Stochastic Stability of a Class of MEMS-Based Vibratory Gyroscopes under Input Rate Fluctuations

Abstract

The influence of stochastic fluctuations in the input angular rate of a class of single axis mass-spring microelectromechanical (MEM) gyroscopes on the system stability is investigated. A white noise fluctuation is introduced in the coupled 2-DOF model that represents the system dynamics for the purposes of stability prediction. Numerical simulations are performed employing the resulting set of stochastic differential equations (SDEs) that govern the system dynamics. The SDEs are discretized using the higher-order Milstein scheme for numerical computations. Simulations via the Euler scheme, as well as the measure of the largest Lyapunov exponent are employed for validation purposes due to a lack of similar analytical solutions or experimental data. Responses have been predicted under different noise fluctuation magnitudes and different input angular rates for stability investigations. A parametric study is performed to estimate the noise intensity stability threshold for a range of quality factor values at different input angular rates. The predicted results show a nonlinear dependence of the threshold on the quality factors for different input rates. Under typical gyroscope operating conditions, a realistic frequency mismatch appears to have insignificant influence on system stability. It is envisaged that the present quantitative predictions will aid improvements in performance, reliability, and the design process for this class of devices.

Asymmetric Oscillations of AFG Microscale Nonuniform Deformable Timoshenko Beams

“…Vibrating [1] standard structural continuous elements (plates, shells, and beams) are the building blocks in many civil structures and machines even at small-scale levels [2][3][4][5][6][7]. The micro/nanoscale version of these structural elements are the building blocks of micro/nanomachines [8][9][10][11]. In some of these microscale devices, high thermal resistance in addition to mechanical resistance is required.…”

Mechanics of Fluid-Conveying Microtubes: Coupled Buckling and Post-Buckling

“…Many microelectromechanical systems (MEMS) using microscale structures such as microshells, microplates and microtubes have been designed and analysed in recent years [1,2]. Fluid-conveying microtubes, as an advanced class of fluid-structure systems, are widely used in different MEMS and microfluidic devices.…”