The axisymmetric love wave in elastic solids and its special properties

With the advances of material processing technology and miniaturization of mechanical devices and components, it is clear now that curvilinear coordinate systems in dealing with special configurations of elastic solids including cylinders are also naturally needed in the analytical process. By adopting the cylindrical coordinates, it is found that the Love wave in semi-infinite solids possess the same velocity as in the Cartesian coordinates, but the displacement is dependent on radius near the origin and decaying slowly with the radius by exhibiting a strong contrast of the uniform displacement in the Cartesian formulation. Numerical examples show that the asymptotic approximation is accurate in one wavelength away from the origin, implying that solutions will be different only in the vicinity of the point of excitation.