Phononic Band Gap Structures as Optimal Designs

  • Jakob S. Jensen
  • Ole Sigmund
Part of the Solid Mechanics and Its Applications book series (SMIA, volume 113)


In this paper we use topology optimization to design phononic band gap structures. We consider 2D structures subjected to periodic loading and obtain the distribution of two materials with high contrast in material properties that gives the minimal vibrational response of the structure. Both in-plane and out-of-plane vibrations are considered.


Topology optimization phononic band gap structures 


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  1. [1]
    M. P. Bendsoe. Optimization of Structural Topology, Shape and Material. Springer Verlag, Berlin Heidelberg, 1995.Google Scholar
  2. [2]
    M. P. Bendsoe and O. Sigmund. Topology Optimization—Theory, Methods and Applications. Springer Verlag, Berlin Heidelberg, 2003.Google Scholar
  3. [3]
    J. D. Joannopoulos, R. D. Meade, and J. N. Winn. Photonic Crystals. Princeton University Press, New Jersey, 1995.zbMATHGoogle Scholar
  4. [4]
    E. Yablonovitch. Photonic crystals: semiconductors of light. Scientific American, 285(6):34–41, 2001.CrossRefGoogle Scholar
  5. [5]
    M. M. Sigalas and E. N. Economou. Elastic and acoustic wave band structure. Journal of Sound and Vibration, 158(2):377–382, 1992.CrossRefGoogle Scholar
  6. [6]
    M. S. Kushwaha. Classical band structure of periodic elastic composites. International Journal of Modern Physics, 10(9):977–1094, 1996.CrossRefGoogle Scholar
  7. [7]
    J. O. Vasseur, P. A. Deymier, G. Frantziskonis, G. Hong, B. Djafari-Rouhani, and L. Dobrzynski. Experimental evidence for the existence of absolute acoustic band gaps in two-dimensional periodic composite media. J. Phys.: Condens. Matter, 10:6051–6064, 1998.CrossRefGoogle Scholar
  8. [8]
    Z. Liu, X. Zhang, Y. Mao, Y. Y. Zhu, Z. Yang, C. T. Chan, and P. Sheng. Locally resonant sonic materials. Science, 289:1734–1736, 2000.CrossRefGoogle Scholar
  9. [9]
    O. Sigmund. Microstructural design of elastic band gap structures. In G. D. Cheng, Y. Gu, S. Liu, and Y. Wang, editors, Proceedings of the Fourth World Congress of Structural and Multidisciplinary Optimization, on CD-rom, Dalian, China, 2001. WCSMO-4.Google Scholar
  10. [10]
    S. J. Cox and D. C. Dobson. Band structure optimization of two-dimensional photonic crystals in h-polarization. Journal of Computational Physics, 158(2):214–224, 2000.CrossRefzbMATHGoogle Scholar
  11. [11]
    O. Sigmund and J. S. Jensen. Topology optimization of elastic band gap structures and waveguides. In H. A. Mang, F. G. Rammerstorfer, and J. Eberhardsteiner, editors, Proceedings of the Fifth World Congress on Computational Mechanics,, Vienna, Austria, 2002. WCCM V.
  12. [12]
    O. Sigmund and J. S. Jensen. Systematic design of phononic band gap materials and structures by topology optimization. Phil. Trans. R. Soc. Lond. A, 361, 1001–1019, 2003.CrossRefMathSciNetzbMATHGoogle Scholar
  13. [13]
    K. Svanberg. The method of moving asymptotes—a new method for structural optimization. International Journal for Numerical Methods in Engineering, 24:359–373, 1987.CrossRefzbMATHMathSciNetGoogle Scholar
  14. [14]
    J. S. Jensen. Phononic band gaps and vibrations in one-and two-dimensional mass-spring structures. Journal of Sound and Vibration, to appear, 2003.Google Scholar

Copyright information

© Kluwer Academic Publishers 2003

Authors and Affiliations

  • Jakob S. Jensen
    • 1
  • Ole Sigmund
    • 1
  1. 1.Department of Mechanical Engineering, Section for Solid Mechanics Nils Koppels AlléTechnical University of DenmarkLyngbyDenmark

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