This paper is concerned with the investigation of the vertical vibration of a rigid circular disc buried at an arbitrary depth in a transversely isotropic half space in such a way the axis of material symmetry of the half space is normal to the surface of it and parallel to the vibration direction. By using the Hankel integral transforms, the mixed boundary-value problem is transformed to a pair of integral equations called dual integral equations, which generally can be reduced to a Fredholm integral equation of the second kind. With the aid of complex variable or contour integration, the governing integral equation is numerically solved in the general dynamic case. Two degenerated cases (i) the disc is buried in a transversely isotropic full space, and (ii) rigid circular disc is attached on the surface of the half space are discussed. The reduced static case of the dual integral equations is solved analytically and the vertical displacement, the contact pressure and the static impedance/compliance function are explicitly found. It is shown that the vertical pressure and the compliance function reduced for isotropic half space are identical to the previous solutions reported in the literature. The dynamic contact pressure under the disc and the impedance function are numerically evaluated in general dynamic case and graphically shown that the singularity exists in the contact pressure at the edge of the disc is the same as the static case. In addition, the impedance functions evaluated here for the isotropic domain are collapsed on the solution given by Luco and Mita. To show the effect of different material anisotropy, the numerical evaluations are given for some different transversely isotropic materials and compared. © 2010 Elsevier Ltd.
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