Buckling of multi wall carbon nanotube cantilevers in the vicinity of graphite sheets using monotone positive method

Noghrehabadia, Aminreza; Ghalambaza, Mohammad; Ghanbarzadeh, Afshin

doi:10.22061/jcarme.2012.27

تعداد نشریات	11
تعداد شماره‌ها	227
تعداد مقالات	2,309
تعداد مشاهده مقاله	3,591,144
تعداد دریافت فایل اصل مقاله	2,631,046

	Buckling of multi wall carbon nanotube cantilevers in the vicinity of graphite sheets using monotone positive method
Journal of Computational & Applied Research in Mechanical Engineering (JCARME)
مقاله 3، دوره 1، شماره 2، فروردین 2012، صفحه 89-98 اصل مقاله (411.74 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22061/jcarme.2012.27
نویسندگان
Aminreza Noghrehabadia^* ؛ Mohammad Ghalambaza؛ Afshin Ghanbarzadeh
Department of Mechanical Engineering, Shahid Chamran University of Ahvaz, Ahvaz, Iran
تاریخ دریافت: 27 مرداد 1390، تاریخ بازنگری: 12 آبان 1390، تاریخ پذیرش: 17 آبان 1390
چکیده
In this paper, a monotone positive solution is studied for buckling of a distributed model of multi walled carbon nanotube (MWCNT) cantilevers in the vicinity of thin and thick graphite sheets subject to intermolecular forces. In the modeling of intermolecular forces, Van der Waals forces are taken into account. A hybrid nano-scale continuum model based on Lennard–Jones potential is applied to simulate the intermolecular force-induced deflection of MWCNT. A positive monotone solution based on Green’s function in the form of a nonlinear iterative integral is introduced to obtain a solution for deflection of MWCNT cantilevers. In order to determine the accuracy of the presented method, the results are compared with numerical results of a numerical method as well as other methods reported in the literature. The results show that the monotone iterative solution is stable and converged to numerical results with a few iterations. The results of the present work are useful to prove the stability and convergence of Green’s function to deal with deflection of nano cantilever actuators in future works and simplifications.
کلیدواژه‌ها
Nano cantilever؛ Monotone solution؛ Green’s function؛ Van der Waals force؛ MWCNT

