scholar
  281. 281.
    A. J. G. Schoofs, P. H. L. Kessels, A. H. W. M. Kuijpers, and M. H. van Houten (2000). Sound and vibration optimization of carillon bells and MRI scanners. InInternational Workshop on Multidisciplinary Design Optimization, 10 pages, Pretoria, South Africa, August.Google Scholar
  282. 282.
    A. J. G. Schoofs, M. B. M. Klink, and D. H. van Campen (1992). Approximation of structural optimization problems by means of designed numerical experiments.Structural Optimization,4, 206–212.CrossRefGoogle Scholar
  283. 283.
    A. J. G. Schoofs, P. J. M. Roozen-Kroon, and D. H. van Campen (1994). Optimization of structural and acoustical parameters of bells. In5th AIAA/USAF/NASA/ISSMO Symposium on Multidisciplinary Analysis and Optimization, 14 pages, Panama City Beach, Florida, September.Google Scholar
  284. 284.
    A. J. G. Schoofs, F. van Asperen, P. Maas, and A. Lehr (1987). A carillon of major-third bells. Part i: Computation of bell profiles using structural optimization.Music Perception,4(3), 245–254.Google Scholar
  285. 285.
    A. J. G. Schoofs and D. H. van Campen (1998). Analysis and optimization of bells systems. In11th Carillon World Congress, 25 pages, Mechelen and Leuven, Belgium, August.Google Scholar
  286. 286.
    A. F. Seybert, A. Charan, and D. W. Herrin (2000). Survey of numerical methods for sound radiation. InProceedings of the 7th International Congress on Sound and Vibration, volume IV, pages 1887–1894, Garmisch-Partenkirchen, Germany.Google Scholar
  287. 287.
    A. F. Seybert, D. A. Hamilton, and P. A. Hayes (1998). Prediction of radiated noise from machine components using the BEM and the Rayleigh integral.Noise Control Engineering Journal,46(3), 77–82.CrossRefGoogle Scholar
  288. 288.
    A. F. Seybert, R. A. Seman, and M. D. Lattuca (1998). Boundary element prediction of sound propagation in ducts containing bulk absorbing materials.Transactions of the ASME,120, 976–981, October.Google Scholar
  289. 289.
    A. F. Seybert, T. W. Wu, and W. L. Li (1991). A coupled FEM/BEM for fluid-structure interaction using Ritz vectors and eigenvectors.ASME Applied Mechanics Division (AMD),128, 171–178. also:NCA Vol. 12.Google Scholar
  290. 290.
    W. S. Shephard Jr. and K. A. Cunefare (1997). Sensitivity of structural acoustic response to attachment feature scales.Journal of the Acoustical Society of America,102(3), 1612–1619.CrossRefGoogle Scholar
  291. 291.
    Q. Shi, I. Hagiwara, A. Azetsu, and T. Ichkawa (1998). Holographic neural network approximations for acoustic optimization.JSAE Review,19, 361–363.CrossRefGoogle Scholar
  292. 292.
    Q. Shi, I. Hagiwara, S. Azetsu, and T. Ichikawa (1998). Optimization of acoustic problem using holographic neural network.Transactions of the society of automotive engineers of Japan,29(3), 93–97, July. (in Japanese).Google Scholar
  293. 293.
    J. Sielaff, A. Kropp, A. Irrgang, and H. P. T. Trong (1998). CAE-gestützte Auslegung der Karosserie am Beispiel der Innenraumakustik. InEntwicklungen im Karosseriebau, pages 231–259. VDI-Report 1398.Google Scholar
  294. 294.
    L. I. Slepyan and S. V. Sorokin (1995). Analysis of structural-acoustic coupling problems by a two-level boundary integral equations method.Journal of Sound and Vibration,184, 195–228.zbMATHCrossRefGoogle Scholar
  295. 295.
    D. C. Smith and R. J. Bernhard (1992). Computation of acoustic shape design sensitivity using a boundary element method.Journal of Vibration and Acoustics,114, 127–132.CrossRefGoogle Scholar
  296. 296.
    J. A. Snyman and N. Stander (1994). New successive approximation method for optimal structural design.AIAA Journal,32(6), 1310–1315.zbMATHCrossRefGoogle Scholar
  297. 297.
    J. Sobieszczanski-Sobieski, S. Kodiyalam, and R. Yang (2001). Optimization of car body under constraints of noise, vibration, and harshness (NVH), and crash.Structural and Multidisciplinary Optimization,22(4), 295–306.CrossRefGoogle Scholar
  298. 298.
    B. Soenarko (1993). A boundary element formulation for radiation of acoustic waves from axisymmetric bodies with arbitrary boundary conditions.Journal of the Acoustical Society of America,93(2), 631–639.CrossRefGoogle Scholar
  299. 299.
    C. Soize and J.-C. Michelucci (2000). Structural shape parametric optimization for an internal structural-acoustic problem.AIAA Journal,4, 263–275.zbMATHGoogle Scholar
  300. 300.
