Forced large amplitude periodic vibrations of non-linear Mathieu resonators for microgyroscope applications

This paper describes a comprehensive non-linear multiphysics model based on the Euler–Bernoulli beam equation that remains valid up to large displacements in the case of electrostatically actuated Mathieu resonators. This purely analytical model takes into account the fringing field effects and is used to track the periodic motions of the sensing parts in resonant microgyroscopes. Several parametric analyses are presented in order to investigate the effect of the proof mass frequency on the bifurcation topology. The model shows that the optimal sensitivity is reached for resonant microgyroscopes designed with sensing frequency four times faster than the actuation one.

► Model for periodic non-linear vibrations of Mathieu resonators in micro-gyroscopes. ► Galerkin method coupled with averaging perturbation technique. ► Parametric analysis with respect to the proof mass frequency out of quasi-periodicity. ► Optimal sensitivity when the sensing frequency is four times faster than the actuation one.