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

Prikazchikov, D

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


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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.

Journal Article Type Article
Acceptance Date Jan 4, 2023
Publication Date Jan 7, 2023
Publicly Available Date Mar 28, 2024
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
Publisher URL https://www.mdpi.com/2571-631X/6/1/5

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