مراجع
[1] A. M. K. Esawi, M. M. Farag, “Carbon nanotube reinforced composites: potential and current challenges”, Mater Des. Vol. 28, pp. 2394-401, (2007). [2] Y. Showkat, J. Chowdhury, B. Howard, “Thermo-Mechanical Properties of Graphite-Epoxy Composite”, International Review of Mechanical Engineering, Vol. 4. No. 6, pp.785-790, (2010). [3] C. Li, T. Thostenson, T. W. Chou, “Sensors and actuators based on carbon nanotubes and their composites: a review”, Compos Sci Technol. Vol. 68, pp. 1227-49, (2008). [4] M. Kitzmantel, E. Neubauer, V. Brueser, M. Chirtoc, M. Attard, “Influence of Manufacturing Method and Interface Activators on the Anisotropic Thermal Behaviour of Copper Carbon Nanofibre Composites”, International Review of Mechanical Engineering, Vol. 5, No. 2, pp. 315-320, (2010). [5] P. Kim, C. M. Lieber, “Nanotube Nanotweezers”, Journal of Science, Vol. 286, pp. 2148, (1999). [6] J. Cumings, A. Zettl, “Low-Friction Nanoscale Linear Bearing Realized from Multiwall Carbon Nanotubes”, Journal of Science, Vol. 289, pp. 602, (2000). [7] P. Poncharal, Z. L. Wang, D. Ugarte, W. A. Heer, “Nanomeasurements in transmission electron microscopy”, Science, Vol. 283, pp. 1513, (1999). [8] A. Husain, J. Hone, H. W. C. Postma, X. M. H. Huang, T. Drake, M. Barbic, A. Scherer, M. L. Roukes, “Nanowire-based very-high-frequency electromechanical resonator”, Applied Physics Letters Vol. 83, pp. 1240-1242, (2003). [9] V. Sazonova, Y. Yaish, H. Üstünel, D. Roundy, T. A. Arias, P. L. McEuen, “A tunable carbon nanotube electromechanical oscillator”, Nature, Vol. 431, pp. 284-287, (2004). [10] P. A. Williams, S. J. Papadakis, A. M. Patel, M. R. Falvo, S. Washburn, R. Superfine, “Torsional response and stiffening of individual multiwalled carbon nanotubes”, Phys. Rev. Lett. Vol. 89, 255502 (2002). [11] A. M. Fennimore, T. D. Yuzvinsky, W. Q. Han, M. S. Fuhrer, J. Cumings, A. Zettl, “Rotational actuators based on carbon nanotubes”, Nature, Vol. 424. pp. 408-410, (2003). [12] S. Akita, “Nanotweezers consisting of carbon nanotubes operating in an atomic force microscope”, Appl Phys Lett. Vol. 79, pp.1591-3, (2001). [13] Y. Cao, Y. Liang, S. Dong, Y. Wang, “A multi-wall carbon nanotube (MWCNT) relocation technique for atomic force microscopy (AFM) samples”, Ultramicroscopy, Vol. 103. No.2, pp. 103-8, (2005). [14] M. Paradise, T. Goswami, “Carbon nanotubes–production and industrial applications”, Mater Des. Vol. 28, No.5, pp. 1477-89, (2007). [15] R. H. Baughman, C. Cui, A. A. Zakhidov, Z. Iqbal, J. N. Barisci, G. M. Spinks, and et al. “Carbon nanotube actuators”, J. Science, Vol. 284, pp. 1340-4, (1999). [16] C. H. Ke, N. Pugno, B. Peng, H. D. Espinosa, “Experiments and modeling of carbon nanotube-based NEMS devices”, J. Mech. Phys. Solids. Vol. 53, pp. 1314-33, (2005). [17] A. Koochi, A. S. Kazemi, A. Noghrehabadi, A. Yekrangi, M. Abayan, “New approach to model the buckling and stable length of multi walled carbon nanotube probes near graphite sheets”, Int. J. Materials and Design Vol. 32, No. 5, pp. 2949-2955, 2011. [18] R. Soroush, A. Koochi, A. S. Kazemi, A. Noghrehabadi, H. Haddadpour, M. Abadyan, “Investigating the effect of Casimir and Van der Waals attractions on the electrostatic pull-in instability of nano-actuators”, J. Phys. Scr., Vol. 82, pp. 045801, 2010. [19] F. M. Serry, D. Walliser, G. J. Maclay, “The role of the Casimir effect in the static deflectionand stiction of membrane strips in MEMS”, J. Appl. Phys. Vol. 84, No. 50, pp. 2501-2506, (2008). [20] H. B. Chan, V. A. Aksyuk, R. N. Kleiman, D. J. Bishop, F. Capasso, “Quantum mechanical actuation of micro-electromechanical systems by the Casimir force”, Science, Vol. 291, pp. 1941-1944, (2001). [21] A. Gusso, G. J. Delben, “Influence of the Casimir force on the pull-in parameters of silicon based electrostatic torsional actuators Sensors”, Actuat. J. A-Phys. Vol. 135, pp. 792-800, (2007). [22] W. H. Lin, Y. P. Zhao, “Casimir effect on the pull-in parameters of nanometer