Wave propagation in elastic lattices subjected to a local harmonic loading. I. A quasi-one-dimensional problem

G. Osharovich, M. Ayzenberg-Stepanenko, O. Tsareva

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

The anti-plane dynamics of infinite (-∞ < x < ∞,-∞ < y < ∞) material-bond rectangular lattices subjected to a uniform monochromatic excitation of the x = 0 line nodes is studied. A quasi-onedimensional model is formulated: the original lattice is considered as an infinite waveguide in the x-direction with periodically joined bonds bounded in the y-direction. In such a structure, the wave pattern consists of waves propagated along x-axis and standing waves along y-axis. Steady and unsteady processes are investigated. Dispersion relations are analyzed and resonance points are detected. A combined analytical-numerical approach is used to describe (i) the quasi-steady propagation of waves when the source frequency is within the pass-band, (ii) development of resonance waves, and (iii) percolation of perturbations to the periphery when the excitation frequency is within the stop-band. Long-wave and short-wave components of solutions are compared with those for a simplified 1D mass-spring lattice (MSL) model.

Original languageEnglish
Pages (from-to)581-597
Number of pages17
JournalContinuum Mechanics and Thermodynamics
Volume22
Issue number6
DOIs
StatePublished - 1 Sep 2010

Keywords

  • Asymptotic solution
  • Computer simulation
  • Dispersion pattern
  • Lattice dynamics
  • Resonance
  • Transient response

ASJC Scopus subject areas

  • Materials Science (all)
  • Mechanics of Materials
  • Physics and Astronomy (all)

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