Dynamic stability of an elastic cylindrical shell being in external contact with an elastic isotropic medium with respect to nonstationary excitations

摘要

The problem of nonstationary vibrations of an infinitely long cylindrical shell of constant thickness, whose internal side is suddenly subjected to tangential and normal displacement velocities but its external side is in welded or smooth contact with an elastic medium, is considered. The shelf is kept under uniform axial pressure. Nonstationary excitation to the shell gives rise to two types of cylindrical shock waves in the contacting elastic isotropic medium. The solution behind the wave front up to the contact boundary is constructed by using ray series. Coefficients of the ray Series are found from recurrent differential equations of the ray method within the accuracy of arbitrary functions dependent on angular and axial coordinates. Arbitrary functions, in their turn, are determined from the conditions of continuity for displacements and stresses on the contact boundary of the shelf and the medium, as well as from the initial conditions. Calculations have been carried out with due account of five terms of the ray series for the functions to be found. The time dependence of the tangential and normal components of the displacement vector for the cylindrical shell has been obtained. It has been shown that, in time, the behavior of the shell's normal displacement is dependent on the magnitude of the axial pressure: under axial pressure in excess of the critical value, the normal displacements of some set of points belonging to the shell may increase essentially in a short time. [References: 7]