Geometrical nonlinearity stabilizes a wave solid-state gyro

Abstract

It was recognized long ago that quasi-harmonic standing waves in a thin-walled axisymmetric resonator, mounted on a rotating platform, are subject to a precession. This significant phenomenon is naturally associated with a concept of a solid-state wave gyro, or an inertial instrument used to measure angular rotation rate, as if any wave may be interpreted as a material particle moving in a rotating frame of reference. Because there are no typical mechanical parts, these wave sensors can be utilized with a lot of advantages. To run such a gyro in vita, one should excite and keep on by certain means a standing wave in the thin-walled axisymmetric resonator. Up to now, there are known two ways how to do it, and namely, using either external or parametric resonant mechanisms of excitation. Although both cases necessarily require an additional feedback control device in order to stabilize instable or other parasite oscillations of the resonator. This paper, following the study of nonlinear waves in a thin circular ring, demonstrates that the solid-state wave gyro may be naturally stabilized just at the expense of the geometrical nonlinearity by combining advantages of both the positional resonant excitation and the parametric resonance.