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

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

doi:10.1098/rspa.2016.0178

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

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

Authors

Julius Kaplunov j.kaplunov@keele.ac.uk

Danila Prikazchikov d.prikazchikov@keele.ac.uk

G.A. Rogerson

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.

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