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We discuss the propagation of anti-plane waves that are localized near a plane interface between two elastic half-spaces. A discrete model based on lattice dynamics is utilized. The square lattice is considered. Each half-space consists of particles that are characterized by their masses and elastic bond stiffness. Additionally, the elastic bonds between the half-spaces differ from those in the bulk. We formulate the equations of motion and derive their solutions. The corresponding dispersion relations were then derived.

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On Anti-plane Waves Localized Near Sharp Interface Between Two Elastic Half-Spaces: Lattice Dynamics Approach

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  • 发表日期：

    2026年

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  • Inna A. Eremeeva,
  • Sergey M. Aizikovich

摘要

We discuss the propagation of anti-plane waves that are localized near a plane interface between two elastic half-spaces. A discrete model based on lattice dynamics is utilized. The square lattice is considered. Each half-space consists of particles that are characterized by their masses and elastic bond stiffness. Additionally, the elastic bonds between the half-spaces differ from those in the bulk. We formulate the equations of motion and derive their solutions. The corresponding dispersion relations were then derived.