Belova M. Critical states of thin-wall elastic shells in simple and compound rotations

Computer simulation of statical and vibrational states of cylindrical, conical, paraboloidal, spherical, ellipsoidal and combined shells under conditions of their simple and compound rotations is performed. Critical values of the shells angular velocities in simple rotation and resonant angular velocities in compound rotations are found for different values of their geometric parameters. It is established that, as a rule, the critical angular velocities are rather less than resonant velocities for elongated shells and there is the inverse effect for shallow shells. It is demonstrated that the critical velocities are realized when the corresponding natural frequencies of rotating shells become equal zero. The resonant states of the considered shells are originated in compound rotation, when the corresponding natural frequency for the mode of inverse precession coincides with the angular velocity value itself. Key words: thin shells, simple rotation, buckling, compound rotation, resonant precession vibrations.