Geometry optimization for resonator nonlinearities and modes controlling

In this paper, we utilize a passive technique based on geometry optimization to control the nonlinearities and the dynamical response of MEMS resonators. To achieve this, we propose a new hybrid shape combining a straight and initially curved microbeam. The Galerkin method is employed to solve the beam equation and study the effect of the different design parameters on the ratios of the frequencies and the nonlinearities of the structure. We show by adequately selecting the parameters of the structure; we can realize systems with strong quadratic or cubic nonlinearities or even zero nonlinearity. Also, we investigate the resonator shape effect on breaking the symmetry and explore different linear coupling phenomena: crossing, veering, and mode hybridization. We demonstrate the possibility of controlling the frequencies of the different modes of vibrations to achieve commensurate ratios necessary for activating internal resonance. The ability to activate the nonlinearities and tuning the frequencies is essential for wide range of applications in signal filtering, sensing, timing, and mass and gas sensing. The proposed method is simple in principle, easy to fabricate, and offers a wide range of controllability on the sensor nonlinearities and response. In addition, the passive techniques does not need additional circuits, to control the frequencies, which help reducing the device size, cost, and power consumption.