Browse > Article
http://dx.doi.org/10.5050/KSNVN.2008.18.11.1118

Topology-optimization-based Partition Design for Maximizing or Minimizing the Eigenfrequency of a Double Cavity  

Lee, Jin-Woo (퍼듀대학교 기계공학과)
Kim, Yoon-Young (서울대학교 기계항공 공학부)
Publication Information
Transactions of the Korean Society for Noise and Vibration Engineering / v.18, no.11, 2008 , pp. 1118-1127 More about this Journal
Abstract
The position and size of holes in the partition of a double cavity are known to strongly affect the eigenfrequency of the longitudinal eigenmodes of the double cavity. To maximize or minimize the eigenfrequency of the hole-partitioned double cavity, two acoustical topology optimization problems are formulated and solved. While two sub-cavities are filled with air, a partition between them is assumed to consist of sub-partitions of variable acoustical properties. One design variable is assigned to each sub-partition, whose material properties are interpolated as those of an intermediate material between air and a rigid body. The penalty parameter of the used interpolation function is adjusted to obtain a distinct air and rigid body distribution at the converged stage in each acoustical topology optimization problem. A special attention is paid to the selection of initial values of design variables to obtain solutions as close to global optimum and symmetric as possible. To show numerical characteristics of these optimization problems, the formulated problems are first solved for the one-dimensional partition design domain and then for the two-dimensional partition design domain.
Keywords
Double Cavity; Topology optimization; Hole; Eigenfrequency; Partition;
Citations & Related Records
Times Cited By KSCI : 1  (Citation Analysis)
연도 인용수 순위
1 Lee, J. W. and Lee, J. M., 2007, 'An Improved Mode Superposition Method Applicable to a Coupled Structural-acoustic System with a Multiple Cavity', Journal of Sound and Vibration, Vol. 301, No. 3-5, pp. 821-845   DOI   ScienceOn
2 Dowell, E. H., Gorman, G. F. and Smith, D. A., 1977, 'Acoustoelasticity : General Theory, Acoustic Natural Modes and Forced Response to Sinusoidal Excitation, Including Comparisons with Experiment', Journal of Sound and Vibration, Vol. 52, No. 4, pp. 519-542   DOI   ScienceOn
3 Morse, P. M. and Ingard, K. U., 1968, Theoretical Acoustics, McGraw-Hill Book Company, New York
4 Fahy, F. J. and Schofield, C., 1980, 'A Note on the Interaction between a Helmholtz Resonator and an Acoustic Mode of an Enclosure', Journal of Sound and Vibration, Vol. 72, No. 3, pp. 365-378   DOI   ScienceOn
5 Sigmund, O. and Jensen, J. S., 2005, 'Systematic Design of Acoustic Devices by Topology Optimization', Proceedings of ICSV12, Lisbon, pp. 197-224
6 Svanberg, K., 1987, 'The Method of Moving Asymptotes : a New Model for Structural Optimization', Internal Journal for Numerical Methods in Engineering, Vol. 24, No. 2, pp. 359-373   DOI   ScienceOn
7 Lee, J. W. and Lee, J. M., 2007, 'Forced Vibro-acoustical Analysis for a Theoretical Model of a Passenger Compartment with a Trunk-Part II : Experimental Part', Journal of Sound and Vibration, Vol. 299, No. 4, pp. 918-932   DOI   ScienceOn
8 Lee, J. W. and Lee, J. M., 2007, 'Forced Vibro-acoustical Analysis for a Theoretical Model of a Passenger Compartment with a Trunk-Part I : Theoretical Part', Journal of Sound and Vibration, Vol. 299, No. 4-5, pp. 900-917   DOI   ScienceOn
9 Lee, J. W. and Kim, Y. Y., 2007, 'Muffler Design Using a Topology Optimization Method', Proceedings of the KSNVE Annual Spring Conference, pp. 1085-1089
10 Lee, J. W. and Kim, Y. Y., 2007, 'Controlling the Fundamental Eigenfrequency of a Holepartitioned Double Cavity by a Topology Optimization Method', Proceedings of the 7th World Congress on Structural and Multidisciplinary Optimization, Seoul, CD-Rom
11 Lee, J. W. and Kim, Y. Y., 2007, 'Partition Hole Design for Maximizing or Minimizing the Fundamental Eigenfrequency of a Double Cavity by Topology Optimization', Proceedings of the 14th International Congress on Sound and Vibration, Cairns, Australia, CD-Rom
12 Bendsoe, M. P. and Sigmund, O., 2003, Topology Optimization : Theory, Methods and Applications, Springer Verlag, Berlin
13 Wadbro, E. and Berggren, M., 2006, 'Topology Optimization of an Acoustic Horn', Computer Methods in Applied Mechanics in Engineering, Vol. 196, No. 1-3, pp. 420-436   DOI   ScienceOn
14 Maeda, Y., Nishiwaki, S., Izui, K., Yoshimura, M., Matsui, K. and Terda, K., 2006, 'Structural Topology Optimization of Vibrating Structures with Specified Eigenfrequencies and Eigenmode Shapes', Internal Journal for Numerical Methods in Engineering, Vol. 67, No. 5, pp. 597-628   DOI   ScienceOn
15 Lee, J. W., Lee, J. M. and Kim, S. H., 2004, 'Acoustical Analysis of Multiple Cavities Connected by Necks in Series with a Consideration of Evanescent Waves', Journal of Sound and Vibration, Vol. 273, No. 4-5, pp. 515-542   DOI   ScienceOn
16 Stople, M. and Svanberg, K., 2001, 'An Alternative Interpolation Scheme for Minimum Compliance Topology Optimization', Structural and Multidisciplinary Optimization, Vol. 22, No. 2, pp 116-124   DOI   ScienceOn
17 Lee, J. W. and Kim, Y. Y., 2008, 'Optimal Distribution of Holes in a Partition Interfacing two Cavities for Controlling Eigenfrequencies by Acoustical Topology Optimization', Submitted
18 Jensen, J. S. and Pedersen, N. L., 2006, 'On Maximal Eigenfrequency Separation in Two-material Structures : the 1D and 2D Scalar Cases', Journal of Sound and Vibration, Vol. 289, No. 4-5, pp. 967-986   DOI   ScienceOn
19 Bendsoe, M. P. and Kikuchi, N., 1988, 'Generating Optimal Topologies in Structural Design Using a Homogenization Method', Computer Methods in Applied Mechanics in Engineering, Vol. 71, No. 2, pp. 197-224   DOI   ScienceOn
20 Lee, J., Wang, S. and Dikec, A., 2004, 'Topology Optimization for the Radiation and Scattering of Sound from Thin-body Using Genetic Algorithms', Journal of Sound and Vibration, Vol. 276, No. 3-5, pp. 899-918   DOI   ScienceOn
21 Lee, J. S., Kim, J. E. and Kim, Y. Y., 2006, 'A Feasibility Study on the Application of the Topology Optimization Method for Structural Damage Identification', Transactions of the Korean Society for Noise and Vibration Engineering, Vol. 16, No. 2, pp. 115-123   과학기술학회마을   DOI   ScienceOn
22 Lee, J. S., Kim, E. I. Kim, Y. Y., Kim, J. S., and Kang, Y. J., 2007, 'Optimal Poroelastic Layer Sequencing for Sound Transmission Loss Maximization by Topology Optimization Method, Journal of the Acoustical Society of America, Vol. 122, No. 4, pp. 2097-2106   DOI   ScienceOn