Document Type : Research Paper
Authors
Shahrekord University
Abstract
Using differential quadrature method (DQM), this study investigated pull-in instability of beam-type nano-switches under the effects of small-scale and intermolecular forces including the van der Waals (vdW) and the Casimir forces. In these nano-switches, electrostatic forces served as the driving force, and von-Karman type nonlinear strain was used to examine nonlinear geometric effects. To derive nonlinear governing equations as well as the related boundary conditions for the nano-beam, variation method was used. Besides, to study the influence of size effect, the nonlocal elasticity theory was employed and the resulting governing equations were solved using DQM. Finally, the pull-in parameters were studied using the nonlocal theory and the results were compared with the numerical results of the classical continuum theory as well as experimental results contained in the references. Results demonstrated that taking into consideration the von-Karman type nonlinear strain increases the beam stiffness and hence, the pull-in voltage. Besides, use of the small scale, compared with the classical theory of elasticity, yields results much closer to experimental results.
Graphical Abstract
)
Keywords
Main Subjects
[1] L. Zhang, S. V. Golod, E. Deckardt, V. Prinz and D. Grutzmacher, “Free-standing Si/SiGe micro- and nano-objects”, Physica E, Vol. 23, No. 3-4, pp. 280–284, (2004).
[2] C. H. Ke and H. D. Espinosa, “Nanoelectromechanical systems (NEMS) and modeling, in: M. Rieth, W. Schommers”, P. D. Gennes (Eds.), Handbook of Theoretical and Computational Nanotechnology, American Scientific Publishers, Valencia, CA, (Chapter 121), (2006).
[3] Hamid M. Sedighi1, Nazanin Farjam, “A modified model for dynamic instability of CNT based actuators by considering rippling deformation, tip-charge concentration and Casimir attraction”,Microsyst. Technol., DOI: 10.1007/s00542-016-2956-6, (2016).
[4] A. Darvishian, H. Moeenfard, M. T. Ahmadian and H. Zohoor, “A coupled two degree of freedom pull-in model for micromirrors under capillary force”, Acta Mech.,Vol. 223, No. 2, pp. 387–394, (2012).
[5] J. Zhang. Y. Fu, “Pull-in analysis of electrically actuated viscoelastic microbeams based on a modified couple stress theory”, Meccanica, Vol. 47, No. 7, pp. 1649-1658, (2012).
[6] Y. TadiBeni, A. Koochi and M. Abadyan, “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, Vol. 43, No. 4, pp. 979-988, (2011).
[7] H. Sadeghian and G. Rezazadeh, “Comparison of generalized differential quadrature and Galerkin methods for the analysis of micro-electro-mechanical coupled systems”, Communications in Nonlinear Science and Numerical Simulation, Vol. 14, No. 6, pp. 2807-2816, (2009).
[8] W. H. Lin and Y. P. Zhao, “Casimir effect on the pull-in parameters of nanometer switches”, Microsystem Technologies, Vol. 11, No. 2, pp. 80–85, (2005).
[9] Y. Ga Hu, K. M. Liew, Q. Wang, X. Q. He and B. I. Yakobson, “Nonlocal shell model for elastic wave propagation in single- and double-walled carbon nanotubes”, Journal of the Mechanics and Physics ofSolids, Vol. 56, No. 12, pp. 3475–3485, (2008).
[10] M. Danesh, A. Farajpour and M. Mohammadi, “Axial vibration analysis of a tapered nanorod based on nonlocal elasticity theory and differential quadrature method”, Mechanics Research Communications, Vol. 39, No. 1, pp. 23–27, (2012).
[11] C. W. Lim, C. Li and J. L. Yu, “Free torsional vibration of nanotubes based on nonlocal stress theory”, Journal of Sound and Vibration, Vol. 331, No. 12, pp. 2798–2808, (2012).
[12] H. Zeighampour and Y. TadiBeni, “Cylindrical thin-shell model based on modified strain gradient theory”, International Journal of Engineering Science, Vol. 78, pp. 27–47, (2014).
[13] M. KarimiZeverdejani and Y. TadiBeni, “The nano scale vibration of protein microtubules based on modified strain gradient theory”, Current. Applled Physics, Vol. 13, No. 8, pp. 1566–1576, (2013).
[14] S. L. Kong, S. J. Zhou, Z. F. Nie and K. Wang, Static and dynamic analysis of micro beams based on strain gradient elasticity theory, International Journal of Engineering Science, Vol. 47, pp. 487-498, (2009).
[15] Y. TadiBeni and M. Abadyan, “Size-dependent pull-in instability of torsional nanoactuator”, Physica Scripta, Vol. 88, No. 5, pp. 055801, (2013).
