Exploring nonlinearity to enhance the sensitivity and bandwidth performance of a novel tapered beam micro-gyroscope

Abstract

In this paper, nonlinearity is used to enhance the sensitivity and bandwidth performance of tapered beam micro-gyroscopes. Considering the electrostatic force nonlinearity and fringing field effects, the governing equations of system are derived by Euler angular transformation and Hamilton principle. The influences of parameters such as the shape factors and DC voltage on static deflection, pull-in voltage and natural frequency of tapered beam micro-gyroscope are analyzed by the Adomian decomposition method (ADM). Galerkin discretization is performed on the governing equations of the tapered beam micro-gyroscope. Frequency-response equation of the system is deduced and solved by applying the method of multi-scale (MMS). The convergence analysis of the frequency response curve is performed, and then verified by the Runge-Kutta method. Finally, the performance of the tapered beam micro-gyroscope is analyzed in terms of bandwidth, sensitivity, and calibration curve nonlinearity under the different shape factors. The maximum amplitude of response in the driving and sensing directions increases significantly with the change of shape factors of the tapered beam in the dynamics analysis. Compared with the straight beam micro-gyroscope, the tapered beam micro-gyroscope has the higher amplitude and pronounced nonlinear characteristics. Due to the electrostatic force nonlinearity, the amplitude of motion in the driving direction has a high response over a wide frequency band, while also effectively increasing the detection bandwidth. In addition, the nonlinear micro-gyroscope has less loss of sensitivity performance during damping fluctuations. Therefore, in view of the contradiction between bandwidth and sensitivity of the traditional micro-gyroscope, this paper proposes a solution from the perspective of structural design and nonlinear characteristics of the tapered beam micro-gyroscope.