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

Khajiyeva, L.A.; Prikazchikov, D.A.; Prikazchikova, L.A.

Abstract

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 s 2, is investigated. Finally, an illustrative example of the Lamb problem is considered, demonstrating the efficiency of the approach.

Citation

Khajiyeva, L., Prikazchikov, D., & Prikazchikova, L. (2018). Hyperbolic-elliptic model for surface wave in a pre-stressed incompressible elastic half-space. Mechanics Research Communications, 92, 49-53. https://doi.org/10.1016/j.mechrescom.2018.07.006

• Journal Article Type: Article
• Acceptance Date: Jul 14, 2018
• Publication Date: Sep 1, 2018
• Journal: Mechanics Research Communications
• Print ISSN: 0093-6413
• Publisher: Elsevier
• Peer Reviewed: Not Peer Reviewed
• Volume: 92
• Pages: 49-53
• DOI: https://doi.org/10.1016/j.mechrescom.2018.07.006
• Keywords: pre-stress, incompressible, surface wave, asymptotic, hyperbolic-elliptic
• Publisher URL: https://doi.org/10.1016/j.mechrescom.2018.07.006