Elastodynamics of a multilayered transversely isotropic half-space due to the rigid motion of foundation

A transversely isotropic multilayered half-space is considered as a support of a massless circular rigid foundation undergoing forced vibrations. The problem formulation adopts the axes of material symmetry of layers with the half-space aligned depth-wise. The problem solution involves two coupled wave equations accompanied by mixed boundary conditions. Employing the influence functions, which contain the effects of the entire domain, i.e. reflecting and refracting phenomena as a consequence of the inhomogeneity of media, the governing equations reduce to a set of Fredholm integral equations of the second kind, which are then solved numerically. To illustrate the method's accuracy, a comparison between the result of this study and the existing solutions for the vibration of a foundation on a layered isotropic half-space is given. Also, the result of the vibration of the disc on a transversely isotropic half-space is determined and compared to the available solution in the literature To explore the effect of stratification as well as material anisotropy on wave motion, dispersion curves corresponding to surface waves are shown. These curves indicate the existence of limiting values for both small and large values of wavenumbers as compared to layers’ thicknesses. Also, exploring the effect of various material properties (e.g., the negative Poisson ratio) and different layers’ arrangements, it is found that the impedance functions of the multilayered medium are closely related to the frequency of excitation while showing almost no sensitivity to properties of the half-space and, in particular, for rocking motion.