Time-harmonic loading over transversely isotropic and layered elastic half-spaces with imperfect interfaces

In this study, we investigate the time-harmonic response of transversely isotropic and layered half-spaces with imperfect interfaces. The solution in each layer is expressed in terms of the cylindrical system of vector functions so that the normal (dilatational) and shear (torsional) deformations can be separated and solved in terms of the LM- and N-types of the vector function system. A new method called DVP (dual variable and position method) is then utilized to solve the corresponding layered problem. Multiple loads in both vertical and horizontal directions over circular regions on the surface of the layered half-space can be applied and multiple imperfect interfaces can be assumed to model the real interface condition. Several imperfect interface models, including the direct thin-layer, spring, and density models, are introduced and their equivalence, difference, as well as their effects on the response of the layered half-space are investigated. The formulation is validated with existing solutions and is further applied to study the time-harmonic responses of various layered half-spaces. Numerical results demonstrate clearly the influence of the input frequency, thin interlayer modulus, and the relative distance between the field point and the imperfect interface location on the time-harmonic response of layered half-spaces.