Nonlinear characteristics and analysis of an exponential variable cross-section beam-based micro-gyroscope with electrostatic driven

In this paper, a novel vibrating beam gyroscope with exponential variable cross-section is designed. Relationship between the width and length of the variable cross-section exponential beam is in the form of an exponential function change. The exponential shape factor (ESF) of beam is less than or equal to zero, and the thickness of the beam remains constant with the beam length. The effects of curvature nonlinearity and inertia nonlinearity on the system are considered. The vibration control equations, boundary conditions, and nonlinear discretization model of the exponential beam micro-gyroscope (EBMG) are developed by using the extended Hamiltonian principle, the single-mode approximation method, and the Lagrange differential equations. The effects of direct current (DC) and alternating current (AC) voltages on the system response in both the drive and sense directions of the gyroscope are analyzed. The static response of the gyroscope system under the different ESF is solved by the Adomian decomposition method (ADM). The nonlinear discretization model is solved by the multi-scale method to analyze the influence of each parameter on the dynamic response of the gyroscope. The results show that with the increase of the ESF, the pull-in voltage and the first-order natural frequency of the EBMG increase gradually, and have a linear change pattern approximately. By adjusting the ESF, the difference between the peak frequency of Coriolis force response and the sense peak frequency can be controlled. Utilizing the nonlinear harden characteristics of the EBMG system, when the AC voltage is applied in the thickness direction of exponential beam, the EBMG system can obtain better bandwidth performance and linear measurable range by choosing the appropriate ESF, damping ratio, and AC voltage; when the AC voltage is applied in the width direction of the exponential beam, the EBMG can not only obtain the higher sensitivity performance, but also increase the linear detectable range by choosing an appropriate ESF.