Bifurcation Behaviour and Stability Analysis of a Nano-Beam Subjected to Electrostatic Pressure

Aydin Azizi; Niloofar Malekzadeh Fard; Hamed Mobki; Adnène Arbi

doi:doi:10.11648/j.acm.s.2018070102.11

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Bifurcation Behaviour and Stability Analysis of a Nano-Beam Subjected to Electrostatic Pressure

Aydin Azizi, Niloofar Malekzadeh Fard, Hamed Mobki, Adnène Arbi

Published in Applied and Computational Mathematics (Volume 7, Issue 1-2)

Received: 16 June 2017 Accepted: 19 June 2017 Published: 11 July 2017

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Abstract

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.

Published in	Applied and Computational Mathematics (Volume 7, Issue 1-2) This article belongs to the Special Issue Recurrent Neural Networks, Bifurcation Analysis and Control Theory of Complex Systems
DOI	10.11648/j.acm.s.2018070102.11
Page(s)	1-11
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2017. Published by Science Publishing Group

Keywords

Nano-Beam, Electrostatic Force, Van der Waals Force, Casimir, Stability

References

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APA Style

Aydin Azizi, Niloofar Malekzadeh Fard, Hamed Mobki, Adnène Arbi. (2017). Bifurcation Behaviour and Stability Analysis of a Nano-Beam Subjected to Electrostatic Pressure. Applied and Computational Mathematics, 7(1-2), 1-11. https://doi.org/10.11648/j.acm.s.2018070102.11

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ACS Style

Aydin Azizi; Niloofar Malekzadeh Fard; Hamed Mobki; Adnène Arbi. Bifurcation Behaviour and Stability Analysis of a Nano-Beam Subjected to Electrostatic Pressure. Appl. Comput. Math. 2017, 7(1-2), 1-11. doi: 10.11648/j.acm.s.2018070102.11

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AMA Style

Aydin Azizi, Niloofar Malekzadeh Fard, Hamed Mobki, Adnène Arbi. Bifurcation Behaviour and Stability Analysis of a Nano-Beam Subjected to Electrostatic Pressure. Appl Comput Math. 2017;7(1-2):1-11. doi: 10.11648/j.acm.s.2018070102.11

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@article{10.11648/j.acm.s.2018070102.11,
  author = {Aydin Azizi and Niloofar Malekzadeh Fard and Hamed Mobki and Adnène Arbi},
  title = {Bifurcation Behaviour and Stability Analysis of a Nano-Beam Subjected to Electrostatic Pressure},
  journal = {Applied and Computational Mathematics},
  volume = {7},
  number = {1-2},
  pages = {1-11},
  doi = {10.11648/j.acm.s.2018070102.11},
  url = {https://doi.org/10.11648/j.acm.s.2018070102.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.s.2018070102.11},
  abstract = {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.},
 year = {2017}
}

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TY  - JOUR
T1  - Bifurcation Behaviour and Stability Analysis of a Nano-Beam Subjected to Electrostatic Pressure
AU  - Aydin Azizi
AU  - Niloofar Malekzadeh Fard
AU  - Hamed Mobki
AU  - Adnène Arbi
Y1  - 2017/07/11
PY  - 2017
N1  - https://doi.org/10.11648/j.acm.s.2018070102.11
DO  - 10.11648/j.acm.s.2018070102.11
T2  - Applied and Computational Mathematics
JF  - Applied and Computational Mathematics
JO  - Applied and Computational Mathematics
SP  - 1
EP  - 11
PB  - Science Publishing Group
SN  - 2328-5613
UR  - https://doi.org/10.11648/j.acm.s.2018070102.11
AB  - 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.
VL  - 7
IS  - 1-2
ER  -

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Author Information

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

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Plain Text BibTeX RIS

APA Style

Aydin Azizi, Niloofar Malekzadeh Fard, Hamed Mobki, Adnène Arbi. (2017). Bifurcation Behaviour and Stability Analysis of a Nano-Beam Subjected to Electrostatic Pressure. Applied and Computational Mathematics, 7(1-2), 1-11. https://doi.org/10.11648/j.acm.s.2018070102.11

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ACS Style

Aydin Azizi; Niloofar Malekzadeh Fard; Hamed Mobki; Adnène Arbi. Bifurcation Behaviour and Stability Analysis of a Nano-Beam Subjected to Electrostatic Pressure. Appl. Comput. Math. 2017, 7(1-2), 1-11. doi: 10.11648/j.acm.s.2018070102.11

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AMA Style

Aydin Azizi, Niloofar Malekzadeh Fard, Hamed Mobki, Adnène Arbi. Bifurcation Behaviour and Stability Analysis of a Nano-Beam Subjected to Electrostatic Pressure. Appl Comput Math. 2017;7(1-2):1-11. doi: 10.11648/j.acm.s.2018070102.11

Copy | Download

@article{10.11648/j.acm.s.2018070102.11,
  author = {Aydin Azizi and Niloofar Malekzadeh Fard and Hamed Mobki and Adnène Arbi},
  title = {Bifurcation Behaviour and Stability Analysis of a Nano-Beam Subjected to Electrostatic Pressure},
  journal = {Applied and Computational Mathematics},
  volume = {7},
  number = {1-2},
  pages = {1-11},
  doi = {10.11648/j.acm.s.2018070102.11},
  url = {https://doi.org/10.11648/j.acm.s.2018070102.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.s.2018070102.11},
  abstract = {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.},
 year = {2017}
}

Copy | Download

TY  - JOUR
T1  - Bifurcation Behaviour and Stability Analysis of a Nano-Beam Subjected to Electrostatic Pressure
AU  - Aydin Azizi
AU  - Niloofar Malekzadeh Fard
AU  - Hamed Mobki
AU  - Adnène Arbi
Y1  - 2017/07/11
PY  - 2017
N1  - https://doi.org/10.11648/j.acm.s.2018070102.11
DO  - 10.11648/j.acm.s.2018070102.11
T2  - Applied and Computational Mathematics
JF  - Applied and Computational Mathematics
JO  - Applied and Computational Mathematics
SP  - 1
EP  - 11
PB  - Science Publishing Group
SN  - 2328-5613
UR  - https://doi.org/10.11648/j.acm.s.2018070102.11
AB  - 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.
VL  - 7
IS  - 1-2
ER  -

Copy | Download