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
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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.
Nano-Beam, Electrostatic Force, Van der Waals Force, Casimir, Stability
To cite this article
Aydin Azizi, Niloofar Malekzadeh Fard, Hamed Mobki, Adnène Arbi, 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. doi: 10.11648/j.acm.s.2018070102.11
Copyright © 2017 Authors retain the copyright of this article.
This article 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.
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