E Young’s modulus

Nonlinear dynamic response and associated instabilities of rotating thin circular rings for use in vibratory angular rate sensors is investigated via an analytical method. The governing equations of in-plane flexural motion of rotating thin circular rings are developed via the Hamilton’s principle. The derived ordinary differential equations represent a two-degree-of-freedom time-varying nonlinear gyroscopic system. The approximate solutions ob-tained via the method of averaging have been shown to exhibit the presence of softening type of nonlinearities. A decoupling technique suitable for de-coupling the gyroscopic coupling is employed in the present analysis. Fur-ther effects of sensor parameters, such as the presence of mass mismatch, stiffness of elastic foundation, and the presence of thermal expansion, are quantified