Bifurcation Type Change of AC Electrostatically Actuated MEMS Resonators due to DC Bias

Caruntu, Dumitru I.; Taylor, Kyle N.

doi:10.1155/2014/542023

Cited by 7 publications

(5 citation statements)

References 42 publications

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“…Although only AC voltage is considered since mass sensing applications are of interest, this work can be extended to a combined DC and AC voltage. The DC component in some cases can alter the bifurcation types [15]. This work can be extended to nonaxisymmetric vibrations, higher natural frequencies, and experimental investigations.…”

Section: Discussionmentioning

confidence: 92%

“…The behavior of circular plates under axisymmetric vibration was investigated [13] using the MMS to obtain the amplitude frequency response of the system and show that circular plates may undergo internal resonance due to interactions between the mode of vibration at certain frequencies. Investigations using MMS and ROM method to obtain the amplitude frequency response of other structures such as cantilever resonators were reported in the literature [6,8,14,15].…”

Section: Introductionmentioning

confidence: 99%

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Voltage Response of Primary Resonance of Electrostatically Actuated MEMS Clamped Circular Plate Resonators

Caruntu

Oyervides

2016

Journal of Computational and Nonlinear Dynamics

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This paper investigates the voltage–amplitude response of soft alternating current (AC) electrostatically actuated micro-electro-mechanical system (MEMS) clamped circular plates for sensing applications. The case of soft AC voltage of frequency near half natural frequency of the plate is considered. Soft AC produces small to very small amplitudes away from resonance zones. Nearness to half natural frequency results in primary resonance of the system, which is investigated using the method of multiple scales (MMS) and numerical simulations using reduced order model (ROM) of seven terms (modes of vibration). The system is assumed to be weakly nonlinear. Pull-in instability of the voltage–amplitude response and the effects of detuning frequency and damping on the response are reported.

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Section: Discussionmentioning

confidence: 92%

Section: Introductionmentioning

confidence: 99%

Voltage Response of Primary Resonance of Electrostatically Actuated MEMS Clamped Circular Plate Resonators

Caruntu

Oyervides

2016

Journal of Computational and Nonlinear Dynamics

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“…Regarding damping, the quality factor Q and damping coefficient per unit length b (Table 1) are for conditions of squeeze film damping in rarefied gas [25]. One should mention that the fringe effect is described by Palmer formula [8,26]. Resonators in this work do not fall in the category of narrow beams.…”

Section: Differential Equation Of Motionmentioning

confidence: 92%

Voltage–Amplitude Response of Superharmonic Resonance of Second Order of Electrostatically Actuated MEMS Cantilever Resonators

Caruntu

Botello

Reyes

et al. 2019

Journal of Computational and Nonlinear Dynamics

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This paper investigates the voltage-amplitude response of superharmonic resonance of second order (order two) of alternating current (AC) electrostatically actuated microelectromechanical system (MEMS) cantilever resonators. The resonators consist of a cantilever parallel to a ground plate and under voltage that produces hard excitations. AC frequency is near one-fourth of the natural frequency of the cantilever. The electrostatic force includes fringe effect. Two kinds of models, namely reduced-order models (ROMs), and boundary value problem (BVP) model, are developed. Methods used to solve these models are (1) method of multiple scales (MMS) for ROM using one mode of vibration, (2) continuation and bifurcation analysis for ROMs with several modes of vibration, (3) numerical integration for ROM with several modes of vibration, and (4) numerical integration for BVP model. The voltage-amplitude response shows a softening effect and three saddle-node bifurcation points. The first two bifurcation points occur at low voltage and amplitudes of 0.2 and 0.56 of the gap. The third bifurcation point occurs at higher voltage, called pull-in voltage, and amplitude of 0.44 of the gap. Pull-in occurs, (1) for voltage larger than the pull-in voltage regardless of the initial amplitude and (2) for voltage values lower than the pull-in voltage and large initial amplitudes. Pull-in does not occur at relatively small voltages and small initial amplitudes. First two bifurcation points vanish as damping increases. All bifurcation points are shifted to lower voltages as fringe increases. Pull-in voltage is not affected by the damping or detuning frequency.Keywords: superharmonic resonance of the second order, MEMS cantilever resonator, electrostatic actuation, voltage-amplitude response, method of multiple scales (MMS), reduced-order model (ROM), boundary value problem (BVP), fringe effect

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“…Rezazadeh et al 23 analyzed the parametric oscillation of microbeams. Moreover, Caruntu et al 24,25 investigated the nonlinear response of micro-resonators under a near-half natural frequency and presented steady-state solutions for MEMS cantilever resonators. Qian et al 26 derived periodic solutions for a high-order nonlinear oscillator that arises in MEMS systems.…”

Section: Introductionmentioning

confidence: 99%

An Analytical Study for Nonlinear Free and Forced Vibration of Electrostatically Actuated MEMS Resonators

Lai

Yang

Wang

et al. 2019

Int. J. Str. Stab. Dyn.

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This work aims to construct accurate and simple lower-order analytical approximation solutions for the free and forced vibration of electrostatically actuated micro-electro-mechanical system (MEMS) resonators, in which geometrical and material nonlinearities are induced by the mid-plane stretching, dynamic pull-in characteristics, electrostatic forces and other intrinsic properties. Due to the complexity of nonlinear MEMS systems, the quest of exact closed-form solutions for these problems is hardly obtained for system design and analysis, in particular for harmonically forced nonlinear systems. To examine the simplicity and effectiveness of the present analytical solutions, two illustrative cases are taken into consideration. First, the free vibration of a doubly clamped microbeam suspended on an electrode due to a suddenly applied DC voltage is considered. Based on the Euler–Bernoulli beam theory and the von Karman type nonlinear kinematics, the dynamic motion of the microbeam is further discretized by the Galerkin method to an autonomous system with general nonlinearity, which can be solved analytically by using the Newton harmonic balance method. In addition to large-amplitude free vibration, the primary resonance response of a doubly clamped microbeam driven by two symmetric electrodes is also investigated, in which the microbeam is actuated by a bias DC voltage and a harmonic AC voltage. Following the same decomposition approach, the governing equation of a harmonically forced beam model can be transformed to a nonautonomous system with odd nonlinearity only. Then, lower-order analytical approximation solutions are derived to analyze the steady-state resonance response of such a problem under a combination of various DC and AC voltage effects. Finally, the analytical approximation results of both cases are validated, and they are in good agreement with those obtained by the standard Runge–Kutta method.

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Bifurcation Type Change of AC Electrostatically Actuated MEMS Resonators due to DC Bias

Cited by 7 publications

References 42 publications

Voltage Response of Primary Resonance of Electrostatically Actuated MEMS Clamped Circular Plate Resonators

Voltage Response of Primary Resonance of Electrostatically Actuated MEMS Clamped Circular Plate Resonators

Voltage–Amplitude Response of Superharmonic Resonance of Second Order of Electrostatically Actuated MEMS Cantilever Resonators

An Analytical Study for Nonlinear Free and Forced Vibration of Electrostatically Actuated MEMS Resonators

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