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Quasi-two-dimensional transfer of elastic waves.
Nicolas P Trégourès1, Bart A van Tiggelen
1Laboratoire de Physique et Modélisation des Milieux Condensés, CNRS/Université Joseph Fourier, Boîte Postale 166, 38042 Grenoble Cedex 09, France.
Summary
This study presents a new theory for elastic wave scattering in heterogeneous plates, detailing mode coupling and wave propagation. It enables analysis of phenomena like coherent backscattering near plate surfaces.
Area of Science:
- Physics
- Wave Propagation
- Materials Science
Background:
- Heterogeneous plates with free surfaces exhibit complex elastic wave behavior.
- Understanding wave scattering and mode coupling is crucial for analyzing wave propagation in such structures.
Purpose of the Study:
- To develop a theoretical framework for multiple scattering of elastic waves in a heterogeneous plate.
- To describe the coupling of eigenmodes (Rayleigh, shear horizontal, Lamb waves) within the plate.
- To investigate coherent backscattering phenomena near the plate surface.
Main Methods:
- Derivation of a time-dependent, quasi-two-dimensional radiative transfer equation.
- Treatment of traction-free boundary conditions at the wave equation level.
- Analysis of mode-coupling rates and mode lifetimes.
- Application of the diffusion approximation for large lapse times.
Main Results:
- Expressions relating small-scale fluctuations to mode lifetimes and coupling rates.
- A model that accounts for elastic transfer over macroscopic horizontal distances.
- The diffusion approximation simplifies the model for later time scales.
Conclusions:
- The developed theory accurately describes elastic wave scattering and mode coupling in heterogeneous plates.
- The model provides a foundation for studying phenomena like coherent backscattering.
- The diffusion approximation offers a simplified approach for analyzing wave propagation at later times.