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The edge wave on an elastically supported Kirchhoff plate
Julius Kaplunov1, Danila A Prikazchikov1, Graham A Rogerson1
1School of Computing and Mathematics, Keele University, Keele, Staffordshire, ST5 5BG, United Kingdom.
The Journal of the Acoustical Society of America
|October 18, 2014
Summary
Bending edge waves on a Kirchhoff plate with a Winkler foundation exhibit a cut-off frequency and minimum phase velocity. This minimum velocity is critical for moving edge loads, similar to beams.
Area of Science:
- Solid Mechanics
- Plate Theory
- Wave Propagation
Background:
- Edge waves are crucial in structural analysis.
- Winkler foundations influence wave behavior.
- Kirchhoff plate theory provides a simplified model.
Purpose of the Study:
- Analyze bending edge waves on a Kirchhoff plate.
- Investigate the effect of a Winkler foundation.
- Determine the critical speed for moving edge loads.
Main Methods:
- Mathematical analysis of wave propagation.
- Application of Kirchhoff plate theory.
- Incorporation of Winkler foundation model.
Main Results:
- A non-zero cut-off frequency for edge waves was identified.
- A local minimum in phase velocity was observed.
- This minimum phase velocity defines a critical load speed.
Conclusions:
- Winkler foundations introduce unique characteristics to edge wave propagation.
- The critical speed is analogous to 1D moving load problems.
- Findings are relevant for structures with elastic foundations.
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