    S. V. Sorokin (1995). Analysis of vibrations of a spatial acoustic system by the boundary integral equations method.Journal of Sound and Vibration,180, 657–667.CrossRefGoogle Scholar
  301. 301.
    R. L. St. Pierre Jr. and G. H. Koopmann (1995). A design method for minimizing the sound power radiated from plates by adding optimally sized, discrete masses.Journal of Mechanical Design,117, 243–251, June.CrossRefGoogle Scholar
  302. 302.
    R. Statnikov and J. Matusov (1995).Multicriteria optimization and engineering. Chapman & Hall, New York.Google Scholar
  303. 303.
    S. Suzuki (1991). Applications in the automotive industry. In R. D. Ciskowski and C. A. Brebbia, editors,Boundary Elements in Acoustics, chapter 7, pages 131–146. Computational Mechanics Publications and Elsevier Applied Science.Google Scholar
  304. 304.
    S. Suzuki, S. Maruyama, and H. Ido (1989). Boundary element analysis of cavity noise problems with complicated boundary conditions.Journal of Sound and Vibrations,130(1), 79–91.CrossRefGoogle Scholar
  305. 305.
    K. Svanberg (1987). The method of moving asymptotes—a new method for structural optimization.International Journal for Numerical Methods in Engineering,24, 359–373.zbMATHMathSciNetCrossRefGoogle Scholar
  306. 306.
    Swanson Analysis System Inc., Houston (1999).ANSYS GUI Help Manual, ANSYS Release 5.6.Google Scholar
  307. 307.
    A. Tadeu and J. Antonio (2000). Use of constant, linear and quadratic boundary elements in 3d wave diffraction analysis.Engineering Analysis with Boundary Elements,24, 131–144.zbMATHCrossRefGoogle Scholar
  308. 308.
    K. C. Tan, T. H. Lee, and E. F. Khor (2001). Evolutionary algorithms with dynamic population size and local exploration for multiobjective optimization.IEEE Transactions on Evolutionary Computation,5(6), 565–588.CrossRefGoogle Scholar
  309. 309.
    M. Tinnsten (2000). Optimization of acoustic response—a numerical and experimental comparison.Structural and Multidisciplinary Optimization,19, 122–129.CrossRefGoogle Scholar
  310. 310.
    M. Tinnsten and P. Carlsson (2002). Numerical optimization of violin top plates.Acustica,88, 278–285.Google Scholar
  311. 311.
    M. Tinnsten, P. Carlsson, and M. Jonsson (2002). Stochastic optimization of acoustic response —a numerical and experimental comparison.Structural and Multidisciplinary Optimization,23(6), 405–411.CrossRefGoogle Scholar
  312. 312.
    M. Tinnsten, B. Esping, and M. Jonsson (1999). Optimization of acoustic response.Structural Optimization,18(1), 36–47.CrossRefGoogle Scholar
  313. 313.
    V.V. Toropov (1989). Simulation approach to structural optimization.Structural Optimization,1, 37–46.CrossRefGoogle Scholar
  314. 314.
    V. V. Toropov, A. A. Filatov, and A. A. Polynkine (1993). Multiparameter structural optimization using FEM and multi-point approximations.Structural Optimization,6, 7–14.CrossRefGoogle Scholar
  315. 315.
    N. Tsujiuchi, T. Koizumi, T. Takenaka, and T. Iwagase (2001). An optimization of rubber mounting for vehicle interior noise reduction.Proceedings-SPIE The International Society for Optical Engineering, Issue 4359, pages 275–281.Google Scholar
  316. 316.
    F. Ursell (1973). On the exterior problems of acoustic.Proc. Cambridge Philos. Soc.,74, 117–125.zbMATHMathSciNetCrossRefGoogle Scholar
  317. 317.
    M. H. van Houten (1998).Function Approximation Concepts for Multidisciplinary Design Optimization. Dissertation, Technische Universiteit Eindhoven.Google Scholar
  318. 318.
    M. H. van Houten, A. J. G. Schoofs, and D. H. van Campen (1997). Damping of bells using experimental and numerical methods. InProceedings of Fifth International Congress on Sound and Vibration, 8 pages, Adelaide, Australia, December.Google Scholar
  319. 319.
    G. N. Vanderplaats and F. Moses (1973). Structural optimization by method of feasible directions.Computers and Structures,3, 739–755.CrossRefGoogle Scholar
  320. 320.
    G. N. Vanderplaats, H. L. Thomas, and Y. K. Shyy (1991). Review of approximation concepts for structural synthesis.Journal of Computing Systems in Engineering,2(1), 17–25.CrossRefGoogle Scholar
  321. 321.
    N. Vincent, P. Bouvet, D. J. Thompson and P. E. Gautier (1996). Theoretical optimization of track components to reduce rolling noise.Journal of Sound and Vibration,193(1), 161–171.CrossRefGoogle Scholar
  322. 322.
    O. von Estorff (Ed) (2000).Boundary Element in Acoustics: Advances and Applications. WIT Press, Southampton.Google Scholar
