Nonlinear analysis of rotating nanocrystalline silicon microbeams for microgyroscope applications

In this paper, we examine the nonlinear dynamical responses of a microgyroscope consisting of a rotating microbeam made of nanocrystalline material with attached proof mass, subject to electric actuation, and operating at high frequency. The working principle of this inertial sensor is based on exploiting the transfer of the mechanical energy among two vibrations modes (drive and sense) via the Coriolis effect to measure the rotation rate. A nonlinear reduced-order model (ROM) governing the microbeam dynamics is developed by the application of the differential quadrature method and finite difference method for space and time discretization, respectively. The developed ROM is used to study the nonlinear behavior of the microbeam near the primary resonance for various grain sizes of the nanocrystalline material and under different electric actuation configurations. The operating DC voltage of the drive mode is selected to ensure that the microgyroscope operates away from the pull-in instability. A sensitivity analysis of the microsystem output parameter to the rotation rate when varying the material properties of the microbeam and electric actuation is then performed. The fringing field of the electrostatic force is found to reduce slightly the pull-in voltage and the natural frequency of the microsystem, amplify the motion in the sense direction, and enlarge the dynamic snap-through bandwidth. As for the effect of the material properties, considering a microbeam with bigger grain size of the constituent nanocrystalline silicon is observed to reduce the motion of the sense mode, increase the natural frequency, and shrink the snap-through bandwidth. Furthermore, operating at high base rotation rates while deploying microbeams with small nanocrystalline grain size is found to switch the dynamic behavior of the sense mode from the nearly-linear to the softening type. Finally, introducing bias in the DC voltage applied along the drive and sense directions is observed to degrade the performance of the electrically-actuated microgyroscope.