Structural and Multidisciplinary Optimization

, Volume 31, Issue 1, pp 60–75

Multiobjective evolutionary optimization of periodic layered materials for desired wave dispersion characteristics

  • Mahmoud I. Hussein
  • Karim Hamza
  • Gregory M. Hulbert
  • Richard A. Scott
  • Kazuhiro Saitou
Research Paper

DOI: 10.1007/s00158-005-0555-8

Cite this article as:
Hussein, M.I., Hamza, K., Hulbert, G.M. et al. Struct Multidisc Optim (2006) 31: 60. doi:10.1007/s00158-005-0555-8

Abstract

An important dispersion-related characteristic of wave propagation through periodic materials is the existence of frequency bands. A medium effectively attenuates all incident waves within stopbands and allows propagation within passbands. The widths and locations of these bands in the frequency domain depend on the layout of contrasting materials and the ratio of their properties. Using a multiobjective genetic algorithm, the topologies of one-dimensional periodic unit cells are designed for target frequency band structures characterizing longitudinal wave motion. The decision variables are the number of layers in the unit cell and the thickness of each layer. Binary and mixed formulations are developed for the treatment of the optimization problems. Designs are generated for the following novel objectives: (1) maximum attenuation of time harmonic waves, (2) maximum isolation of general broadband pulses, and (3) filtering signals at predetermined frequency windows. The saturation of performance with the number of unit-cell layers is shown for the first two cases. In the filtering application, the trade-off between the simultaneous realization of passband and stopband targets is analyzed. It is shown that it is more difficult to design for passbands than it is to design for stopbands. The design approach presented has potential use in the development of vibration and shock isolation structures, sound isolation pads/partitions, and multiple band frequency filters, among other applications.

Keywords

Periodic materialsPhononic and photonic crystalsWave dispersionBand gapStopbandPassbandTopology optimizationMultiobjective genetic algorithmsVibration and shock isolation

Copyright information

© Springer-Verlag 2005

Authors and Affiliations

  • Mahmoud I. Hussein
    • 1
  • Karim Hamza
    • 1
  • Gregory M. Hulbert
    • 1
  • Richard A. Scott
    • 1
  • Kazuhiro Saitou
    • 1
  1. 1.Department of Mechanical EngineeringThe University of MichiganAnn ArborUSA