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Nonlocal Effect on the Pull-in Instability Analysis of Graphene Sheet Nanobeam Actuator

Published online by Cambridge University Press:  08 August 2019

M. X. Lin ,
S. Y. Lee  and
C. K. Chen
M. X. Lin
Affiliation:
Department of Mechanical EngineeringNational Cheng-Kung University Tainan, Taiwan
S. Y. Lee
Affiliation:
Department of Mechanical EngineeringNational Cheng-Kung University Tainan, Taiwan
C. K. Chen*
Affiliation:
Department of Mechanical EngineeringNational Cheng-Kung University Tainan, Taiwan
*
* Corresponding author (ckchen@mail.ncku.edu.tw)
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Abstract

In this study, the pull-in phenomenon of a Nano-actuator is investigated employing a nonlocal Bernoulli-Euler beam model with clamped-clamped conditions. The model accounts for viscous damping, residual stresses, the van der Waals (vdW) force and electrostatic forces with nonlocal effects. The hybrid differential transformation/finite difference method (HDTFDM) is used to analyze the nonlocal effects on a graphene sheet nanobeam, which is electrostatically actuated under the influence of the coupling effect, the von Kármán nonlinear strains and the fringing field effect. The pull-in voltage as calculated by the presented model deviates by no more than 0.29% from previous literature, verifying the validity of the HDTFDM. Furthermore, the nonlocal nonlinear behavior of the electrostatically actuated nanobeam is investigated, and the effects of viscous damping, residual stresses, and length-gap ratio are examined in detail. Overall, the results reveal that small scale effects significantly influence the characteristics of the graphene sheet nanobeam actuator.

Keywords

Pull-in voltageNonlocal elasticity theoryThe hybrid differential transformation/finite difference methodNanoactuator
Type
Research Article
Information
Journal of Mechanics , Volume 35 , Issue 5 , October 2019 , pp. 767 - 778
Copyright
© The Society of Theoretical and Applied Mechanics 2019 

