Modeling for Nonlinear Vibrational Response of Mechanical Systems

Shaw, Steven W.; Shoshani, Oriel; Polunin, Pavel M.

doi:10.1007/978-3-319-40256-7_5

Cited by 3 publications

(2 citation statements)

References 37 publications

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“…when the gyroscope drive mode is operated at the a cr ∝ |γ| −1/2 condition on its frequency response, that is, at the onset of nonlinearity [39,41]. While this may not be the preferred operating condition for some gyroscopes, it provides a meaningful and physically intuitive constraint for the present optimization problem.…”

Section: Objective Functionmentioning

confidence: 99%

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Maximizing the rate sensitivity of resonating gyroscopes using nonlinear shape optimization

Polunin¹,

Shaw²

2022

J. Micromech. Microeng.

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In this work we demonstrate how one can improve the angular rate sensitivity of ring/disk resonating gyroscopes by tailoring their nonlinear behavior by systematic shaping of the gyroscope body and electrodes, and by the tuning of bias voltages on segmented electrodes. Of speciﬁc interest are the drive and sense mode Duﬃng nonlinearities, which limit their dynamic ranges, and the intermodal dispersive coupling between these modes that provides parametric ampliﬁcation of the sense mode output signal. These two eﬀects have the same physical origins and are in competition in terms of system performance, which naturally calls for optimization considerations. The present analysis is based on a systematic modeling of the nonlinear response of these devices by which we explore ways in which one can optimize the angular rate sensitivity by manipulating the mechanical and electrostatic contributions to the nonlinearities. In particular, non-uniform modiﬁcations of the gyroscope body thickness are employed to aﬀect the mechanical contributions to these parameters, while the electrostatic components are manipulated via shaping of the resonator-electrode gap and by applying non-uniform bias voltages among segmented electrodes around the gyroscope body. These models predict that such relatively simple alterations can achieve improvements in gain by about an order of magnitude when compared to devices with uniform layouts.

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Section: Objective Functionmentioning

confidence: 99%

“…3 , for which the system response is single-valued when F < F cr and multivalued for F > F cr , [39,40]. An AC drive voltage corresponding to F = F cr results in a peak amplitude of a cr = 2…”

Section: Drive Mode Dynamicsmentioning

confidence: 99%

Maximizing the rate sensitivity of resonating gyroscopes using nonlinear shape optimization

Polunin¹,

Shaw²

2022

J. Micromech. Microeng.

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Analysis of imperfections sensitivity and vibration immunity of MEMS vibrating wheel gyroscope

et al. 2021

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Tailoring the nonlinear response of MEMS resonators using shape optimization

Polunin

Dou

et al. 2017

Applied Physics Letters

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We demonstrate systematic control of mechanical nonlinearities in micro-electromechanical (MEMS) resonators using shape optimization methods. This approach generates beams with nonuniform profiles, which have nonlinearities and frequencies that differ from uniform beams. A set of bridge-type microbeams with selected variable profiles that directly affect the nonlinear characteristics of in-plane vibrations was designed and characterized. Experimental results have demonstrated that these shape changes result in more than a threefold increase and a twofold reduction in the Duffing nonlinearity due to resonator mid-line stretching. The manipulation of this nonlinearity has significant interest in many applications, including precise mass sensing, accurate measurement of angular rates, and timekeeping. Published by AIP Publishing.

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Modeling for Nonlinear Vibrational Response of Mechanical Systems

Cited by 3 publications

References 37 publications

Maximizing the rate sensitivity of resonating gyroscopes using nonlinear shape optimization

Maximizing the rate sensitivity of resonating gyroscopes using nonlinear shape optimization

Analysis of imperfections sensitivity and vibration immunity of MEMS vibrating wheel gyroscope

Tailoring the nonlinear response of MEMS resonators using shape optimization

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