Wave localization in stratified square-cell lattices: The antiplane problem

G. G. Osharovich, M. V. Ayzenberg-Stepanenko

Research output: Contribution to journalArticlepeer-review

16 Scopus citations


Steady-state and transient antiplane dynamic processes in a structured solid consisting of uniform periodic square-cell lattices connected by a lattice layer of different bond stiffnesses and point masses are analyzed. A semi-infinite lattice covered by a layer is also considered. Localization phenomena that are characterized by a waveguide-like propagation along the layer direction and exponential attenuation along its normal are studied. Waveguide pass-bands and attenuation factors are obtained analytically, while transient processes developed under the action of a monochromatic local source are numerically simulated. As a result, it is shown how a two-dimensional problem is transformed with time into a quasi-one-dimensional one and how a layer traps the source energy. Special attention is paid to revealing particularities of transient waves in cases where steady-state solutions are absent: resonant waves with frequencies demarcating pass- and stop-bands at the ends of the Brillouin zone and wave transition in the vicinities of transition points in dispersion curves. In the latter case, a simultaneous onset of different localization phenomena a spatial star-like beaming and a one-dimensional waveguide-like localization is shown.

Original languageEnglish
Pages (from-to)1378-1397
Number of pages20
JournalJournal of Sound and Vibration
Issue number6
StatePublished - 12 Mar 2012

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Mechanics of Materials
  • Acoustics and Ultrasonics
  • Mechanical Engineering


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