On the nonlinear resonances and dynamic pull-in of electrostatically actuated resonators

Alsaleem, Fadi; Younis, Mohammad I.; Ouakad, Hassen M.

doi:10.1088/0960-1317/19/4/045013

Cited by 135 publications

(78 citation statements)

References 40 publications

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“…The stiffening effects at the resonance branch were due to the positive cubic term. 21 In the nonlinear model, these results compare favorably with a previous experimental study 22 and the reduced-order model analysis 23 of a resonating microcantilever beam. The nonlinear behavior of a nano-resonator with tip mass exhibits jump-tocontact that indicates stability changes between the saddle and the center on the phase plane at a saddle node (SN) bifurcation with softening effects.…”

Section: Nonlinear Dynamic Response Of Cnt Cantilever Modelsupporting

confidence: 60%

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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Section: Nonlinear Dynamic Response Of Cnt Cantilever Modelsupporting

confidence: 60%

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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“…Equations (13) and (14) show that there are no trivial solution at a = 0. For non-trivial solution i.e.…”

Section: Formulation Of the Problem And Perturbation Analysismentioning

confidence: 99%

“…Kacem et al [13] studied the nonlinear dynamics of nanomechanical beam resonators to improve the performance of MEMS-based sensors. Alsaleem et al [14] investigated the nonlinear phenomena, including primary resonance, superharmonic and subharmonic resonances, in electrostatically actuated resonators both experimentally and theoretically. Zhang and Meng [15] analyzed the nonlinear dynamics of the electrostatically actuated resonant MEMS sensors under parametric excitation.…”

Section: Introductionmentioning

confidence: 99%

Harmonic and sub-harmonic resonance of MEMS subjected to a weakly non-linear parametric and external excitations

Mosa

El-Naggar

El-Bassiouny

2013

International Journal of Applied Mathematical Research

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This paper presents a simplified mathematical model for the purpose of studying the resonant responses of a nonlinear dynamical system, (micro -electro -mechanical systems (MEMS)), which represented by a Van-der Pol equation subjected to a weakly non-linear parametric and forcing excitations. Using Multiple scales method, the Van-der Pol equation is transformed to a system of second order differential equation up to first order of small parameter ε. Three types of resonances are studied (harmonic resonance and subharmonic resonances of even order (onehalf and one -fourth )). The modulation equations for each resonances, steady state solutions, frequency-response equations, stability analysis are determined. Numerical analysis for frequency-response equations and stability conditions are carried out. Results are presented graphically by group of figures. Finally discussion for these figures are given.

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“…However, electrostatic forces are inherently nonlinear, thus adding complexity to the dynamics of these resonators, especially when they undergo large motions. The nonlinear dynamics of electrostatically actuated resonators have been thoroughly studied over the past two decades [12][13][14][15][16][17][18][19] . There has been increasing interest in obtaining resonant sensors with large-frequency bands, especially with a highquality factor range and near higher order modes of vibrations, where a high sensitivity of detection is demanded 1,2 .…”

Section: Introductionmentioning

confidence: 99%

Multifrequency excitation of a clamped–clamped microbeam: Analytical and experimental investigation

2016

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Using partial electrodes and a multifrequency electrical source, we present a large-bandwidth, large-amplitude clamped-clamped microbeam resonator excited near the higher order modes of vibration. We analytically and experimentally investigate the nonlinear dynamics of the microbeam under a two-source harmonic excitation. The first-frequency source is swept around the first three modes of vibration, whereas the second source frequency remains fixed. New additive and subtractive resonances are demonstrated. We illustrated that by properly tuning the frequency and amplitude of the excitation force, the frequency bandwidth of the resonator is controlled. The microbeam is fabricated using polyimide as a structural layer coated with nickel from the top and chromium and gold layers from the bottom. Using the Galerkin method, a reduced order model is derived to simulate the static and dynamic response of the device. A good agreement between the theoretical and experimental data are reported.

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On the nonlinear resonances and dynamic pull-in of electrostatically actuated resonators

Cited by 135 publications

References 40 publications

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

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

Harmonic and sub-harmonic resonance of MEMS subjected to a weakly non-linear parametric and external excitations

Multifrequency excitation of a clamped–clamped microbeam: Analytical and experimental investigation

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