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Surface wave across crack-tip in a lattice model.

Basant Lal Sharma1

  • 1Department of Mechanical Engineering, Indian Institute of Technology Kanpur, Kanpur, India.

Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences
|July 20, 2022
PubMed
Summary

This study investigates surface waves interacting with crack tips in a triangular lattice. Transmission and reflection coefficients were calculated, revealing optimal conditions for wave propagation and minimal energy leakage.

Keywords:
Wiener–Hopfedge modelocalized wavemode III crackscattering

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Area of Science:

  • Solid mechanics
  • Wave physics
  • Materials science

Background:

  • Surface waves exist in triangular lattices with nearest-neighbor interactions and traction-free boundaries for out-of-plane motion.
  • Understanding wave interactions with crack tips is crucial for material integrity and wave transmission analysis.

Purpose of the Study:

  • Investigate the interaction between surface waves and stationary crack tips in Mode III.
  • Analyze wave scattering, transmission, and energy leakage at the crack tip.
  • Explore surface wave excitation by incident bulk waves.

Main Methods:

  • Solved the discrete Helmholtz equation for scattered waves, incorporating an anisotropy parameter.
  • Derived closed-form expressions for transmission and reflection coefficients.
  • Estimated the energy fraction leaked as bulk waves at the crack tip.

Main Results:

  • Obtained exact solutions for transmission and reflection coefficients.
  • Found that the transmission coefficient peaks above the mid-band frequency.
  • Identified minimum energy leak at the upper-band limit of the surface wave band.

Conclusions:

  • Surface wave behavior at crack tips is frequency-dependent and anisotropic.
  • Optimal transmission and minimal energy loss occur within specific surface wave band ranges.
  • The study provides insights into wave phenomena in structured media with defects.