Voltage–amplitude response of alternating current near half natural frequency electrostatically actuated MEMS resonators

Caruntu, Dumitru I.; Martinez, Israel; Taylor, Kyle N.

doi:10.1016/j.mechrescom.2013.06.001

Cited by 19 publications

(31 citation statements)

References 21 publications

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“…To model the hard excitation of the system, the first term on the right-hand side of Eq. (8) does not contain the bookkeeping parameter e [20][21][22]. The bookkeeping parameter indicates small terms in Eq.…”

Section: Methods Of Multiple Scalesmentioning

confidence: 99%

“…The following dimensionless partial differential equation (PDE), and boundary and initial conditions describe the motion of electrostatically actuated Euler-Bernoulli cantilever resonators [2,22]…”

Section: Differential Equation Of Motionmentioning

confidence: 99%

“…[3] and [15][16][17]. The methods used in this work for predicting the behavior of MEMS cantilever resonators are the MMS [20][21][22], numerical integration, and continuation and bifurcation analysis of ROMs [13,23,24].…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Methods Of Multiple Scalesmentioning

confidence: 99%

Section: Differential Equation Of Motionmentioning

confidence: 99%

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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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“…In [15], Singh et al studied the linear and nonlinear frequency characteristics of non-uniform beam with tip mass using the method of multiple scales to obtain the approximate solution. The amplitude-voltage response of MEMS resonator cantilevers under soft electrostatic actuation is studied by Caruntu et al [16]. The electrostatic actuation is of the voltage of frequency near half natural frequency of the system.…”

Section: Introductionmentioning

confidence: 99%

Optimal homotopy asymptotic method to large post-buckling deformation of MEMS

Herişanu

Marinca

2018

MATEC Web Conf.

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Abstract. In the present paper, the post-buckling response of an axially stressed clampedclamped actuator, modeled as a beam and subjected to a symmetric electrostatic field is analyzed. An analytical approximate method, namely the Optimal Homotopy Asymptotic Method (OHAM) is applied to the governing nonlinear integro-differential equation. The analytical results obtained through the proposed procedure show excellent agreement with numerical solution, proving the validity of the proposed procedure, which is simple and easy to use.

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“…They reported both frequency and voltage responses. Both methods MMS and ROM were used to investigate primary and parametric resonance of electrostatically actuated MEMS resonators [4][5][6][7][8][9][10].…”

Section: Introductionmentioning

confidence: 99%

Bifurcation and pull-in voltages of primary resonance of electrostatically actuated SWCNT cantilevers to include van der Waals effect

Caruntu

Luo

2016

Meccanica

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In this work the voltage response of primary resonance of electrostatically actuated single wall carbon nano tubes (SWCNT) cantilevers over a parallel ground plate is investigated. Three forces act on the SWCNT cantilever, namely electrostatic, van der Waals and damping. While the damping is linear, the electrostatic and van der Waals forces are nonlinear. Moreover, the electrostatic force is also parametric since it is given by AC voltage. Under these forces the dynamics of the SWCNT is nonlinear parametric. The van der Waals force is significant for values less than 50 nm of the gap between the SWCNT and the ground substrate. Reduced order model method (ROM) is used to investigate the system under soft excitation and weak nonlinearities. The voltageamplitude response and influences of parameters are reported for primary resonance (AC near half natural frequency).

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Voltage–amplitude response of alternating current near half natural frequency electrostatically actuated MEMS resonators

Cited by 19 publications

References 21 publications

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

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

Optimal homotopy asymptotic method to large post-buckling deformation of MEMS

Bifurcation and pull-in voltages of primary resonance of electrostatically actuated SWCNT cantilevers to include van der Waals effect

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