Nonlinear dynamics and parameter identification of electrostatically coupled resonators

Li, Lei; Han, Jianxin; Zhang, Qichang; Liu, Canchang; Guo, Zonghe

doi:10.1016/j.ijnonlinmec.2018.12.008

Cited by 21 publications

(11 citation statements)

References 45 publications

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“…u0 is the excitation source of the system, M represents the coupling inductor ( = ), and k is the coupling coefficient which reflects a transmission distance of the MCR-WPT system. Considering the non-linearities of a capacitor [28,29], the coulomb-volt characteristics of capacitors can be expressed by = ⁄ + + (n = 1,2), where C0 is a linear capacitance, and κ1 and κ2 are non-linear charge coefficients of capacitors. The non-linear coupled dynamics equations can be rewritten following form:…”

Section: Circuit Model and Transmission Equationsmentioning

confidence: 99%

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Frequency Splitting and Transmission Characteristics of MCR-WPT System Considering Non-Linearities of Compensation Capacitors

Liu

Wang

et al. 2020

Electronics

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The frequency splitting phenomenon and transmission characteristics have been research hotspots in the field of magnetically coupled resonance wireless power transfer (MCR-WPT). In this paper, non-linear dynamics theory was innovatively introduced into the research, and non-linear coupled transmission dynamics modelling of the MCR-WPT system was established considering the non-linearities of the compensation capacitor. The mechanism of the frequency splitting phenomenon of the MCR-WPT system was revealed through systematic mathematical analyses based on the modelling. The analysis results showed that the system usually has dual natural frequencies which are low resonance frequency and high resonance frequency. Based on non-linear dynamics theory, the transmission characteristics of the system with different non-linear parameters were discussed comprehensively in relation to the modelling. The results of the numerical simulations and theoretical analyses showed that non-linear parameters can cause the jumping phenomena with the output responses, and the output responses in the vicinities of the lower resonance frequencies were extremely sensitive to changes in the coupling coefficient. According to analyses of the linear and non-linear systems, the energy transmissions performed in the vicinity of the high resonance frequency had a wider working frequency band and a better transmission stability under non-linear conditions.

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Section: Circuit Model and Transmission Equationsmentioning

confidence: 99%

“…Then, the following fourth-order differential equation can be obtained: Considering the non-linearities of a capacitor [28,29], the coulomb-volt characteristics of capacitors can be expressed by…”

Section: Theory Analysesmentioning

confidence: 99%

Frequency Splitting and Transmission Characteristics of MCR-WPT System Considering Non-Linearities of Compensation Capacitors

Liu

Wang

et al. 2020

Electronics

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“…Recently, nonlinear MEMS mass sensors have attracted attention due to their unique advantages. Firstly, the nonlinear parameter identification method of mass sensors can solve the error caused by nonlinear stiffness [12]. Besides, the sensitivity and accuracy of the sensor can be improved by using frequency stability and amplitude jump in nonlinear vibration [13].…”

Section: Introductionmentioning

confidence: 99%

Anti-Symmetric Mode Vibration of Electrostatically Actuated Clamped–Clamped Microbeams for Mass Sensing

Zhang

et al. 2019

Micromachines

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This paper details study of the anti-symmetric response to the symmetrical electrostatic excitation of a Micro-electro-mechanical-systems (MEMS) resonant mass sensor. Under higher order mode excitation, two nonlinear coupled flexural modes to describe MEMS mass sensors are obtained by using Hamilton’s principle and Galerkin method. Static analysis is introduced to investigate the effect of added mass on the natural frequency of the resonant sensor. Then, the perturbation method is applied to determine the response and stability of the system for small amplitude vibration. Through bifurcation analysis, the physical conditions of the anti-symmetric mode vibration are obtained. The corresponding stability analysis is carried out. Results show that the added mass can change the bifurcation behaviors of the anti-symmetric mode and affect the voltage and frequency of the bifurcation jump point. Typically, we propose a mass parameter identification method based on the dynamic jump motion of the anti-symmetric mode. Numerical studies are introduced to verify the validity of mass detection method. Finally, the influence of physical parameters on the sensitivity of mass sensor is analyzed. It is found that the DC voltage and mass adsorption position are critical to the sensitivity of the sensor. The results of this paper can be potentially useful in nonlinear mass sensors.

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“…It can be concluded that coupled vibration behaviors caused by internal resonance are gradually considered, and the jump phenomenon is also focused on [65,66,67]. The phenomenon is interesting, but the application of this phenomenon is scarce.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear Behavior of Electrostatically Actuated Microbeams with Coupled Longitudinal–Transversal Vibration

Cao

et al. 2019

Micromachines

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Microelectromechanical switch has become an essential component in a wide variety of applications, ranging from biomechanics and aerospace engineering to consumer electronics. Electrostatically actuated microbeams and microplates are chief parts of many MEMS instruments. In this study, the nonlinear characteristics of coupled longitudinal–transversal vibration are analyzed, while an electrostatically actuated microbeam is designed considering that the frequency ratio is two to one between the first longitudinal vibration and transversal vibration. The nonlinear governing equations are truncated into a set of coupled ordinary differential equations by the Galerkin method. Then the equations are solved using the multiple-scales method and the nonlinear dynamics of the internal resonance is investigated. The influence of bias voltage, longitudinal excitation and frequency detuning parameters are mainly analyzed. Results show that using the pseudo-arclength continuation method, the nonlinear amplitude–response curves can be plotted continuously. The saturation and jump phenomena are greatly affected by the bias voltage and the detuning frequency. Beyond the critical excitation amplitude, the response energy will transfer from the longitudinal motion to the transversal motion, even the excitation is employed on the longitudinal direction. The large-amplitude jump of the low-order vibration mode can be used to detect the variation of the conditions or parameters, which shows great potential in improving precision of MEMS switches.

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Nonlinear dynamics and parameter identification of electrostatically coupled resonators

Cited by 21 publications

References 45 publications

Frequency Splitting and Transmission Characteristics of MCR-WPT System Considering Non-Linearities of Compensation Capacitors

Frequency Splitting and Transmission Characteristics of MCR-WPT System Considering Non-Linearities of Compensation Capacitors

Anti-Symmetric Mode Vibration of Electrostatically Actuated Clamped–Clamped Microbeams for Mass Sensing

Nonlinear Behavior of Electrostatically Actuated Microbeams with Coupled Longitudinal–Transversal Vibration

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