The motion of one-component surface waves
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.
linear homogeneous anisotropic elastic semi-space
scientific article; zbMATH DE number 429368
scientific article