Bifurcation Behaviour and Stability Analysis of a Nano-Beam Subjected to Electrostatic Pressure
Applied and Computational Mathematics
Volume 7, Issue 1-2, January 2018, Pages: 1-11
Received: Jun. 16, 2017;
Accepted: Jun. 19, 2017;
Published: Jul. 11, 2017
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Aydin Azizi, Department of Engineering, German University of Technology, Muscat, Oman
Niloofar Malekzadeh Fard, Department of Biomedical Engineering, Islamic Azad University, Science and Research Branch, Tehran, Iran
Hamed Mobki, Department of Mechanical Engineering, University of Tabriz, Tabriz, Iran
Adnène Arbi, Higher Institute of Applied Sciences and Technology of Kairouan, Department of Mathematics Physics and Computer Science, University of Kairouan, Kairouan, Tunisia; Laboratory of Engineering Mathematics, Tunisia Polytechnic School, University of Carthage, Tunis, Tunisia
This paper deals with the study of bifurcation behavior of a capacitive nano-beam considering electrostatic, Casimir and van der Waals forces. A modified mass-spring model has been implemented for analysis of the nano-beam behavior. The model has been adjusted and corrected with Euler-Bernoulli beam model, because of its less accuracy compared to distributed models. Fixed or equilibrium points of the nano-beam have been obtained, and has been shown that with variation of the applied voltage and the length of the nano-beam as control parameters the number of equilibrium points is changed. The stability of the fixed points has been investigated drawing motion trajectories in phase portraits and basins of attractions and repulsion have been illustrated. Critical values of the applied voltage and the length of the nano-beam leading to qualitative changes in the nano-beam behavior have been obtained.
Niloofar Malekzadeh Fard,
Bifurcation Behaviour and Stability Analysis of a Nano-Beam Subjected to Electrostatic Pressure, Applied and Computational Mathematics. Special Issue:Recurrent Neural Networks, Bifurcation Analysis and Control Theory of Complex Systems.
Vol. 7, No. 1-2,
2018, pp. 1-11.
P. Kim, C. M. Lieber, Nanotube nanotweezers, science. 286 (1999) 2148-2150.
G-W. Wang, Y. Zhang, Y.-P. Zhao, G. T. Yang, Pull-in instability study of carbon nanotube tweezers under the influence of van der Waals force, Journal of Micromechanics and Microengineering. 14 (2004) 1119-1125.
C. K. W. Adu, G. U. Sumanasekera, B. K. Pradhan, H. E. Romero, P. C. Eklund, Carbon nanotubes: a thermoelectric nano-nose, Chem. Phys. Lett. 337 (2001) 31-35.
P. G. Collins, K. B. Bradley, M. Ishigami, A. Zettl, Extreme oxygen sensitivity of electronic properties of carbon nanotubes, Science. 287 (2000) 1801-1804.
J. Arcamone, G. Rius, G. Abadal, J. Teva, N. Barnoli, F. Perez-Murano, Micro/nanomechanical resonators for distributed mass sensing with capacitive detection, Microelectronic Engineering. 83 (2006) 1216-1220.
M. Dequesnes, Z. Tang, N. R. Aluru, Static and Dynamic Analysis of Carbon Nanotube-Based Switches, Journal of Engineering Materials and Technology. 126 (2004) 230-237.
C.-H. Ke, N. Pugno, B. Peng, H. D. Espinosa, Experiments and modeling of carbon nanotube-based NEMS devices, Journal of the Mechanics and Physics of solids. 53 (2005) 1314-1333.
T. Rueckes, K. Kim, E. Joselevich, G. Y. Tseng, C. L. Cheung, C. M. Lieber, Carbon nanotube-based nonvolatile random access memory for molecular computing, science. 289 (2000) 94-97.
C. Li, E. T. Thostenson, T-W. Chou, Sensors and actuators based on carbon nanotubes and their composites: A review, Composites and Science and Technology. 68 (2008) 1227-1249.
