Dynamic stability of a cylindrical shell contacting with an anisotropic medium

The problem of dynamic stability of an elastic cylindrical shell, whose internal side is suddenly subjected to radial velocities but its external side is in welded contact with an elastic curvilinearly anisotropic medium, is considered. Besides, the shell is under uniform axial pressure. Transient excitation of the shell gives rise to three types of cylindrical shock waves in the contacting elastic transversely isotropic medium. The solution behind the contact boundary is constructed by the ray method. It has been shown that the behaviour of the shell's radial displacement in time is dependent on the level of axial pressure: under the axial pressure in excess of the critical value, the normal displacements of some set of points belonging to the shell may increase significantly in a short time.