[16] A. C. M. Chong and D. C. C. Lam, “Strain gradient plasticity effect in indentation hardness of polymers”, Journal of Materials Research, Vol. 14, No. 10, pp. 4103–4110, (1999).
[17] P. Mohammadi Dashtaki and Y. TadiBeni, “Effects of Casimir force and thermal stresses on the buckling of electrostatic nano-bridges based on couple stress theory”, Arabian Journal for Science and Engineering, Vol. 39, No. 7, pp. 5753–5763, (2014).
[18] Y. TadiBeni, A. Koochi and M. Abadyan, “Using modified couple stress theory for modeling the size dependent pull-in instability of torsional nano-mirror under Casimir force”, International Journal of Optomechatronics, Vol. 8, No. 1, pp. 47–71, (2014).
[19] H. Zeighampour and Y. TadiBeni, “Size-dependent vibration of fluid-conveying double-walled carbon nanotubes using couple stress shell theory”, Physica E, Vol. 61, pp. 28–39, (2014).
[20] S. Kong, S. Zhou, Z. Nie and K. Wang, “The size-dependent natural frequency of Bernoulli–Euler micro-beams”, International Journal of Engineering Science, Vol. 46, pp. 427–437, (2008).
[21] H. Zeighampour and Y. Tadi Beni, “Analysis of conical shells in the framework of coupled stresses theory”, International Journal of Engineering Science, Vol. 81, pp. 107–122, (2014).
[22] J. Yang, X. L. Jia and S. Kitipornchai, “Pull-in instability of nano-switches using nonlocal elasticity theory”, Journal of Physics D: Applied Physics, Vol. 41, No. 3, pp. 035103, (2008).
[23] J. Abdi, Y. Tadi, A. Noghrehabadi, A. Koochi, A. S. Kazemi, A. Yekrangi, M. “Abadyan and M. Noghrehabadi, Analytical Approach to compute the Internal stress field of NEMS Considering Casimir Forces”, Procedia Engineering,Vol. 10, pp. 3757–3763, (2011).
[24] Y. TadiBeni, M. R. Abadyan and A. Noghrehabadi, “Investigation of Size Effect on the Pull-in Instability of Beam-type NEMS under van der Waals Attraction”, Procedia Engineering, Vol. 10, pp. 1718–1723, (2011).
[25] X. L. Jia, J. Yang and S. Kitipornchai, “Pull-in instability of geometrically nonlinear micro-switches under electrostatic and Casimir forces”, Acta Mech., Vol. 218, No. 1, pp. 161–174, (2011).
[26] J. G. Guo, Y. P. Zhao, “Influence of van der Waals and Casimir Forces on Electrostatic Torsional Actuators”, Journal of Micro electromechanical Systems, Vol. 13, No. 6, pp. 1027–1035, (2004).
[27] A. Ramezani, A. Alasty and J. Akbari, “Influence of van der Waals force on the pull-in parameters of cantilever type nanoscale electrostatic actuators”, Microsystem Technologies, Vol. 12, No. 12, pp. 1153–1161, (2006).
[28] S. Malihi, Y. TadiBeni, H. Golestanian, “Analytical modeling of dynamic pull-in instability behavior of torsional nano/micromirrors under the effect of Casimir force”, Optik-International Journal for Light and Electron Optics, Vol. 127, No. 10, pp. 4426–4437, (2016).
[29] A. C. Eringen, “Nonlocal polar elastic continua”, International Journal of Engineering Science, Vol. 10, pp. 1-16, (1972).
[30] A. C. Eringen, Nonlocal Continuum Field Theories, Springer-Verlag, New York, USA (2002).
[31] A. C. Eringen and D. G. B. Edelen, “On nonlocal elasticity, International Journal of Engineering Science, Vol. 10, pp. 233–248, (1972).
[32] B. Fang, Y. X. Zhen, C. P. Zhang and Y. Tang, “Nonlinear vibration analysis of double-walled carbon nanotubes based on nonlocal elasticity theory”, Applied Mathematical Modelling, Vol. 37, No. 3, pp. 1096-1107, (2013).
[33] S. Malihi, Y. TadiBeni, H. Golestanian,“Size dependent pull-in instability analysis of torsional nano/micromirrors in the presence of molecular force using 2D model”, Optik-International Journal for Light and Electron Optics, Vol. 127, No. 19, pp. 7520–7536, (2016).
[34] W. Chena, C. Shu, W. He and T. Zhong, “The application of special matrix product to differential quadrature solution of geometrically nonlinear bending of orthotropic rectangular plates”, Computers and Structures, Vol. 74, No. 1, pp. 65-76, (2000).
