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Asymptotic Formulation for the Rayleigh Wave on a Nonlocally Elastic Half-Space

Prikazchikov, Danila A.

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Abstract

This paper deals with the Rayleigh wave, propagating on a nonlocally elastic, linearly isotropic half-space, excited by a prescribed surface loading. The consideration develops the methodology of hyperbolic–elliptic models for Rayleigh and Rayleigh-type waves, and relies on the effective boundary conditions formulated recently, accounting for the crucial contributions of the nonlocal boundary layer. A slow-time perturbation scheme is established, leading to the reduced model for the Rayleigh wave field, comprised of a singularly perturbed hyperbolic equation for the longitudinal wave potential on the surface, acting as a boundary condition for the elliptic equation governing the decay over the interior. An equivalent alternative formulation involving a pseudo-differential operator acting on the loading terms, with parametric dependence on the depth coordinate, is also presented.

Citation

Prikazchikov, D. A. (2023). Asymptotic Formulation for the Rayleigh Wave on a Nonlocally Elastic Half-Space. Vibration, 6(1), 57-64. https://doi.org/10.3390/vibration6010005

Journal Article Type Article
Acceptance Date Jan 4, 2023
Online Publication Date Jan 7, 2023
Publication Date Jan 7, 2023
Journal Vibration
Print ISSN 2571-631X
Publisher MDPI
Peer Reviewed Peer Reviewed
Volume 6
Issue 1
Pages 57-64
DOI https://doi.org/10.3390/vibration6010005
Keywords Rayleigh wave; nonlocal; boundary layer; asymptotic
Public URL https://keele-repository.worktribe.com/output/425383
Publisher URL https://www.mdpi.com/2571-631X/6/1/5

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