A large deflection model for the pull-in analysis of electrostatically actuated microcantilever beams

Chaterjee, S.; Pohit, G.

doi:10.1016/j.jsv.2008.11.046

Cited by 156 publications

(93 citation statements)

References 41 publications

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“…They obtained these models by considering five different capacitor models and used them to calculate the range of motion of these beams. Chaterjee et al [15] studied static and dynamic behavior of a microcantilever with a comparatively large air gap relative to beam length which was subjected to an electrostatic force. Gorthi et al [16] investigated the behavior of cantilever electrostatic actuators with regard to pull-in voltage by employing a beam model along with an insulation layer.…”

Section: Introductionmentioning

confidence: 99%

A hybrid solution for analyzing nonlinear dynamics of electrostatically-actuated microcantilevers

Sadeghzadeh

Kabiri

2017

Applied Mathematical Modelling

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Highlights A hybrid solution for nonlinear dynamics of microcantilevers has been introduced  The pure odd-order nonlinear model combined with a distributed parameter system.  A comprehensive model for MEMS before, during and after switching was presented  Two distinct model for before pull-in and after pull-in regimes are combined ACCEPTED MANUSCRIPT AbstractThis paper introduces a closed-form approximation of dynamic response of microcantilevers.The applied load on the system was linearized by Taylor series expansion and to obtain approximate solutions, model of a pure odd-order nonlinear oscillator, subjected to constant excitation was assumed. Pull-in voltage was investigated to analyze the different parameters of the examined microbeam. In order to obtain a comprehensive dynamic model for MEMS devices, before, during and after switching, the pure odd-order nonlinear model was combined with a distributed parameter system and solved after reaching the pull-in voltage.The obtained results demonstrate correct prediction of the static pull-in voltage and also the dynamic deflection of microbeams. By using the same approach, the sensitivity of the pull-in voltage to various geometrical parameters was also investigated. The obtained results indicate that excessive increase in the air gap causes substantial increase in the pull-in voltage; while increasing thickness of microcantilever has even greater effect. It was also observed that for a given thickness of microcantilever, increasing its length beyond a certain amount has no effect on the pull-in voltage.

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Section: Introductionmentioning

confidence: 99%

A hybrid solution for analyzing nonlinear dynamics of electrostatically-actuated microcantilevers

Sadeghzadeh

Kabiri

2017

Applied Mathematical Modelling

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“…Also the convergence of the ROM due to increasing the number of modes of vibration considered has been showed. Chaterjee and Pohit [11] used ROM for voltage-amplitude response of MEMs cantilever under DC and AC voltage actuation.…”

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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“…Electronic mail: leesooil@uos.ac.kr. Chaterjee and Pohit 14 and considered external forces such as electrostatic and van der Waals interactions between the CNT and a surface plane. We derived the nonlinear responses of the nano-resonator driven by electrostatic excitation and various tip mass effects.…”

Section: Introductionmentioning

confidence: 99%

Theoretical investigation of nonlinear resonances in a carbon nanotube cantilever with a tip-mass under electrostatic excitation

Kim

Lee

2013

Journal of Applied Physics

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The nonlinear dynamics of a resonating carbon nanotube (CNT) cantilever having an attached mass at the tip ("tip mass") were investigated by incorporating electrostatic forces and intermolecular interactions between the CNT and a conducting plane surface. This work enables applications of CNT resonating sensors for tiny mass detection and provides a better understanding of the dynamics of CNT cantilevers. The effect of tip mass on a resonating CNT cantilever is normally characterized by the fundamental frequency shift in the linear resonance regime. However, there are more complex dynamics in the nonlinear resonance regime, such as secondary resonances with parametric excitation. The latter have been limited to nano-cantilevers without tip mass or to axially excited micro-beams. To analyze the nonlinear dynamics, we developed a differential equation model that includes both geometric and inertial nonlinear terms for the large vibration amplitudes at increasing drive forces. In our approach, we used Galerkin discretization techniques and numerical integration methods. The CNT cantilever exhibited complex nonlinear responses due to the applied AC and DC voltages and various tip masses. The nonlinear model had a softer response for increasing tip mass than those of the linear model with the same driving conditions. At low applied voltages, the cantilever had linear amplitude and phase responses at primary and secondary superharmonic resonance frequencies. The response branches were softened at the primary resonance through saddle-node (SN) bifurcation from harmonic electrostatic excitation at higher applied voltages. After SN bifurcation, the lower branch of the solution near resonance became unstable. In addition, theoretical analyses were performed on more complex nonlinear responses and stability changes with tip mass variations, such as perioddoubling (PD) bifurcation at subharmonic resonance frequencies.

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A large deflection model for the pull-in analysis of electrostatically actuated microcantilever beams

Cited by 156 publications

References 41 publications

A hybrid solution for analyzing nonlinear dynamics of electrostatically-actuated microcantilevers

A hybrid solution for analyzing nonlinear dynamics of electrostatically-actuated microcantilevers

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

Theoretical investigation of nonlinear resonances in a carbon nanotube cantilever with a tip-mass under electrostatic excitation

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