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Nonlinear electrostatic effects in MEMS ring-based rate sensors under shock excitation

Sieberer, Stefan; Mcwilliam, Stewart; Popov, Atanas A


Stefan Sieberer

Professor of Engineering Dynamics


The vibration response of a capacitive ring-based Coriolis Vibrating Gyroscope (CVG) subjected to in-plane shock is modelled and analysed to quantify the effect of shock on angular velocity measurement. The model developed considers a ring resonator with 8 uniformly spaced support legs and describes the in-plane ring response as the sum of the first 3 modes of a perfect ring and the nonlinear electrostatic force as a Taylor series. When a severe in-plane shock is applied, the rigid body response of the ring reduces the electrode gap significantly and a high order expansion is needed to represent the electrostatic force. These nonlinear forces are shown to cause direct and mixed mode coupling to occur, which can significantly modify the response characteristics. Numerical results are presented and interpreted for a range of shock cases to demonstrate the importance of mode coupling, and estimates are made to quantify the angular rate measurement error caused by shock for devices based on 2?- and 3?-modes of operation. To aid the design of devices that are more resilient to shock, a parameter study is performed to identify the modal frequency ratios that minimise this coupling.


Sieberer, S., Mcwilliam, S., & Popov, A. A. (2019). Nonlinear electrostatic effects in MEMS ring-based rate sensors under shock excitation. International Journal of Mechanical Sciences, 157-158, 485-497.

Journal Article Type Article
Acceptance Date Apr 15, 2019
Online Publication Date Apr 16, 2019
Publication Date Jul 1, 2019
Deposit Date Apr 25, 2019
Publicly Available Date Apr 17, 2020
Journal International Journal of Mechanical Sciences
Print ISSN 0020-7403
Publisher Elsevier
Peer Reviewed Peer Reviewed
Volume 157-158
Pages 485-497
Keywords Micro Electro Mechanical System (MEMS); Ring resonator; Gyroscopic sensor; Shock sensitivity analysis; Nonlinear electrostatics; Modal coupling
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