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Wave scattering on lattice structures involving an array of cracks
Gaurav Maurya1, Basant Lal Sharma1
1Department of Mechanical Engineering, Indian Institute of Technology Kanpur, Kanpur, India.
Proceedings. Mathematical, Physical, and Engineering Sciences
|May 14, 2020
Summary
This study analyzes wave scattering from periodic crack arrays in waveguides. Findings enable tunable interfaces for controlling energy transmission at the atomic scale.
Area of Science:
- Wave mechanics
- Condensed matter physics
- Materials science
Background:
- Wave scattering phenomena are crucial in various physical systems.
- Understanding wave interaction with defects like cracks is essential for material integrity and energy control.
- Periodic structures offer unique properties for wave manipulation.
Purpose of the Study:
- To investigate the scattering of waves by a vertical array of equally spaced cracks on a square lattice.
- To develop a semi-analytical solution for wave scattering from finite and semi-infinite cracks in a waveguide.
- To analyze the reflectance and transmittance properties of such crack arrays.
Main Methods:
- Utilizing Floquet periodicity to simplify the problem to scattering from a single crack in a waveguide.
- Employing the discrete Green's function for finite cracks.
- Applying the Wiener-Hopf technique for semi-infinite cracks.
Main Results:
- A semi-analytical solution was obtained for wave scattering from crack arrays.
- Reflectance and transmittance were analyzed in relation to incident wave parameters.
- The study provides insights into wave behavior at crack interfaces.
Conclusions:
- The scattering of waves by periodic crack arrays can be effectively modeled.
- The developed methods allow for the analysis of energy transmission control.
- Potential applications include the design of tunable atomic-scale interfaces for frequency-dependent energy control.
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