The motion of one-component surface waves
type: Item
instance of: scholarly article
title: The motion of one-component surface waves
zbMATH Open document ID: 0792.73025
DOI: 10.1016/0022-5096(92)90042-Z
published in: Journal of the Mechanics and Physics of Solids
publication date: 1993-11-03T00:00:00Z
review text: The author shows that in a linear homogeneous anisotropic elastic semi- space \(| x_ 1|<\infty\), \(x_ 2\geq 0\), \(| x_ 3|<\infty\) there is a surface wave propagating in the \(x_ 1\)- direction of the form \(\underline{u}= (u_ 1,0,u_ 3)\), where \(u_ 1= a_ 1\exp [ik(x_ 1+ px_ 2-vt)]\), \(u_ 3=a_ 3 \exp[ik(x_ 1+ px_ 2-vt)]\), provided a number of conditions on the elastic compliances are postulated. In the above expressions \(u_ 1\) and \(u_ 3\) denote the displacement components in the \(x_ 1\) and \(x_ 3\) directions, respectively; \(a_ 1\) and \(a_ 3\) are the amplitudes of \(u_ 1\) and \(u_ 3\); \(k\) is a given positive wave number, \(i^ 2=-1\), and \(p\) and \(v\) can be expressed in terms of the elastic compliances. Also, the author shows that the wave has the unique feature that the deformation is both plane strain and plane stress with respect to the \((x_ 1,x_ 3)\)- plane, and the pair \((u_ 1,u_ 3)\) as well as the associated pairs like \(\underline{v}=(\dot u_ 1,\dot u_ 3)\) \((\cdot=\partial/\partial t)\) describe elliptic paths on a plane parallel to the \((x_ 1,x_ 3)\)- plane.
Mathematics Subject Classification ID: 74J15
Mathematics Subject Classification ID: 74E10
zbMATH DE Number: 429368
zbMATH Keywords: linear homogeneous anisotropic elastic semi-space
zbMATH Keywords: elastic compliances
zbMATH Keywords: elliptic paths
author: Ting, T. C. T.
reviewed by: Józef Ignaczak
MaRDI profile type: Publication
cites work: Q4003888
cites work: The behaviour of elastic surface waves polarized in a plane of material symmetry. I. Addendum
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cites work: Some identities and the structure of 𝑁ᵢ in the Stroh formalism of anisotropic elasticity
description: scientific article; zbMATH DE number 429368