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Simple parametric resonance in an electrostatically actuated microelectromechanical gyroscope: Theory and experiment

Lookup NU author(s): Dr Barry Gallacher, Emeritus Professor James Burdess, Professor Jeffrey Neasham


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One of the major issues facing electrostatically actuated and sensed microelectromechanical systems (MEMS) sensors is electrical feed-through between the drive and the sense electrodes due to parasitic capacitances. This feed-through, in the case of a 'tuned' MEMS gyroscope, limits the sensor sensitivity. In the current paper, the first practical step towards demonstrating reduced feed-through using a combined harmonic forcing and parametric excitation scheme is demonstrated. The equation of motion for the primary mode of vibration of the electrostatically actuated MEMS ring gyroscope is shown to contain a stiffness modulating term which, when modulated at a frequency near twice the natural frequency of the mode, results in parametric resonance. A solution for the equation of motion is assumed, based on Floquet theory, and the method of harmonic balance is employed for analysis. Regions of stability and instability and the stability boundary demarcating the stable and unstable regions are detennined. Frequency sweeps, centred on twice the measured resonant frequency of the primary mode, were performed at various values of voltage amplitudes of the parametric excitation and the parametric resonance was observed electrically at half the excitation frequency. This data were used to map the stability boundary of the parametric resonance. The theoretical and experimental stability boundaries are shown to demonstrate significant similarity. © IMechE 2008.

Publication metadata

Author(s): Harish KM, Gallacher BJ, Burdess JS, Neasham JA

Publication type: Article

Publication status: Published

Journal: Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science

Year: 2008

Volume: 222

Issue: 1

Pages: 43-52

Print publication date: 01/01/2008

ISSN (print): 0954-4062

ISSN (electronic): 2041-2983

Publisher: Professional Engineering Publishing Ltd.


DOI: 10.1243/09544062JMES742


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