Dynamic Reissner–Sagoci problem for a transversely isotropic half-space containing finite length cylindrical cavity

Abstract

A transversely isotropic linear elastic half-space containing a circular cylindrical cavity of finite length with a depth-wise axis of material symmetry is considered to be under the effect of a mono-harmonic torsional motion applied on a rigid circular disc with the same radius of the cavity and welded at the bottom of the cavity. With the aid of Fourier sine and cosine integral transforms, the mixed boundary value problem is reduced to a generalized Cauchy singular integral equation for the unknown shear stress. The Cauchy integral equation involved in this paper is analytically investigated such that the solution is written in the form of a known singular function multiplied by an unknown regular function. The regular part of the shear stress is numerically determined with the use of Gauss–Jacobi integration formula. Series representation of the stress and displacement are obtained, and it is shown that their degenerated form to the static problem of isotropic material is coincide with the existing solutions in the literature. To investigate the effects of material anisotropy and the length of cavity, the tangential displacement and the shear stress in between the rigid disc and the bottom of cavity are numerically evaluated and illustrated, where some differences are distinguished. With the differences illustrated in this paper for different length of cavity, it is recognized that the effect of length of cavity cannot be neglected in analysis and design. Different results for different degrees of anisotropy shows that the anisotropy of the material is a normal behavior, which should be considered in this kind of medium.