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An asymptotic hyperbolic-elliptic model for flexural-seismic metasurfaces.
P T Wootton1, J Kaplunov1, D J Colquitt2
1School of Computing and Mathematics, Keele University, Keele ST5 5BG, UK.
Proceedings. Mathematical, Physical, and Engineering Sciences
|August 20, 2019
Summary
This study introduces a new model for elastic surface waves using flexural resonators. The simplified model accurately predicts wave speeds and shows how junction conditions control stop bands in elastic metasurfaces.
Area of Science:
- Physics
- Materials Science
- Mechanical Engineering
Background:
- Previous research focused on compressional resonators in periodic arrays on elastic half-spaces.
- Flexural motion of resonators was less explored, limiting understanding of elastic surface wave propagation.
Purpose of the Study:
- To investigate the impact of flexural resonator motion on elastic surface waves.
- To develop a simplified, accurate model for Rayleigh-like wave propagation.
- To analyze the influence of junction conditions on wave propagation characteristics.
Main Methods:
- Adaptation of an asymptotic methodology to model flexural vibrations of Euler-Bernoulli beams on an elastic half-space.
- Derivation of an explicit scalar hyperbolic equation for wave propagation.
- Analysis of dispersion relations and closed-form solutions.
Main Results:
- A significantly simpler dispersion relation compared to classical approaches.
- Accurate prediction of surface wave speeds near Rayleigh wave speeds.
- Demonstration that junction conditions dramatically influence stop band distribution and size.
Conclusions:
- Flexural motion offers new possibilities for modeling elastic surface waves.
- The simplified asymptotic model provides insights into wave behavior and metasurface design.
- Novel experimental setups for elastic metasurfaces can be developed by leveraging flexural vibrations.
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