A second-order asymptotic model for Rayleigh waves on a linearly elastic half plane

Wootton, Peter T; Prikazchikov, Danila; Kaplunov, Julius

Abstract

We derive a second-order correction to an existing leading-order model for surface waves in linear elasticity. The same hyperbolic–elliptic equation form is obtained with a correction term added to the surface boundary condition. The validity of the correction term is shown by re-examining problems which the leading-order model has been applied to previously, namely a harmonic forcing, a moving point load and a periodic array of compressional resonators.

Citation

Wootton, P. T., Prikazchikov, D., & Kaplunov, J. (2020). A second-order asymptotic model for Rayleigh waves on a linearly elastic half plane. IMA Journal of Applied Mathematics, 85(1), 113 - 131. https://doi.org/10.1093/imamat/hxz037

• Journal Article Type: Article
• Acceptance Date: Dec 13, 2019
• Online Publication Date: Feb 24, 2020
• Publication Date: 2020-02
• Journal: IMA Journal of Applied Mathematics
• Print ISSN: 0272-4960
• Publisher: Oxford University Press
• Peer Reviewed: Peer Reviewed
• Volume: 85
• Issue: 1
• Pages: 113 - 131
• DOI: https://doi.org/10.1093/imamat/hxz037
• Keywords: Rayleigh waves; asymptotic; second order
• Publisher URL: https://academic.oup.com/imamat/article-abstract/85/1/113/5743496?redirectedFrom=fulltext