  323. 323.
    B. P. Wang (1992). Eigenvalue sensitivity with respect to location of internal stiffness and mass attachments.AIAA Journal,31 (4), 791–794.CrossRefGoogle Scholar
  324. 324.
    S. Wang (1999). Design sensitivity analysis of noise, vibration, and harshness of vehicle body structure.Mechanics of Structures and Machines,27 (3), 317–336.CrossRefGoogle Scholar
  325. 325.
    S. Wang and J. Lee (2001). Acoustic design sensitivity analysis and optimization for reduced exterior noise.AIAA Journal,39(4), 574–580.CrossRefGoogle Scholar
  326. 326.
    X. Wang and K.-J. Bathe (1997). Displacement/pressure based mixed finite element formulations for acoustic fluid structure interaction problems.International Journal for Numerical Methods in Engineering 40, 2001–2017.zbMATHCrossRefGoogle Scholar
  327. 327.
    D. Watts and J. Starkey (1990). Design optimization of response amplitudes in viscously damped structures.Journal of Vibration and Acoustics,112, 275–280, July.CrossRefGoogle Scholar
  328. 328.
    J. H. Wilkinson (1965).The algebraic eigenvalue problem. Oxford University Press.Google Scholar
  329. 329.
    E. L. Wilson, M. W. Yuan, and J. M. Dickens (1982). Dynamic analysis by direct superposition of Ritz vectors.Earthquake Engineering and Structural Dynamics, 10, 813–821.CrossRefGoogle Scholar
  330. 330.
    H.-W. Wodtke and J. S. Lamancusa (1998). Sound power minimization of circular plates through damping layer placement.Journal of Sound and Vibration,215(5), 1145–1163.CrossRefGoogle Scholar
  331. 331.
    S. Y. Woon, O. M. Querin, and G. P. Steven (2001). Structural application of a shape optimization method based on a genetic algoithm.Structural and Multidisciplinary Optimization,22, 57–64.CrossRefGoogle Scholar
  332. 332.
    T. W. Wu (Ed) (2000).Boundary Element in Acoustics: Fundamentals and Computer Codes. WIT Press, Southampton.Google Scholar
  333. 333.
    H. Xia and J. L. Humar (1992). Frequency dependent Ritz vectors.Earthquake Engineering and Structural Dynamics,21, 215–231.CrossRefGoogle Scholar
  334. 334.
    Y. M. Xie and G. P. Steven (1996). Evolutionary structural optimization for dynamic problems.Computers and Structures,58, 1067–1073.zbMATHCrossRefGoogle Scholar
  335. 335.
    Y. M. Xie and G. P. Steven (1997).Evolutionary structural optimization. Springer Verlag, London.zbMATHGoogle Scholar
  336. 336.
    Y. G. Xu, G. R. Li, and Z. P. Wu (2001). A novel hybrid genetic algorithm using local optimizer based on heuristic pattern move.Applied Artificial Intelligence,15, 601–631.CrossRefGoogle Scholar
  337. 337.
    I. Yamazaki and T. Inoue (1989). An application of structural-acoustic coupling analysis to boom noise.SAE-paper 891966, pages 1–9.Google Scholar
  338. 338.
    S. Yang, G. Ni, Y. Li, B. Tian, and R. Li (1998). An universal tabu search algorithm for global optimization of multimodal functions with continuous variables in electromagnetics.IEEE Transactions on Magnetics,34(5), 2901–2904.CrossRefGoogle Scholar
  339. 339.
    T. C. Yang, C. H. Tseng, and S. F. Ling (1986). A boundary-element-based optimization technique for design of enclosure acoustical treatments.Journal of the Acoustical Society of America,98(1), 302–312.CrossRefGoogle Scholar
  340. 340.
    H. J. Yim and S. B. Lee (1997). Design optimization of vehicle structures for idle shake vibration.Proceedings-SPIE The International Society for Optical Engineering, Issue 3089//PT1, pages 432–437.Google Scholar
  341. 341.
    J. Yoo and P. Hajela (1998). Immune network simulations in multicriterion design.Structural Optimization,18, 85–94.Google Scholar
  342. 342.
    J. Yoo and P. Hajela (2001). Fuzzy multicriterion design using immune network simulation.Structural and Multidisciplinary Optimization,22, 188–197.CrossRefGoogle Scholar
  343. 343.
    C. B. Zhao, G. P. Steven, and Y. M. Xie (1997). Evolutionary optimization of maximizing the difference between two natural frequencies of a vibrating structure.Structural Optimization,13, 148–154.CrossRefGoogle Scholar
  344. 344.
    O. C. Zienkiewicz (1977).The Finite Element Method. McGraw Hill, Berkshire, 3 edition.zbMATHGoogle Scholar

Copyright information

© CIMNE 2002

Authors and Affiliations

  • Steffen Marburg
    • 1
  1. 1.Institut für FestkörpermechanikTechnische UniversitätDresdenGermany

Personalised recommendations