Effect of nonlinear electrostatic forces on the dynamic behaviour of a capacitive ring-based Coriolis Vibrating Gyroscope under severe shock

•A MEMS CVG is modelled as a supported ring under electrostatic nonlinear forces.•The number of modes needed to correctly predict the sensor dynamics is investigated.•Convergence analyses on the nonlinear force polynomial approximation are performed.•Nonlinear electrostatic effects cause mode coupling.•Nonlinear effects can degrade sensor performance under severe chock. This paper investigates the dynamic behaviour of capacitive ring-based Coriolis Vibrating Gyroscopes (CVGs) under severe shock conditions. A general analytical model is developed for a multi-supported ring resonator by describing the in-plane ring response as a finite sum of modes of a perfect ring and the electrostatic force as a Taylor series expansion. It is shown that the supports can induce mode coupling and that mode coupling occurs when the shock is severe and the electrostatic forces are nonlinear. The influence of electrostatic nonlinearity is investigated by numerically simulating the governing equations of motion. For the severe shock cases investigated, when the electrode gap reduces by ∼60%, it is found that three ring modes of vibration (1θ,2θ and 3θ) and a 9th order force expansion are needed to obtain converged results for the global shock behaviour. Numerical results when the 2θ mode is driven at resonance indicate that electrostatic nonlinearity introduces mode coupling which has potential to reduce sensor performance under operating conditions. Under some circumstances it is also found that severe shocks can cause the vibrating response to jump to another stable state with much lower vibration amplitude. This behaviour is mainly a function of shock amplitude and rigid-body motion damping.