Nonlinear Dynamics of Resonant Microelectromechanical System (MEMS): A Review

Chakraborty, Goutam; Jani, Nikul

doi:10.1007/978-981-15-5712-5_3

Cited by 9 publications

(3 citation statements)

References 50 publications

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“…In an actual working environment, a microresonator is subject to interactions with multiple physical fields, including electrostatic fields, fluid fields, and temperature fields. There are few studies on the multifield coupling characteristics and the nonlinear dynamic behavior characteristics of MEMS systems, including nonlinear effects on the response of resonant MEMS devices [ 9 ], collective behaviors of mechanically and electrically coupled M/NEMS resonators [ 10 ], and geometric and electrostatic nonlinearities of double-ended tuning fork MEMS resonators [ 11 ]. Therefore, to accurately predict the characteristic parameters of a MEMS resonator, including the resonance frequency, amplitude, and resonant mode, it is of great significance to study the multifield coupling nonlinear dynamics of microcomb resonators and to build a multifield coupling numerical model.…”

Section: Introductionmentioning

confidence: 99%

Electrostatic-Fluid-Structure 3D Numerical Simulation of a MEMS Electrostatic Comb Resonator

Shi-ping

Mou

et al. 2022

Sensors

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The reliability and stability of MEMS electrostatic comb resonators have become bottlenecks in practical applications. However, there are few studies that comprehensively consider the nonlinear dynamic behavior characteristics of MEMS systems and devices in a coupled field so that the related simulation accuracy is low and cannot meet the needs of design applications. In this paper, to avoid the computational complexity and the uncertainty of the results of three-field direct coupling and take into the damping nonlinearity caused by coupled fields, a novel electrostatic-fluid-structure three-field indirect coupling method is proposed. Taking an actual microcomb resonant electric field sensor as an example, an electrostatic-fluid-structure multiphysics coupling 3D finite element simulation model is established. After considering the influence of nonlinear damping concerning the large displacement of the structure and the microscale effect, multifield coupling dynamics research is carried out using COMSOL software. The multiorder eigenmodes, resonant frequency, vibration amplitude, and the distribution of fluid load of the microresonator are calculated and analyzed. The simulated data of resonance frequency and displacement amplitude are compared with the measured data. The results show that the fluid load distribution of the microelectrostatic comb resonator along the thickness direction is high in the middle and low on both sides. The viscous damping of the sensor under atmospheric pressure is mainly composed of the incompressible flow damping of the comb teeth, which is an order of magnitude larger than those of other parts. Compared with the measured data, it can be concluded that the amplitude and resonance frequency of the microresonator considering the nonlinear damping force and residual thermal stress are close to the experimental values (amplitude error: 15.47%, resonance frequency error: 12.48%). This article provides a reference for studies on the dynamic characteristics of electrostatically driven MEMS devices.

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Section: Introductionmentioning

confidence: 99%

Electrostatic-Fluid-Structure 3D Numerical Simulation of a MEMS Electrostatic Comb Resonator

Shi-ping

Mou

et al. 2022

Sensors

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“…Recently, the vibrations of micro-and nano-electromechanical resonators have provided a new realm of applications for nonlinear vibrations [1][2][3][4]. Many significant advances have been made in theory [5][6][7], experiments [8][9][10], and applications [11][12][13], including exploring new phenomena uncovered in previously unattainable parameter regimes [14][15][16].…”

Section: Introductionmentioning

confidence: 99%

A hybrid averaging and harmonic balance method for weakly nonlinear asymmetric resonators

2022

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Models for nonlinear vibrations commonly employ polynomial terms that arise from series expansions about an equilibrium point. The analysis of symmetric systems with cubic terms is very common, and the inclusion of asymmetric quadratic terms is known to modify the effective cubic nonlinearity in weakly nonlinear systems. The net effect is a monotonic dependence of the vibration frequency on the amplitude squared in both cases. However, in many applications, such a monotonic dependence is not observed, necessitating the use of techniques for strongly nonlinear systems or the inclusion of higher-order terms in a weakly nonlinear formulation. In either case, the analysis involves very tedious and/or numerical approaches for determining the system response. In the present work, we propose a method that is a hybrid of the methods of averaging and harmonic balance, which provides, with relatively straightforward calculations, good approximations for the amplitude-frequency dependence and for the steady-state response of damped, driven vibrations, including information about overtone harmonics and stability. The method is described, and general results are obtained for an asymmetric system with up to quintic nonlinear terms. The results are applied to a numerical example and validated using simulations. This approach will be useful for analyzing various systems with higher-order polynomial nonlinearities.

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“…Many MEMS (microelectromechanical systems) feature inherent nonlinearities, and a continuing and rich area of research in the MEMS community centers around understanding and exploiting nonlinear frequency response characteristics in such devices. Nonlinearities in microresonators generally arise from three distinct sources (Rhoads et al 2010;Hajjaj et al 2020;Chakraborty and Jani 2021): large structural deformations, large, nonlinear displacement-dependent excitations and forcing, and interaction potentials, such as the Lennard-Jones potential (Belikov and Magonov 2011), which arise, for example, in atomic force microscopy. Investigation in microresonators has typically emphasized forced harmonic oscillators with nonlinearities arising from the first two categories.…”

Section: Introductionmentioning

confidence: 99%

Multiple Equilibrium States in Large Arrays of Globally Coupled Resonators

Borra

Bajaj

Rhoads

et al. 2022

Preprint

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This work considers the response of a globally coupled array of oscillators, each with cubic nonlinear stiffness, in the presence of global reactive and dissipative coupling. Based on the continuum formulation for this system first presented in C. Borra et al (Journal of Sound and Vibration, 393:232–239, 2017), in the present work the individual resonators are excited to sufficient amplitude to allow for multiple coexisting equilibrium distributions. The method of multiple scales is then applied to the system to describe evolution equations for the amplitude and phase of each resonator. Because of the global nature of the coupling, this leads to an integro-differential equation for the stationary populations. Moreover, the characteristic equation used to determine the stability of these states is also an integral equation and admits both a discrete and continuous spectrum for its eigenvalues. The equilibrium structure of the system is studied as the reactive and dissipative coupling parameters are varied. For specific families of the equilibrium distributions two-parameter bifurcation sheets can be constructed. These sheets are connected as individual resonators transition between different branches for the corresponding individual resonators. The resulting one-parameter bifurcation curves are then understood in terms of the collections of these identified bifurcation sheets. The analysis is demonstrated for a system of N = 10 coupled resonators with mass detuning and extended results with N = 100 coupled resonators are illustrated.

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Nonlinear Dynamics of Resonant Microelectromechanical System (MEMS): A Review

Cited by 9 publications

References 50 publications

Electrostatic-Fluid-Structure 3D Numerical Simulation of a MEMS Electrostatic Comb Resonator

Electrostatic-Fluid-Structure 3D Numerical Simulation of a MEMS Electrostatic Comb Resonator

A hybrid averaging and harmonic balance method for weakly nonlinear asymmetric resonators

Multiple Equilibrium States in Large Arrays of Globally Coupled Resonators

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