Investigation of the internal stress effects on static and dynamic characteristics of an electrostatically actuated beam for MEMS and NEMS application

Bhushan, Anand; Inamdar, Mandar M.; Pawaskar, Dnyanesh N.

doi:10.1007/s00542-011-1367-y

Cited by 16 publications

(4 citation statements)

References 33 publications

(44 reference statements)

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“…We can observe that the centre deflection increases nonlinearly with the increase in the magnitude of DC voltage till pull-in point [14]. Pull-in is a kind of instability that occurs in electrostatically actuated MEMS and NEMS devices due to the interaction of geometric and electrostatic force nonlinearities [41]. From the figures, one can deduce that the presence of positive pressure causes more deflection of the microplate at a particular DC voltage and attain pullin at a lower value of DC voltage, whereas the effects of negative pressure are just opposite.…”

Section: Static Characteristics Of An Imperfect Circular Platementioning

confidence: 97%

Investigation of an electrostatically actuated imperfect circular microplate under transverse pressure for pressure sensor applications

Das

Bhushan

2021

Eng. Res. Express

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In this paper, we present static and dynamic analysis of an electrostatically actuated imperfect circular microplate under transverse pressure. In modelling of the microplate, we have included both von Kármán geometric and electrostatic force nonlinearities in the development of the equation of motion. The equation of motion has been solved using Galerkin based reduced order modelling technique. The developed reduced order model has been first validated by comparing it with finite element simulation results. Further, the effects of imperfection as initial curvature and uniform transverse pressure have been investigated on the static and dynamic characteristics of the electrostatically actuated circular microplate. We have also investigated the effects of imperfection and applied DC voltage on the pressure sensitivity of the circular microplate. We have found that both imperfection and electrostatic load are responsible for appreciable variations in sensitivity. This detailed investigation is useful to design an imperfect micro pressure sensor.

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Section: Static Characteristics Of An Imperfect Circular Platementioning

confidence: 97%

Investigation of an electrostatically actuated imperfect circular microplate under transverse pressure for pressure sensor applications

Das

Bhushan

2021

Eng. Res. Express

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“…Residual stresses have thermal origins due to fabrication techniques of the CNT [30]. We model this effect here by adding an axial force constant along the length of the CNT.…”

Section: Effect Of Residual Stressmentioning

confidence: 99%

Nonlinear Analysis of Electrically Actuated Carbon Nanotube Resonator Using a Novel Discretization Technique

Ouakad

Najar

Hattab

2013

Mathematical Problems in Engineering

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Static as well as dynamic analyses have been performed on clamped-clamped carbon nanotube (CNT) resonator. The nonlinear CNT model is investigated with a novel discretization technique: a differential quadrature method (DQM) to discretize the spatial variables and a finite difference method (FDM) for limit-cycle solutions. Parametric study is performed by varying the electric load, as well as the initial curvature (due to fabrication). It is found that the pull-in voltage decreases nonlinearly with initial curvature and linearly with residual stresses. The eigenvalue problem is also solved to obtain the bending natural frequencies of the system as function of the DC voltage as well as the initial curvature of the CNT. Frequency-response curves near some selected resonant frequencies are plotted to better understand the nanotubes' dynamic behavior. Different linear and nonlinear phenomena are depicted such as dynamic pull-in, hardening, and softening behavior and veering of the odd modes. We have found that even when exciting the CNT near its first natural frequency, the vibration mode located at the veering process significantly alters the CNT's motion and hence may decrease its overall quality factor.

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“…Equation ( 1) is the set of coupled partial differential equations, where coupling is due to geometric nonlinearity through beam stretching ∆ = (1/2) L 0 û′2 + v′2 dx. Nonlinear electrostatic driving force Fe (û) is generated by applying bias voltage V between the plate electrode and the nanowire as [6,27] Fe (û) = πε 0 ε r VDC + VAC cos(ω f t)…”

Section: Mathematical Modellingmentioning

confidence: 99%

“…To study whirling dynamics of a nanowire oscillator, we have adopted Galerkin based reduced order modelling technique for reducing governing partial differential equations of motion (3) into system of ordinary differential equations [4,27,28]. To do so, planar and nonplanar displacements have been assumed as…”

Section: Reduced Order Modellingmentioning

confidence: 99%

Effects of DC voltage on initiation of whirling motion of an electrostatically actuated nanowire oscillator

Bhushan¹,

Inamdar²,

Pawaskar³

2013

Preprint

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Planar driven nanowire oscillators are susceptible to undergo whirling motion due to coupling between flexural planar and nonplanar modes of vibration. This investigation is concerned with planar to whirling motion transition in the oscillation of an electrostatically actuated nanowire, which is pre-deflected due to applied DC voltage. We have derived dynamical equations of motion using Euler-Bernoulli beam theory and Galerkin formulation as reduced order model of the governing coupled partial differential equations. The dynamical equations have been solved using second-order averaging method and the averaging solution has been validated by comparing with the numerical solution of the reduced order model. Further, planar to whirling motion transition has been investigated by studying qualitative changes in resonance curves with variation of electrostatic actuation. In this paper, we provide a simple analytical condition which takes into account the effects of DC voltage for prediction of initiation of whirling motion. Our main observation of the present investigation is that DC voltage can tune the initiation pattern of the whirling motion and change the qualitative nature of resonance curves.

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Investigation of the internal stress effects on static and dynamic characteristics of an electrostatically actuated beam for MEMS and NEMS application

Cited by 16 publications

References 33 publications

Investigation of an electrostatically actuated imperfect circular microplate under transverse pressure for pressure sensor applications

Investigation of an electrostatically actuated imperfect circular microplate under transverse pressure for pressure sensor applications

Nonlinear Analysis of Electrically Actuated Carbon Nanotube Resonator Using a Novel Discretization Technique

Effects of DC voltage on initiation of whirling motion of an electrostatically actuated nanowire oscillator

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