Nonlinear dynamics of vibrating MEMS

Let us consider a MEMS translational gyroscope. When significantly displacing the proof mass, the nonlinear hardening characteristic of the supporting beams becomes visible. Thus, the resonance peak of the structure bends towards the higher frequencies. This property is useful to easily synchronise sense and drive resonances thus increasing the sensibility of the MEMS gyroscope. Through a test structure designed to access the high deformation range of the supporting beams, its nonlinear vibrations were investigated both experimentally and numerically. It is shown that a simple nonlinear lumped parameter model is sufficient to schematise the gyroscope and that a semi-analytical integration method allows to quickly determine both stable and unstable branches of the system's dynamic response.