On a Hyperbolic Equation for the Rayleigh Wave

Kaplunov, J. D.; Prikazchikov, D. A.; Sabirova, R. F.

Abstract

A 1D hyperbolic equation is derived for the Rayleigh wave induced by prescribed surface loading. The wave operator turns out to be independent of the vertical coordinate, which appears only in the right hand side of the equation as a parameter within the pseudo-differential operator acting on the given load. It is shown that in case of the classical 2D Lamb problem this operator causes smoothening of the surface concentrated impulse as the depth increases. The suggested formulation enables revealing of the peculiarities of surface elastic wave.

Citation

Kaplunov, J. D., Prikazchikov, D. A., & Sabirova, R. F. (2023). On a Hyperbolic Equation for the Rayleigh Wave. Доклады Академии Наук / Doklady Physics, 67(10), 424-427. https://doi.org/10.1134/S1028335822100056

• Journal Article Type: Article
• Acceptance Date: Jul 26, 2022
• Online Publication Date: Mar 24, 2023
• Publication Date: Mar 24, 2023
• Deposit Date: Jun 5, 2023
• Journal: DOKLADY PHYSICS
• Print ISSN: 1028-3358
• Electronic ISSN: 1562-6903
• Publisher: MAIK Nauka/Interperiodica
• Peer Reviewed: Peer Reviewed
• Volume: 67
• Issue: 10
• Pages: 424-427
• DOI: https://doi.org/10.1134/S1028335822100056
• Keywords: Rayleigh wave; hyperbolic equation; pseudo-differential operator; Lamb problem