[35] J. Zhao, S. Zhou, B. Wang and X. Wang, “Nonlinear microbeam model based on strain gradient theory”, Applied Mathematical Modelling, Vol. 36, No. 6, pp. 2674-1107, (2012).
[36] C. W. Bert and M. Malik, “Differential quadrature method in computational mechanics, a review”, Applied Mechanics Reviews, Vol. 49, No. 1, pp. 1-27, (1996).
[37] C. Shu and H. Du, “A generalized approach for implementing general boundary conditions in the GDQ free vibration analysis of plates”, International Journal of Solids and Structures, Vol. 34, No. 4, pp. 837-846, (1997).
[38] G. L. Klimchitskaya and V. M. MohhideenUMostepanenko, “Casimir and van der waals Forces between Two Plates or a sphere (lens) above a Plate Made of Real Metals”, Physics Review A, Vol. 61, pp. 62107, (2000).
[39] M. Bestrom and B. E. Sernelius, “Fractional Van Der Waals Interaction”, Physics Review B, Vol. 61, pp. 2204, (2000).
[40] J. N. Israelachvili and D. Tabor, “Measurement of van Der Waals Dispersion Forces in the Range 1.5 to 130 nm”, Proceedings of the Royal society A, Vol. 331, pp. 19-38, (1972).
[41] P. M. Osterberg, Electrostatically actuated micromechanical test structure for material property measurement, Ph.D. Dissertation, Massachusetts Institute of Technology, (1995).
[42] M. Ahmadi and W. C. Miller, “A closed-form model for the pull-in voltage of electrostatically actuated cantilever beam”, Journal of Micromechanics and Microengineering, Vol. 15, No. 4, pp.756-763, (2005).
[43] T. Mousavi, S. Bornassi and H. Haddadpour, “The effect of small scale on the pull-in instability of nano-switches using DQM”, International Journal of Solids and Structures, Vol. 50, No. 9, pp. 1192-1202.
[44] H. Ataei, Y. TadiBeni, “Size-Dependent Pull-In Instability of Electrically Actuated Functionally Graded Nano-Beams Under Intermolecular Forces”, Iranian Journal of Science and Technology, Transactions of Mechanical Engineering, Vol. 40, No. 4, pp. 289-301, (2016).
[45] D. Son, J.-h. Jeong, D. Kwon, “Film-thickness considerations in microcantilever-beam test in measuring mechanical properties of metal thin film”, Thin Solid Films, Vol. 437, No. 1-
2, pp. 182-187, (2003).
[46] Y. Cao, D. Nankivil, S. Allameh, W. Soboyejo, “Mechanical properties of Au films on silicon substrates”, Materials and Manufacturing Processes, Vol. 22, No. 2, pp. 187-194, (2007).
[47] D.C.C. Lam, F. Yang, A.C.M. Chong, J. Wang, P. Tong, “Experiments and theory in strain gradient elasticity”, Journal of the Mechanics and Physics of Solids, Vol. 51, No. 8, pp. 14477-1508, (2003).
[48] Jamal Zare,“Pull-in behavior analysis of vibrating functionally graded micro-cantilevers under suddenly DC voltage”, Journal of applied and computational mechanics, Vol. 1, No. 1, pp. 17-25, (2015).
[49] Morteza Karimi, Mohammad Hossein Shokrani, Ali Reza Shahidi, “Size-dependent free vibration analysis of rectangular nanoplates with the consideration of surface effects using finite difference method”, Journal of applied and computational mechanics, Vol. 1, No. 3, pp. 122-133, (2015).
[50] Hamid M. Sedighi,“The influence of small scale on the Pull-in behavior of nonlocal nano-Bridges considering surface effect, Casimir and van der Waals attractions”, International Journal of Applied Mechanics, Vol. 6, No. 3, pp. 1450030, (2014).
[51] Hamid M. Sedighi, Farhang Daneshmand, Mohamadreza Abadyan, “Modeling the effects of material properties on the pull-in instability of nonlocal functionally graded nano-actuators”, Zeitschrift fur Angewandte Mathematik und Mechanik, Vol. 96, No. 3, pp. 385-400, (2016).
[52] R. Maranganti, P. Sharma, “A novel atomistic approach to determine strain-gradient elasticity constants: Tabulation and comparison for various metals, semiconductors, silica, polymers and the (ir) relevance for nanotechnologies”, J. Mech. Phys. Solids, Vol. 55, No. 9, pp. 1823-1852, (2007).
', './data/jcarme/coversheet/cover_en.jpg'))
Send comment about this article