Transition from transient response to steady state for an anisotropic layered medium under dynamic antiplane loading

In this study, the transition from transient to steady-state responses for anisotropic layered media subjected to antiplane time harmonic loading is investigated. To solve this complicated problem, a linear coordinate transformation is introduced and successfully used to transform the anisotropic layered medium problem to an isotropic problem. The transient responses are obtained by the convolution of time harmonic loading function with transient solutions derived analytically from an effective matrix method. The steady-state problem is solved by applying the wave number integral representation. For numerical calculations, the transient and steady-state responses of an anisotropic thin layer overlying a half-space are considered. The transition behavior from transient solution to steady state is presented and discussed in detail.