S. Senturia, Microsystem Design. Kluwer. Norwell. MA. USA; (2001).
Y. Zhang, Y. P. Zhao, Numerical and analytical study on the pull-in instability of micro- structure under electrostatic loading, J Sens Actuators A Phys. 127 (2006) 366-367.
H. B. G. Casimir On the attraction between two perfectly conducting plates. Proc K Ned Akad Wet. 51 (1948) 793–6.
W. H. Lin, Y. P. Zhao, Nonlinear behavior for nanoscale electrostatic actuators with Casimir force, Chaos, Solitons and Fractals. 23 (2005) 1777-1785.
E. M. Lifshitz, Sov. Phys. JETP, 2, 73 (1956).
F. Vakili-Tahami, H. Mobki, A-A. keyvani-janbahan, G., Rezazadeh, Pull-in Phenomena and Dynamic Response of Capacitive Nano-beam Switch, sensors and transducers journal. 110 (2009) 26-37.
W. H. Lin, Y. P. Zhao, Dynamic behavior of Nanoscale Electrostatic actuators, CHIN. PHYS. LETT. 20 (2003) 2070-2073.
Azizi, A., H. Mobki, and G. Rezazadeh. "Bifurcation Behavior of a Capacitive Micro-Beam Suspended between Two Conductive Plates." Int J Sens Netw Data Commun 5. 149 (2016): 1-10.
H. Mobki, M. H. Sadeghi, G. Rezazadeh, Design of Direct Exponential Observers for Fault Detection of Nonlinear MEMS Tunable Capacitor, IJE TRANSACTIONS A: Basics Vol. 28, No. 4, (2015) 634-641.
H. Mobki, G. Rezazadeh, M. Sadeghi, F. Vakili-Tahami, M.-M. Seyyed-Fakhrabadi, A comprehensive study of stability in an electro-statically actuated micro-beam, International Journal of Non-Linear Mechanics. 48 (2013) 78-85.
H. Mobki, M. H. Sadeghi, G. Rezazadeh, State Estimation of MEMs Capacitor Using Taylor Expansion, IJE TRANSACTIONS B: Applications Vol. 28, No. 5, (2015) 764-770.
Fathi N. Mayoof, Muhammad A. Hawwa, Chaotic behavior of a curved carbon nanotube under harmonic excitation, Chaos, Solitons & Fractals, Volume 42, Issue 3, 2009, Pages 1860-1867.
W. H. Lin, Y.-P. Zhao, Casimir effect on the pull-in parameters of nanometer switches, Microsystem Technologies. 11 (2005) 80-85.
W.-H. Lin, Y.-P., Zhao, Stability and bifurcation behavior of electrostatic torsional NEMS varactor influence by dispersion forces, Journal of Physics D: Applied Physics. 40 (2007) 1649-1654.
Zarei, O., Rezazadeh, G.,  “A Novel Approach to Study of Mechanical Behavior of NEM Actuators Using Galerkin Method”, International Journal of Nanosystems 1 (2), pp. 161-169.
J. D. Jackson, Classical Electrodynamics, 3rd Ed, Wiley, New York (1998).
J. N. Israelachvili, Intermolecular and surface forces, Academic, London (1992).
J. G. Guo, Y. P. Zhao, Influence of van der Waals and Casimir Force on Electrostatic Tensional Actuators, microelectromechanical systems. 13 (2004) 1027-1035.
G. K. Ananthasuresh, R. K. Gupta, S. D. Senturia, An approach to macromodeling of MEMS for nonlinear dynamic simulation, In Proceedings of the ASME International Conference of Mechanical Engineering Congress and Exposition (MEMS), Atlanta, GA (1996) 401–407.
Y. A. Kuznetsov, Elements of Applied Bifurcation Theory. Second Edition, Springer-Verlag, New York (1997).