PRECESSION OF VIBRATIONAL-MODES OF A ROTATING HEMISPHERICAL SHELL

The precession of flexural vibrational modes of a rotating hemispheric al thin shell is investigated. Niordson's thin shell theory which allo ws the stretch of the middle surface, is employed to derive the equati ons of bending vibration of a rotating shell. The shell is assumed to rotate at a low constant speed, so the centrifugal force is neglected and only the Coriolis inertial force is included in the equations of m otion. The ratio of the rotating speed of the shell to the natural fre quency of the first flexural mode, which is denoted by epsilon, is ass umed small. The solutions of displacements are expanded in the power s eries of epsilon. The unperturbed (zero-order) equations, which repres ent the free vibration of the nonrotating shell, are proved to be self -adjoint. The perturbed frequency can be extracted from the equation o f solvability condition directly without solving the perturbed system. The precession rate of the vibrational modes obtained theoretically i n an analytical Expression is verified by experiment. These results ar e helpful for the design of hemispherical resonant gyroscope.