Pull-in instability analyses for NEMS actuators with quartic shape approximation

doi:10.1007/s10483-015-2007-6

Applied Mathematics and Mechanics (English Edition) ›› 2016, Vol. 37 ›› Issue (3): 303-314.doi: https://doi.org/10.1007/s10483-015-2007-6

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Pull-in instability analyses for NEMS actuators with quartic shape approximation

Junsheng DUAN¹, Zongxue LI², Jinyuan LIU³

1. School of Sciences, Shanghai Institute of Technology, Shanghai 201418, China;
2. College of Computer and Information, Inner Mongolia Medical University, Hohhot 010110, China;
3. Department of Information Management, Party School of the Inner Mongolia Committee of the Communist Party of China, Hohhot 010070, China

Received:2015-01-09 Revised:2015-04-18 Online:2016-03-01 Published:2016-03-01
Contact: Junsheng DUAN E-mail:duanjs@sit.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (No. 11201308), the Natural Science Foundation of Shanghai (No. 14ZR1440800), and the Innovation Program of the Shanghai Municipal Education Commission (No. 14ZZ161)

Abstract

Abstract:

The pull-in instability of a cantilever nano-actuator model incorporating the effects of the surface, the fringing field, and the Casimir attraction force is investigated. A new quartic polynomial is proposed as the shape function of the beam during the deflection, satisfying all of the four boundary values. The Gaussian quadrature rule is used to treat the involved integrations, and the design parameters are preserved in the evaluated formulas. The analytic expressions are derived for the tip deflection and pull-in parameters of the cantilever beam. The micro-electromechanical system (MEMS) cantilever actuators and freestanding nano-actuators are considered as two special cases. It is proved that the proposed method is convenient for the analyses of the effects of the surface, the Casimir force, and the fringing field on the pull-in parameters.

Key words: nano-electromechanical system (NEMS), pull-in instability, quartic shape function, Casimir force, micro-electromechanical system (MEMS)

2010 MSC Number:

Junsheng DUAN, Zongxue LI, Jinyuan LIU. Pull-in instability analyses for NEMS actuators with quartic shape approximation. Applied Mathematics and Mechanics (English Edition), 2016, 37(3): 303-314.

