Vibration of a hemispherical shell gyro excited by an electrostatic field

Abstract

In this paper the stability and precession phenomenon of the modal pattern of a rotating hemispherical shell gyro excited parametrically by electrostatic forces is investigated. Nonlinear modal equations of the rotating shell under small strain and moderate rotation are derived by following Niordson’s thin shell theory. The method of multiple time scales is used to determine quantitatively the vibration displacement of the shell from which the precession rate of the modal vibration pattern can be extracted. Floquet theory is employed to study the stability of the analytical solution. Numerical simulation verifies the analytical results.