Edge bending wave on a thin elastic plate resting on a Winkler foundation

Kaplunov, J.; Prikazchikov, D.A.; Rogerson, G.A.

Abstract

This paper is concerned with elucidation of the general properties of the bending edge wave in a thin linearly elastic plate that is supported by a Winkler foundation. A homogeneous wave of arbitrary profile is considered, and represented in terms of a single harmonic function. This serves as the basis for derivation of an explicit asymptotic model, containing an elliptic equation governing the decay away from the edge, together with a parabolic equation at the edge, corresponding to beam-like behaviour. The model extracts the contribution of the edge wave from the overall dynamic response of the plate, providing significant simplification for analysis of the localized near-edge wave field.

Citation

Kaplunov, J., Prikazchikov, D., & Rogerson, G. (2016). Edge bending wave on a thin elastic plate resting on a Winkler foundation. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 472(2190), https://doi.org/10.1098/rspa.2016.0178

• Journal Article Type: Article
• Acceptance Date: Apr 14, 2016
• Online Publication Date: Jun 1, 2016
• Publication Date: 2016-06
• Publicly Available Date: May 26, 2023
• Journal: Proceedings of the Royal Society of London: Mathematical, Physical and Engineering Sciences
• Print ISSN: 1364-5021
• Publisher: The Royal Society
• Peer Reviewed: Peer Reviewed
• Volume: 472
• Issue: 2190
• DOI: https://doi.org/10.1098/rspa.2016.0178
• Keywords: Bending edge wave, harmonic function, dual parabolic-elliptic formulation, perturbation
• Publisher URL: http://dx.doi.org/10.1098/rspa.2016.0178