Professor of Mechanical Engineering and Smart Structures, School of Computing Engineering and Mathematics, Western Sydney University, Australia. His research interests cover Industry 4.0, Additive Manufacturing, Advanced Engineering Materials and Structures (Metals and Composites), Multi-scale Modelling of Materials and Structures, Metal Forming and Metal Surface Treatment.
Abstract — This paper is a study of the geometrical non-linearity influence of the elastic suspension in micromechanical gyroscope under the conditions of angular vibration. The spatial non-linear oscillations of the elastic suspension were considered. A quasi-linear system of equations of Mathieu–Hill, describing the motion of sensitive element on vibrating conditions close to the main parametric resonance, was obtained. In this paper an averaged equation of motion and found stationary regimes of oscillations was built. The case of losing stability of oscillations in terms of the main parametric resonance was analyzed. And the angular vibration in the resonance case leads to additional deflection of gyroscope. It is shown that for certain parameters of the system the regime of plane stationary oscillations of the sensitive element of the MMG becomes unstable. The conditions for the appearance and stability of spatial stationary oscillations in the vicinity of the main resonance are investigated depending on the parameters of the system.
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