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Area of Science:

  • Solid Mechanics
  • Materials Science
  • Acoustics

Background:

  • Non-linear wave propagation is crucial for understanding material behavior under stress.
  • Rayleigh waves are surface acoustic waves sensitive to material properties.
  • Characterizing material inhomogeneities, like dislocations, is vital for structural integrity.

Purpose of the Study:

  • To theoretically investigate non-linear Rayleigh waves in materials with inhomogeneous third-order and homogeneous second-order elastic properties.
  • To analyze the frequency dependence of harmonic coupling constants.
  • To assess sensitivity to Murnaghan's constants for material characterization.

Main Methods:

  • Theoretical analysis of non-linear wave propagation.
  • Application of quasi-linear approximation for mono- and bi-chromatic inputs.
  • Numerical simulations using depth profiles of dislocation densities.

Main Results:

  • Harmonic coupling constants are found to be frequency-dependent, unlike in homogeneous materials.
  • Sensitivity analysis highlights the role of Murnaghan's constants in wave response.
  • Numerical examples demonstrate relevance for characterizing dislocation densities in shot-peened metals.

Conclusions:

  • The frequency dependence of harmonic coupling offers a new avenue for probing material properties.
  • The theoretical framework provides a basis for non-destructive evaluation of materials with microstructural variations.
  • Low-frequency predictions align with recent experimental observations in relevant materials.