Influence of System and Actuator Nonlinearities on the Dynamics of Ring-Type MEMS Gyroscopes

Abstract

This study investigates the nonlinear dynamic response behavior of a rotating ring that forms an essential element of MEMS (Micro Electro Mechanical Systems) ring-based vibratory gyroscopes that utilize oscillatory nonlinear electrostatic forces. For this purpose, the dynamic behavior due to nonlinear system characteristics and nonlinear external forces was studied in detail. The partial differential equations that represent the ring dynamics are reduced to coupled nonlinear ordinary differential equations by suitable addition of nonlinear mode functions and application of Galerkin’s procedure. Understanding the effects of nonlinear actuator dynamics is essential for characterizing the dynamic behavior of such devices. For this purpose, a suitable theoretical model to generate a nonlinear electrostatic force acting on the MEMS ring structure is formulated. Nonlinear dynamic responses in the driving and sensing directions are examined via time response, phase diagram, and Poincare’s map when the input angular motion and nonlinear electrostatic force are considered simultaneously. The analysis is envisaged to aid ongoing research associated with the fabrication of this type of device and provide design improvements in MEMS ring-based gyroscopes.

Nonlinear Dynamics Study of Giant Magnetostrictive Actuators with Fractional Damping

“…Nam et al [20] established a new model of beam, this new beam model is free of shear-locking for both thick and thin beams, is easy to apply in computation, and has efficiency in simulating the variable thickness beams. Gebrel et al [21] developed a suitable theoretical model to generate nonlinear electrostatic forces acting on the MEMS ring structure and examined the nonlinear dynamic response in the drive and sensing directions by time response, phase diagram and Poincare mapping when both input angular motion and nonlinear electrostatic forces were considered. Although some progress has been made in the study of chaos in GMA systems, there is a lack of more accurate dynamical model descriptions for GMA systems generating chaotic phenomena.…”