Transient analysis of anisotropic multilayered media subjected to dynamic antiplane loadings

The transient responses of anisotropic multilayered media subjected to arbitrarily distributed antiplane loadings are investigated. To solve the complicated problem, a linear coordinate transformation is introduced and successfully used to transform the anisotropic layered medium problem to an isotropic problem. The relationship between field quantities of the anisotropic problem and the corresponding isotropic problem are established for a Cartesian coordinate system. The boundary value problem is solved by using the integral transform method. The solutions in the Laplace transform domain are constructed in the form of a power series of the phase-related reflection and transmission matrices. Each term in the series represents a reflected or transmitted wave. The transient solution is then obtained by means of Cagniard's method. The corresponding static solution is also derived by application of the final value theorem. For numerical calculations, the transient responses of an anisotropic thin layer overlying a half-space are considered. The transition behavior from transient response to static value is presented and discussed in detail.