Waves in elastic bodies with discrete and continuous dynamic microstructure

Gennady Mishuris, Alexander B. Movchan, Leonid I. Slepyan

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This paper presents a unified approach to the modelling of elastic solids with embedded dynamic microstructures. General dependences are derived based on Green's kernel formulations. Specifically, we consider systems consisting of a master structure and continuously or discretely distributed oscillators. Several classes of connections between oscillators are studied. We examine how the microstructure affects the dispersion relations and determine the energy distribution between the master structure and microstructures, including the vibration shield phenomenon. Special attention is given to the comparative analysis of discrete and continuous distributions of the oscillators, and to the effects of non-locality and trapped vibrations
Original languageEnglish
Article number20190313
JournalPhilosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
Issue number2162
Early online date25 Nov 2019
Publication statusPublished - 10 Jan 2020


  • dynamic microstructure
  • wave equations
  • Green's functions
  • integral transforms
  • dispersion relations
  • Dispersion relations
  • Dynamic microstructure
  • Green’s functions
  • Wave equations
  • Integral transforms


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