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Low Frequency Band Gaps and Localised Modes for Arrays of Coated Inclusions

  • S. B. Platts
  • N. V. Movchan
Conference paper
Part of the Solid Mechanics and Its Applications book series (SMIA, volume 113)

Abstract

We study the scattering of plane elastic waves (pressure and shear) by a finite stack of gratings, infinite and periodic in the x-direction, of circular cylindrical elastic inclusions placed in an infinite elastic medium. The inclusions are connected to the surrounding medium via a thin soft elastic layer. The constitutive equations for the layer are derived using an asymptotic technique [1]. The problem is then solved using the method of multipole expansions. Results show regular arrays of cylinders which act as elastic polarisers (i.e. they reflect one type of wave and transmit the other) and elastic filters, structures that do not transmit elastic waves. We also demonstrate that an elastic inclusion surrounded by a thin soft “coating” layer is responsible for creating localised modes in the low frequency range.

Keywords

Localise Mode Multipole Expansion Phononic Crystal Elastic Inclusion Shear Problem 
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.

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References

  1. [1]
    Bigoni, D., Serkov, S.K., Valentini, M. & Movchan, A.B. Asymptotic models of dilute composites with imperfectly bonded inclusions. Int. J. Solids Structures, 35(1998), 3239–3258.CrossRefMathSciNetzbMATHGoogle Scholar
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    Jensen, J.S. Phononic band gaps and vibrations in one-and two-dimensional mass-spring structures. (to appear in Journal of Sound and Vibration), 2003.Google Scholar
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    Platts, S.B., Movchan, N.V., McPhedran, R.C. & Movchan, A.B. Two-dimensional phononic crystals and scattering of elastic waves by an array of voids. Proc. R. Soc. Lond. A, 458(2002), 2327–2374.MathSciNetzbMATHGoogle Scholar
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    Platts, S.B., Movchan, N.V., McPhedran, R.C. & Movchan, A.B. Band gaps and elastic waves in disordered stacks: normal incidence. Proc. R. Soc. Lond. A, 459(2003), 221–240.MathSciNetCrossRefzbMATHGoogle Scholar
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    Platts, S.B. & Movchan, N.V. Scattering of elastic waves by a disorderd array of fluid filled cylinders: normal incidence. In: Applied Problems in Mechanics, 2002, St. Petersburg, Russia, 530–536.Google Scholar

Copyright information

© Kluwer Academic Publishers 2003

Authors and Affiliations

  • S. B. Platts
    • 1
  • N. V. Movchan
    • 1
  1. 1.Department of Mathematical SciencesUniversity of LiverpoolUK

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