MATHEMATICAL SIMULATION OF THE DYNAMICS OF SHALLOWLY SUBMERGED TUNNELS AND PIPE LINES
The model transport problem of the dynamics of an elastic half-space with a cylindrical cavity is considered. Along the cavity, which is supported by an elastic cylindrical shell, the transport load is moving with constant velocity. Using the method of incomplete division of variables, analytical solutions are obtained for subsonic and supersonic velocities of the transport loads and its computer realization is carried out for the subsonic case. The stressed-strained state of an elastic shell and of the surrounding medium for various motion velocities is determined using numerical experiments. The effect of the parameters of the shell, of the contact conditions and velocities of the motion on the stressed-strained state of the array and the free surface is studied. The dispersion curves are analyzed for the cases of slipping and strong contact of the shell with the surrounding medium; the critical velocity of the displacement of the load, for which the resonance phenomena in tunnels appear, is determined.