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References

[1] Pelesko, J. A. and Bernstein, D. H. Modeling MEMS and NEMS, Chapman and Hall/CRC, Boca Raton (2003)
[2] Zhang, W. M., Yan, H., Peng, Z. K., and Meng, G. Electrostatic pull-in instability in MEMS/NEMS: a review. Sensors and Actuators, A: Physical, 214, 187-218 (2014)
[3] Kuang, J. H. and Chen, C. J. Adomian decomposition method used for solving non-linear pull-in behavior in electrostatic micro-actuators. Mathematical and Computer Modelling, 41, 1479-1491 (2005)
[4] Lin, W. H. and Zhao, Y. P. Pull-in instability of micro-switch actuators: model review. Interna- tional Journal of Nonlinear Sciences and Numerical Simulation, 9, 175-183 (2008)
[5] Koochi, A., Kazemi, A. S., Beni, Y. T., Yekrangi, A., and Abadyan, M. Theoretical study of the effect of Casimir attraction on the pull-in behavior of beam-type NEMS using modified Adomian method. Physica E: Low-dimensional Systems and Nanostructures, 43, 625-632 (2010)
[6] 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, 4925-4941 (2007)
[7] Lin, W. H. and Zhao, Y. P. Non-linear behavior for nano-scale electrostatic actuators with Casimir force. Chaos, Solitons and Fractals, 23, 1777-1785 (2005)
[8] Koochi, A. and Abadyan, M. Efficiency of modified Adomian decomposition for simulating the instability of nano-electromechanical switches: comparison with the conventional decomposition method. Trends in Applied Sciences Research, 7, 57-67 (2012)
[9] Abadyan, M. R., Beni, Y. T., and Noghrehabadi, A. Investigation of elastic boundary condition on the pull-in instability of beam-type NEMS under van der Waals attraction. Procedia Engineering, 10, 1724-1729 (2011)
[10] Soroush, R., Koochi, A., Kazemi, A. S., Noghrehabadi, A., Haddadpour, H., and Abadyan, M. Investigating the effect of Casimir and van der Waals attractions on the electrostatic pull-in instability of nano-actuators. Physica Scripta, 82, 045801 (2010)
[11] Salekdeh, A. Y., Koochi, A., Beni, Y. T., and Abadyan, M. Modeling effects of three nano-scale physical phenomena on instability voltage of multi-layer MEMS/NEMS: material size dependency, van der Waals force and non-classic support conditions. Trends in Applied Sciences Research, 7, 1-17 (2012)
[12] Beni, Y. T., Koochi, A., and Abadyan, M. Theoretical study of the effect of Casimir force, elastic boundary conditions and size dependency on the pull-in instability of beam-type NEMS. Physica E: Low-dimensional Systems and Nanostructures, 43, 979-988 (2011)
[13] Koochi, A., Kazemi, A., Khandani, F., and Abadyan, M. Influence of surface effects on size- dependent instability of nano-actuators in the presence of quantum vacuum fluctuations. Physica Scripta, 85, 035804 (2012)
[14] Noghrehabadi, A., Ghalambaz, M., and Ghanbarzadeh, A. A new approach to the electrostatic pull-in instability of nano-cantilever actuators using the ADM-Padé technique. Computers and Mathematics with Applications, 64, 2806-2815 (2012)
[15] Ramezani, A., Alasty, A., and Akbari, J. Closed-form approximation and numerical validation of the influence of van der Waals force on electrostatic cantilevers at nano-scale separations. Nanotechnology, 19, 015501 (2008)
[16] Lin, W. H. and Zhao, Y. P. Dynamic behavior of nano-scale electrostatic actuators. Chinese Physics Letters, 20, 2070-2073 (2003)
[17] Ma, J. B., Jiang, L., and Asokanthan, S. F. Influence of surface effects on the pull-in instability of NEMS electrostatic switches. Nanotechnology, 21, 505708 (2010)
[18] Duan, J. S. and Rach, R. A pull-in parameter analysis for the cantilever NEMS actuator model including surface energy, fringing field and Casimir effects. International Journal of Solids and Structures, 50, 3511-3518 (2013)
[19] Israelachvili, J. N. Intermolecular and Surface Forces, Academic Press, London (1992)
[20] Mostepanenko, V. M. and Trunov, N. N. The Casimir Effect and Its Application, Oxford Science Publications, New York (1997)
[21] Lamoreaux, S. K. The Casimir force: background, experiments, and applications. Reports on Progress in Physics, 68, 201-236 (2005)
[22] Rodriguez, A. W., Capasso, F., and Johnson, S. G. The Casimir effect in microstructured geome- tries. Nature Photonics, 5, 211-221 (2011)
[23] Guo, J. G. and Zhao, Y. P. Dynamic stability of electrostatic torsional actuators with van der Waals effect. International Journal of Solids and Structures, 43, 675-685 (2006)
[24] Guo, J. G. and Zhao, Y. P. Influence of van der Waals and Casimir forces on electrostatic torsional actuators. Journal of Microelectromechanical Systems, 13, 1027-1035 (2004)
[25] Lin, W. H. and Zhao, Y. P. Stability and bifurcation behaviour of electrostatic torsional NEMS varactor influenced by dispersion forces. Journal of Physics, D: Applied Physics, 40, 1649-1654 (2007)
[26] Duan, J. S., Rach, R., and Wazwaz, A. M. Solution of the model of beam-type micro-and nano- scale electrostatic actuators by a new modified Adomian decomposition method for non-linear boundary value problems. International Journal of Non-Linear Mechanics, 49, 159-169 (2013)
[27] Gurtin, M. E. and Murdoch, A. I. A continuum theory of elastic material surfaces. Archive for Rational Mechanics and Analysis, 57, 291-323 (1975)
[28] He, J. and Lilley, C. M. Surface effect on the elastic behavior of static bending nano-wires. Nano Letters, 8, 1798-1802 (2008)
[29] Wang, G. F. and Feng, X. Q. Surface effects on buckling of nano-wires under uniaxial compression. Applied Physics Letters, 94, 141913 (2009)
[30] Fu, Y. and Zhang, J. Size-dependent pull-in phenomena in electrically actuated nano-beams in- corporating surface energies. Applied Mathematical Modelling, 35, 941-951 (2011)
[31] Miller, R. E. and Shenoy, V. B. Size-dependent elastic properties of nano-sized structural elements. Nanotechnology, 11, 139-147 (2000)
[32] Jiang, L. Y. and Yan, Z. Timoshenko beam model for static bending of nano-wires with surface effects. Physica E: Low-dimensional Systems and Nanostructures, 42, 2274-2279 (2010)
[33] Gupta, R. K. Electrostatic Pull-in Test Structure Design for In-situ Mechanical Property Measure- ments of Microelectromechanical Systems (MEMS), Ph.D. dissertation, Massachusetts Institute of Technology, Cambridge (1997)
[34] Huang, J. M., Liew, K. M., Wong, C. H., Rajendran, S., Tan, M. J., and Liu, A. Q. Mechanical design and optimization of capacitive micromachined switch. Sensors Actuators, A: Physical, 93, 273-285 (2001)
[35] Duan, J. S. and Rach, R. A new modification of the Adomian decomposition method for solving boundary value problems for higher order non-linear differential equations. Applied Mathematics and Computation, 218, 4090-4118 (2011)

Pull-in instability analyses for NEMS actuators with quartic shape approximation

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