Effect of nonlinearity and axial force on frequency drift of a T-shaped tuning fork micro-resonator

In this paper, the effect of nonlinearity on axial force sensitivity is investigated in a T-shaped micromechanical tuning fork resonator. Firstly, a unified model of this resonator for both in-phase and anti-phase modes is established, in which the quadratic and cubic nonlinearities are considered. The validity of this proposed model is verified by the experimental results. Then, the effects of the axial force on the frequency shift and of the nonlinearity on the axial force sensitivity are analyzed theoretically and experimentally. The sensitivity to frequency shift caused by the axial force is observed to be slightly enhanced by soft spring nonlinearity. These results can be used to provide reference for some practical applications, e.g. electrometers, force sensors, etc.