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References

REFERENCES

Lin, M. X. and Lai, H. Yi., “Analysis of Nonlocal Nonlinear Behavior of Graphene Sheet Circular Nanoplate Actuators Subject to Uniform Hydrostatic Pressure,” Microsystem Technologies, 24, pp. 919–928 (2018).CrossRefGoogle Scholar
Park, S. and Horowitz, R., “Adaptive Control for the Conventional Mode of Operation of MEMS Gyroscopes,” Journal of Microelectromechanical Systems, 12, pp. 101–108 (2003).CrossRefGoogle Scholar
Rutherglen, C., Jain, D. and Burke, P., “Nanotube Electronics for Radiofrequency Applications,” Nature Nanotechnology, 4, pp. 811–819 (2009).CrossRefGoogle ScholarPubMed
Deotare, P. B., McCutcheon, M. W., Frank, I. W., Khan, M. and Lončar, M., “High Quality Factor Photonic Crystal Nanobeam Cavities,” Applied Physics Letters, 94, 121106 (2009).CrossRefGoogle Scholar
Pei, J., Tian, F. and Thundat, T., “Glucose Biosensor Based on the Microcantilever,” Analytical Chemistry, 76, pp. 292–297 (2004).CrossRefGoogle ScholarPubMed
Decca, R. S. et al., “Precise Comparison of Theory and New Experiment for the Casimir Force Leads to Stronger Constraints on Thermal Quantum Effects and Long-Range Interactions,” Annals of Physics, 318, pp. 37–80 (2005).CrossRefGoogle Scholar
Sedighi, H. M., Daneshmand, F. and Zare, J., “The Influence of Dispersion Forces on the Dynamic Pull-in Behavior of Vibrating Nano-Cantilever Based NEMS Including Fringing Field Effect,” Archives of Civil and Mechanical Engineering, 14, pp. 766–775 (2014).CrossRefGoogle Scholar
Soroush, R. et al., “Investigating the Effect of Casimir and Van Der Waals Attractions on the Electrostatic Pull-in Instability of Nano-Actuators,” Physica Scripta, 82, 045801 (2010).CrossRefGoogle Scholar
Ramezani, A., Alasty, A. and Akbari, J., “Closed-Form Solutions of the Pull-in Instability in Nano-Cantilevers under Electrostatic and Intermolecular Surface Forces,” International Journal of Solids and Structures, 44, pp. 4925–4941 (2007).CrossRefGoogle Scholar
Mousavi, T., Bornassi, S. and Haddadpour, H., “The Effect of Small Scale on the Pull-in Instability of Nano-Switches Using DQM,” International Journal of Solids and Structures, 50, pp. 1193–1202 (2013).CrossRefGoogle Scholar
Dequesnes, M., Rotkin, S. V. and Aluru, N. R., “Calculation of Pull-in Voltages for Carbon-Nanotube-Based Nanoelectromechanical Switches,” Nanotechnology, 13, pp. 120–131 (2002).CrossRefGoogle Scholar
Ramezani, A., Alasty, A. and Akbari, J., “Influence of Van Der Waals Force on the Pull-in Parameters of Cantilever Type Nanoscale Electrostatic Actuators,” Microsystem Technologies, 12, pp. 1153–1161 (2006).CrossRefGoogle Scholar
Lin, W. H. and Zhao, Y. P., “Nonlinear Behavior for Nanoscale Electrostatic Actuators with Casimir Force,” Chaos, Solitons & Fractals, 23, pp. 1777–1785 (2005).CrossRefGoogle Scholar
Pradhan, S. C. and Murmu, T., “Small Scale Effect on the Buckling of Single-Layered Graphene Sheets under Biaxial Compression via Nonlocal Continuum Mechanics,” Computational Materials Science, 47, pp. 268–274 (2009).CrossRefGoogle Scholar
Murmu, T. and Pradhan, S. C., “Buckling Analysis of a Single-Walled Carbon Nanotube Embedded in an Elastic Medium Based on Nonlocal Elasticity and Timoshenko Beam Theory and Using DQM,” Physica E: Low-Dimensional Systems and Nanostructures, 41, pp. 1232–1239 (2009).CrossRefGoogle Scholar
Eringen, A. C., “Nonlocal Polar Elastic Continua,” International Journal of Engineering Science, 10, pp. 1–16 (1972).CrossRefGoogle Scholar
Eringen, A. C. and Edelen, D. G. B., “On Nonlocal Elasticity,” International Journal of Engineering Science, 10, pp. 233–248 (1972).CrossRefGoogle Scholar
Eringen, A. C., “On Differential Equations of Non-local Elasticity and Solutions of Screw Dislocation and Surface Waves,” Journal of Applied Physics, 54, pp. 4703–4710 (2009).CrossRefGoogle Scholar
Eringen, A. C., Nonlocal Continuum Field Theories, Springer Science & Business Media, 2002.Google Scholar
Murmu, T. and Pradhan, S. C., “Vibration Analysis of Nano-Single-Layered Graphene Sheets Embedded in Elastic Medium Based on Nonlocal Elasticity Theory,” Journal of Applied Physics, 105, 064319 (2009).CrossRefGoogle Scholar
Yang, J., Jia, X. L. and Kitipornchai, S., “Pull-in Instability of Nano-Switches Using Nonlocal Elasticity Theory,” Journal of Physics D: Applied Physics, 41, 035103 (2008).CrossRefGoogle Scholar
Reddy, J. N., “Nonlocal Nonlinear Formulations for Bending of Classical and Shear Deformation Theories of Beams and Plates,” International Journal of Engineering Science, 48, pp. 1507–1518 (2010).CrossRefGoogle Scholar
Najar, F., El-Borgi, S., Reddy, J. N. and Mrabet, K., “Nonlinear Nonlocal Analysis of Electrostatic Nanoactuators,” Composite Structures, 120, pp. 117–128 (2015).CrossRefGoogle Scholar
Zhou, J. K., “Differential Transformation and its Applications for Electrical Circuits,” pp. 1279–1289 (1986).Google Scholar
Yu, L. T. and Chen, C. K., “The Solution of the Blasius Equation by the Differential Transformation Method,” Mathematical and Computer Modelling, 28, pp. 101–111 (1998).Google Scholar
Chen, C. K., Lai, H. Y. and Liu, C. C., “Numerical Analysis of Entropy Generation in Mixed Convection Flow with Viscous Dissipation Effects in Vertical Channel,” International Communications in Heat and Mass Transfer, 38, pp. 285–290 (2011).CrossRefGoogle Scholar
Chen, C. K., Lai, H. Y. and Liu, C. C., “Application of Hybrid Differential Transformation/Finite Difference Method to Nonlinear Analysis of Micro Fixed-Fixed Beam,” Microsystem Technologies, 15, pp. 813–820 (2009).CrossRefGoogle Scholar
Shaat, M. and Mohamed, S. A., “Nonlinear-Electrostatic Analysis of Micro-Actuated Beams Based on Couple Stress and Surface Elasticity Theories,” International Journal of Mechanical Sciences, 84, pp. 208–217 (2014).CrossRefGoogle Scholar
Hu, Y. C., Chang, C. M. and Huang, S. C., “Some Design Considerations on the Electrostatically Actuated Microstructures,” Sensors and Actuators A: Physical, 112, pp. 155–161 (2004).CrossRefGoogle Scholar