switches”, Microsyst. Thechnol. Vol. 11, pp. 80-85, (2005). [23] W. H. Lin, Y. P. Zhao, “Nonlinear behavior for nanoscale electrostatic actuators with Casimir force”, Chaos Soliton. Fract. Vol. 23, pp. 1777-1785, (2005). [24] A. Ramezani, A. Alasty, J. Akbari., “Closed-form approximation and numerical validation of the influence of Van der Waals force on electrostatic cantilevers at nano-scale separations”, Nanotechnology Vol. 19, pp. 15501-15509, (2008). [25] A. Ramezani, A. Alasty, J. Akbari, “Analytical investigation and numerical verification of Casimir effect on electrostatic nano-cantilevers”, Microsystem Technologies, Vol. 14, pp. 145-157, (2008). [26] A. Noghrehabadi, M. Ghalambaz, Y. Tadi Beni, M. Abadyan, M. Noghrehabadi, M. Noghrehabadi, “A new solution on the buckling and stable length of multi wall carbon nanotube probes near graphite sheets”, Procedia Engineering, Vol. 10, pp. 3733-3741, (2011). [27] M. Abadyan, A. Novinzadeh, A. Kazemi., “Approximating the effect of the Casimir force on the instability of electrostatic nano-cantilevers”, Phys. Scr. Vol. 81, pp. 15801-15811, (2010). [28] G. Failla, A. Santini, On Euler–Bernoulli discontinuous beam solutions via uniform-beam Green’s functions”, Int. J. Solids Struct. Vol. 44, pp. 7666-7687, (2007). [29] E. Alves, T. F. Ma, M. L. Pelicer, “Monotone positive solutions for a fourth order equation with nonlinear boundary conditions” J. Nonlinear Analysis. Vol. 71. pp. 3834-3841, (2009). [30] A. R. Aftabizadeh, “Existence and uniqueness theorems for fourth-order boundary value problems”, J. Math. Anal. Appl. Vol. 116, pp. 415-426 (1986). [31] R. P. Agarwal, Y. M. Chow, “Iterative methods for a fourth order boundary value problem”, Comput. Appl. Math. Vol. 10, pp. 203-217, (1985). [32] R. P. Agarwal, “On the fourth-order boundary value problems arising in bean analysis”, Differen. Integ. Equations Vol. 2, pp. 91-110, (1989). [33] G. Han, F. Li, “Multiple solutions of some fourth-order boundary value problems”, Nonlinear Anal. Vol. 66. pp. 2591- 2603, (2007). [34] R. Y. Ma, J. H. Zhang, S. M. Fu, “The method of lower and upper solutions for fourth-order two-point boundary value problems”, J. Math. Anal. Appl. Vo. 215, pp. 415-422, (1997). [35] M. Pei, S. K. Chang, “Monotone iterative technique and symmetric positive solutions for a fourth-order boundary value problem”, Math. Comput. Modell. Vol. 51, pp. 1260-1267, (2010). [36] X. Lin, D. Jiang, X. Li., “Existence and uniqueness of solutions for singular fourth-order, boundary value problems”, Journal of Computational and Applied Mathematics Vol. 196, pp. 155-161, (2006). [37] S. S. Gupta, R. C. Batra, Continuum structures equivalent in normal mode vibrations to single-walled carbon nanotubes”, Comput. Mater. Sci., Vol. 43, pp. 715-23, (2008). [38] M. Desquenes, S. V. Rotkin, N. T. Alaru, “Calculation of pull-in voltages for carbonnanotube- based nanoelectromechanical switches”, Nanotechnology Vol. 13, pp. 120-31, (2002). [39] J. E. Lennard-Jones, “Perturbation problems in quantum mechanics”, Proc. Roy. Soc.:A, Vol. 129, pp. 598–615, (1930). [40] C. Ke, H. D. Espinosa, “Nanoelectromechanical systems (NEMS) and modeling”, Handbook of theoretical and computational nanotechnology Rieth M, Schommers W, Gennes PD., Valencia, CA: American Scientific Publishers, 2006. [41] L. A. Girifalco, M. Hodak, R. S. Lee, “Carbon nanotubes, buckyballs, ropes, and a universal graphitic potential”, Phys. Rev: B Vol. 62, No. 19, pp. 13104-10, (2000). [42] H. Amann, “Fixed point equations and nonlinear eigenvalue problem in ordered Banach space”, SIAM Review Vol. 18, pp. 620-709, (1976). [43] Na T. Y. “Computational method in engineering boundary value problems”, Academic Press, New York, (1979).
آمار تعداد مشاهده مقاله: 2,674 تعداد دریافت فایل اصل مقاله: 1,744

سامانه مدیریت نشریات علمی. طراحی و پیاده سازی از سیناوب

پیوندهای مفید

آمار

Buckling of multi wall carbon nanotube cantilevers in the vicinity of graphite sheets using monotone positive method