Coupled horizontal and rocking vibrations of a rigid circular disc on a transversely isotropic and layered half-space with imperfect interfaces

Abstract

A new semi-analytical method is developed for solving the coupled horizontal and rocking vibrations of a rigid circular disc on the surface of a transversely isotropic multilayered half-space with imperfect interfaces. By virtue of the dual variable and position method, the recursive relation among different layers is established so that the final expansion coefficients of the displacement and traction vectors corresponding to the surface loading can be expressed in terms of the cylindrical system of vector functions. The physical-domain response by the surface loading (i.e., the forward solution) is obtained by carrying out the semi-infinite line integral involved. To solve for the corresponding coupled interaction problem between the surface rigid disc and layered elastic medium, the loading disc area is discretized into annular load-rings containing basic horizontal constant and vertical linear loads with unknown weights. These weights are then determined by applying an integral least-square approach with a Lagrange multiplier. Finally, the coupled time-harmonic compliances are derived by virtue of the equilibrium of the applied load on the disc and the reaction force on the half-space side. Selected numerical examples on the horizontal, moment and coupling compliances are presented to study the effect of material layering, anisotropy, interface behavior as well as input frequency. The coupling compliance is investigated in detail for the first time as compared to the horizontal and moment ones. The fully coupled, semi-coupled and decoupled schemes are also discussed with numerical examples so that one can easily access the relative accuracy among them when an actual layered structure is under both horizontal and rocking vibrations. This is important since the coupling compliance could significantly contribute to the vibrational behavior of the layered system at certain frequency.