MODAL PRECESSION OF A HEMISPHERICAL SHELL GYRO EXCITED BY ELECTROSTATIC-FIELD

In this paper the precessional phenomenon of the modal pattern of a ro tating hemispherical shell gyro excited parametrically by electrostati c forces is investigated. Niordson's thin shell theory, which included the extensional deformation of the middle surface and was derived in an invariant form; is employed and the rotary inertia is added. The mo dal equations of motion are coupled by the Coriolis force and the appl ied electric field. The method of multiple scales is used to determine quantitatively the vibrational displacement of the shell from which t he precessional rate of the modal vibration pattern can be extracted. It is also shown that the modal precessional rate for the parametrical ly excited vibration case is found to be the same as that of the freel y vibrating one. Experiments are performed on a rotating quartz hemisp herical shell excited electrostatically to verify the theoretical resu lts.