GYROSCOPICALLY INDUCED VIBRATIONS OF PLATES AND MEMBRANES

An analytical study is presented for the vibrational response of simply supported rectangular plates and membranes subjected to gyroscopically induced inertia loads. The members are considered to be spinning at a constant rate while simultaneously undergoing a constant precession at a fixed angle of nutation. The equations of motion are formulated for members mounted either parallel or perpendicular to the spin axis. It is found that these equations contain distributed harmonic inertia forces whose amplitudes and frequencies are dependent on the spin and precessional angular velocities. The solutions of these equations show that the natural frequencies of the plates and membranes are reduced by the effects of spin and precession and that this effect may be appreciable, particularly for membranes. It is also shown that only certain modes of vibration will respond to the gyroscopically induced inertia loading and that, for members mounted parallel to the spin axis, the motion is governed by a set of Mathieu equations along with the associated stability characteristics. © 1968 American Institute of Aeronautics and Astronautics, Inc., All rights reserved.