Hyperbolic-elliptic model for surface wave in a pre-stressed incompressible elastic half-space

•A hyperbolic-elliptic model for surface wave in a pre-stressed incompressible half-space induced by surface loading.•Representation of displacements in terms of a single harmonic function.•Hyperbolic equations for surface displacements. The paper aims at derivation of the asymptotic model for surfa...

Full description

Saved in:
Bibliographic Details
Published in:Mechanics research communications 2018-09, Vol.92, p.49-53
Main Authors: Khajiyeva, L.A., Prikazchikov, D.A., Prikazchikova, L.A.
Format: Article
Language:English
Subjects:
Asymptotic
Hyperbolic-elliptic
Incompressible
Pre-stress
Surface wave
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:•A hyperbolic-elliptic model for surface wave in a pre-stressed incompressible half-space induced by surface loading.•Representation of displacements in terms of a single harmonic function.•Hyperbolic equations for surface displacements. The paper aims at derivation of the asymptotic model for surface wave propagating in a pre-stressed incompressible elastic half-space, subject to prescribed surface loading. The approach relies on the slow-time perturbation procedure, extending the previously known hyperbolic-elliptic formulations for surface waves in compressible linearly elastic solids. Within the derived model, the decay away from the surface is governed by a pseudo-static elliptic equation, whereas wave propagation is described by a hyperbolic equation on the surface. The effect of pre-stress, namely, the principal Cauchy stress σ2, is investigated. Finally, an illustrative example of the Lamb problem is considered, demonstrating the efficiency of the approach.
ISSN:0093-6413
1873-3972
DOI:10.1016/j.mechrescom.2018.07.006