An analtical model for vibration analysis of disk resonator gyroscopes

Disk resonator gyroscopes (DRGs) utilize the circular symmetry of a set of concentric rings to realize high-performance MEMS gyroscopes. We set forth an analytical method to calculate the mode shapes of the rings and then obtain the corresponding modal mass, Coriolis mass, and stiffness. Following the Ritz method, we minimize the total potential energy of the rings subject to the boundary conditions imposed by the spokes that connect the rings. We show the efficacy of our method using the frequency response of a fabricated DRG and comparison with the finite element method (FEM). With respect to the FEM, our modeling is more straightforward, more intuitive, and can be extended to model imperfections and ensuing effects such as quadrature error and frequency split.