Nonlinear size dependent analysis and effectiveness of nanocrystalline micro/nanogyroscopes
Vibratory micro/nanogyroscopes made of nanocrystalline silicon have a complex microstructure consisting of grains, voids, and interface material phases. Given that the length scale of such inertial sensors is close to the size of the grains themselves, classical continuum mechanics theories are no longer adequate to accurately model the dynamic behaviors of these sensors. In this work, the couple stress and surface elasticity are incorporated to the governing equations of an electrically-actuated, amplitude-based, capacitive sensing cantilever gyroscope to obtain a comprehensive model of the nano-system. Then, the impact of the size dependent effects on the nonlinear dynamic behavior of the gyroscope is investigated by studying its performance for gyroscopes ranging in size from the micro-to the nano-scale. The present numerical study shows that the additional stiffness contributions from the couple stress and surface elasticity and changes in scale cause significant changes in the frequency response, nonlinear behaviors, and sensitivity of the gyroscope to the rotation rates. Furthermore, this numerical analysis demonstrates the importance of accounting for size dependent effects for micro/nanogyroscopes in order to avoid any deterioration of the effectiveness of the gyroscope operability.