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Actuators 2018, 7(1), 3; https://doi.org/10.3390/act7010003

Comprehensive Analytical Approximations of the Pull-In Characteristics of an Electrostatically Actuated Nanobeam under the Influences of Intermolecular Forces

Department of Mechanical Engineering, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia
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Received: 14 December 2017 / Revised: 4 January 2018 / Accepted: 9 January 2018 / Published: 12 January 2018
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Abstract

In this paper, analytical closed-form expressions to accurately estimate the pull-in characteristics of an electrostatically-actuated doubly-clamped nanobeam are derived and examined. In this regard, a coupled electro-mechanical problem for the nano-actuator is first presented assuming a single mode approximation while taking into account all the possible structural, electrical and nanoscale effects: the fringing of the electrical actuating force, the geometric mid-plane stretching and intermolecular (van der Walls and Casimir) forces. The complicated nonlinear resultant equations are numerically approximated in order to derive the closed-form expressions for the important nano-actuator pull-in characteristics: i.e., the detachment length, the minimum reachable gap size before the collapse and the respective pull-in voltage. The resulting closed-form expressions are first quantitatively validated with other previously published results, and comparisons showed an acceptable agreement. Unlike the reported expressions in the literature, the proposed closed-form expressions in this work are proper approximations, fairly accurate and, more importantly, provide a quick estimate of the critical design pull-in parameters of the nano-actuator. In addition, the analysis of these expressions demonstrated that the consideration of the intermolecular forces together with the fringe effect tends to significantly reduce the threshold pull-in voltage, whereas the mid-plane stretching parameter tends to the contrary to increase the voltage at the pull-in collapse. The derived expressions of these analytical/approximate solutions could hopefully be appropriately used by NEMS engineers as simple/quick procedures for successful design and fabrication of electrostatically-actuated nano-devices. View Full-Text
Keywords: NEMS; actuator; analytical solution; pull-in characteristics; mid-plane stretching; van der Waals force; Casimir force NEMS; actuator; analytical solution; pull-in characteristics; mid-plane stretching; van der Waals force; Casimir force
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).
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Ouakad, H.M.; AlQasimi, J.E. Comprehensive Analytical Approximations of the Pull-In Characteristics of an Electrostatically Actuated Nanobeam under the Influences of Intermolecular Forces. Actuators 2018, 7, 3.

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