Shear waves in finite strain generated at the surface of a viscoelastic half-space

An initially undisturbed viscoelastic half-space is subjected to a monotonically increasing transverse particle velocity at the surface. The ensuing transient wave motion in finite strain is studied. By employing the theory of propagating surfaces of discontinuity the complete solution for the displacement is obtained as a Taylor expansion about the time of arrival of the wave front. It is shown that the coefficients in the expansion are the solutions of linear, inhomogeneous, ordinary differential equations of the first-order. The series solution is valid at all times, if the elastic stress-deformation curve corresponding to the initial values of the viscoelastic kernel functions are concave with respect to the deformation gradient axis.