| Abstract: | A method of determining the regions of dynamic instability of an orthotropic cylindrical shell "bonded" to an elastic cylinder is proposed. An expression for the core reaction is obtained from the coupling conditions for the forces normal to the lateral surface and the radial displacements of the shell and the core at the contact surface. When the reaction is substituted in the system of equations of motion of the shell, the part corresponding to the free vibrations of the cylinder is discarded. The system of equations of motion of the shell is reduced to an equation of Mathieu type, from which transcendental equations for determining the boundaries of the regions of dynamic instability are obtained. These regions are analyzed for various modes of loss of stability and different values of the core modulus of elasticity. |
