Stability analysis of a new class of MEMS gyroscopes with parametric resonance

In this paper, a parametrically resonated MEMS gyroscope is considered, and the effect of its parameters on the system stability is studied. Unlike the general case of MEMS gyroscopes with harmonic excitation, in this new class of gyroscopes with parametric excitation, the origin is one stationary point of the system. The study starts with the stability analysis of the origin, and then it goes on to analyze the effect of each parameter on the stability of periodic orbits. Stabilities are studied by means of Floquet theory. As the results indicate, presence of a non-trivial response for the system is closely interconnected to the stabilities (and instabilities) of the system. It is demonstrated that the stability of the origin always contributes to a zero response for the sensor, and hence the instability of origin is required for the occurrence of parametric resonance. In contrast, stability of a periodic orbit does not necessarily guarantee a resonant response for the gyroscope, and again it is the instability of the origin which is required for this purpose. Because in the case of linear stiffness—linear parametric excitation the instability of the origin results in instability of the system, it is concluded that nonlinearities are required for a parametrically actuated gyroscope.

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