Nonlinear elastic coupling in tether-suspended MEMS

This paper presents stiffness coefficients for the geometrical nonlinear elastic coupling inherent to typical MEMS suspensions. In addition, our model provides an explanation for quadrature error in vibratory gyroscopes, which has commonly been attributed to device asymmetries and other imperfections. Through numerical simulations we show that significant quadrature error motion exists even for devices with perfectly ideal symmetry. The simulated dynamics are compared to experimental measurements in the literature. Another finding is the existence of optimal MEMS suspension designs free of cubic nonlinearity, which is confirmed by finite element analysis.