DYNAMICAL TORSION OF VISCOELASTIC CONE

Propagation of torsion waves in a viscoelastic cone of semi-infinite and finite length are examined by the Laplace integral transform method and the method of separation of variables. The inverse transforms for elastic cone are obtained using the contour integration method and the residue theory. Using this solution and the solution of auxiliary one-dimensional problem for viscoelastic half-space with any hereditary function, it is proved that the solution for viscoelastic cone is in the form of generalized convolution of these solutions. The solution of the auxiliary problem for any creep kernel is constructed in the form of absolutely and uniformly convergent series. As an example the solution of the auxiliary problem has been obtained for the creep kernel as the sum of exponential functions, for Maxwell and the standard linear solid models and for the weakly singular Abel kernel. Solutions for dynamical problems of viscoelastic half-space under the torsion point action, half-space with the spherical cavity on the surface and circular cylinder are obtained as particular cases.