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Research Papers

Surface and Thermal Effects on the Pull-In Behavior of Doubly-Clamped Graphene Nanoribbons Under Electrostatic and Casimir Loads

[+] Author and Article Information
Wei Lu

e-mail: weilu@umich.edu
Department of Mechanical Engineering,
University of Michigan,
Ann Arbor, MI 48109

1Corresponding author.

Manuscript received November 16, 2012; final manuscript received December 22, 2012; accepted manuscript posted February 14, 2013; published online August 21, 2013. Editor: Yonggang Huang.

J. Appl. Mech 80(6), 061014 (Aug 21, 2013) (9 pages) Paper No: JAM-12-1519; doi: 10.1115/1.4023683 History: Received November 16, 2012; Revised December 22, 2012; Accepted February 14, 2013

In this study, a comprehensive analytical model is established based on Euler–Bernoulli beam theory with von Kármán geometric nonlinearity to investigate the effect of residual surface tension, surface elasticity, and temperature on the static pull-in voltages of multilayer graphene nanoribbon (MLGNR) doubly-clamped beams under electrostatic and Casimir forces and axial residual stress. An explicit closed-form analytical solution to the governing fourth-order nonlinear differential equation of variable coefficients is presented for the static pull-in behavior of electrostatic nanoactuators using a Fredholm integral equation of the first kind. The high accuracy of the present analytical model is validated for some special cases through comparison with other existing numerical, analytical, and experimental models. The effects of the number of graphene nanoribbons (GNRs), temperature, surface tension, and surface elasticity on the pull-in voltage and displacement of MLGNR electrostatic nanoactuaotrs are investigated. Results indicate that the thermal effect on the pull-in voltage is significant especially when a smaller number of GNRs are used. It is found that the surface effects become more dominant as the number of GNRs decreases. It is also demonstrated that the residual surface tension exerts a greater influence on the pull-in voltage in comparison with the surface elasticity.

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Figures

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Fig. 2

MLGNR beam with surface effects and subject to electrostatic and Casimir loads

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Fig. 1

Schematic of the MLGNR doubly-clamped actuator

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Fig. 3

Coefficient of thermal expansion of the monolayer graphene, triple-layer graphene, and the graphite as a function of temperature. The same markers with different colors represent the number of graphene/graphite samples tested.

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Fig. 4

Variation of the proposed CTE function, Eq. (9), as a function of temperature for the monolayer graphene, few-layered graphene, and many-layered graphene (graphite)

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Fig. 7

Effect of the Casimir force on the pull-in voltages of [111] Al and [100] Si doubly-clamped nanobeams using the continuum surface elasticity model

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Fig. 8

Effect of the number of GNRs on the pull-in voltage and pull-in displacement (at the middle point) of MLGNR doubly-clamped electrostatic nanoactuators when the residual, thermal, and surface effects are neglected

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Fig. 5

Theoretical and measured pull-in voltages of the doubly-clamped microbeams with different beam lengths

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Fig. 6

Comparison of the pull-in voltages of [111] Al and [100] Si doubly-clamped nanobeams without Casimir force obtained by the present method and the AEM [51]

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Fig. 9

Effect of the temperature on the pull-in voltage of MLGNR doubly-clamped electrostatic nanoactuators when the residual and surface effects are neglected

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Fig. 10

Variation of the residual surface stress and the surface elastic modulus versus the pull-in voltages of the MLGNR electrostatic nanoactuators when (a) n=100 and (b) n=300

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