Static and dynamic pull-in instability of multi-walled carbon nanotube probes by He’s iteration perturbation method

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• 作者：Hamid M. Sedighi ; Farhang Daneshmand
• 关键词：Carbon nanotubes ; Van der Waals attraction ; Pull ; in instability ; Graphite sheets ; Iteration perturbation method ; Electrostatic actuation
• 刊名：Journal of Mechanical Science and Technology
• 出版年：2014
• 出版时间：September 2014
• 年：2014
• 卷：28
• 期：9
• 页码：3459-3469
• 全文大小：1,212 KB
• 参考文献：1. C. Ke, H. D. Espinosa and N. Pugno, N., Numerical analysis of nanotube based NEMS devices-Part II: Role of finite Kinematics, Stretching and Charge Concentrations, / Journal of Applied Mechanics, 72 (2005) 726-31. CrossRef
  2. Y. Cao, Y. Liang, S. Dong and Y. Wang, A multi-wall carbon nanotube (MWCNT) relocation technique for atomic force microscopy (AFM) samples, / Ultramicroscopy, 103 (2) (2005) 103-. CrossRef
  3. M. Dequesnes, Z. Tang and N. R. Aluru, Static and dynamic analysis of carbon nanotube-based switches, / Journal of Engineering Materials and Technology, 126 (2004) 230-37. CrossRef
  4. A. Farrokhabadi, R. Rach and M. Abadyan, Modeling the static response and pull-in instability of CNT nanotweezers under the Coulomb and van der Waals attractions, / Physica E: Low-dimensional Systems and Nanostructures, 53 (2013) 137-45. CrossRef
  5. A. Farrokhabadi, A. Koochi and M. Abadyan, Modeling the instability of CNT tweezers using a continuum model, / Microsystem Technologies, 20 (2) (2014) 291-02. CrossRef
  6. R. Soroush, A. Koochi, A. S. Kazemi, A. Noghrehabadi, H. Haddadpour and M. Abadyan, Investigating the effect of Casimir and van der Waals attractions on the electrostatic pull-in instability of nano-actuators, / Phys. Scr., 82 (2010) 045801. CrossRef
  7. A. Koochi, A. S., Kazemi, A. Noghrehabadi, A. Yekrangi and M. Abadyan, New approach to model the buckling and stable length of multi walled carbon nanotube probes near graphite sheets, / Materials and Design, 32 (2011) 2949-955. CrossRef
  8. A. Vahdati, M. Vahdati and R. A. Mahdavinejad, Simulating the buckling deflection of carbon nanotube-made detectors used in medical detections by applying a continuum mechanics model, / Life Science Journal, 10 (1) (2013) 186-91.
  9. H. Zeighampour and Y. Tadi Beni, Cylindrical thin-shell model based on modified strain gradient theory, / International Journal of Engineering Science, 78 (2014) 27-7. CrossRef
  10. P. Wang, X. Yan, Y. Jiang and L. Lin, Fabrication and characterization of electrostatic oscillators based on CNT bundles, / Sensors and Actuators A, 177 (2012) 93-8. CrossRef
  11. A. Koochi, N. Fazli, R. Rach and M. Abadyan, Modeling the pull-in instability of the CNT-based probe/actuator under the coulomb force and the van der waals attraction, / Latin American Journal of Solids and Structures, 11 (8) (2014) 1315-328. CrossRef
  12. F. Daneshmand, M. Rafiei, S. R. Mohebpour and M. Heshmati, Stress and strain-inertia gradient elasticity in free vibration analysis of single walled carbon nanotubes with first order shear deformation shell theory, / Applied Mathematical Modelling, 37 (16-7) (2013) 7983-003. CrossRef
  13. E. Ghavanloo, F. Daneshmand and M. Rafiei, Vibration and instability analysis of carbon nanotubes conveying fluid and resting on a linear viscoelastic Winkler foundation, / Physica E: Low-dimensional Systems and Nanostructures, 42 (9) (2010) 2218-224. CrossRef
  14. F. Daneshmand, H. Farokhi and M. Amabili, A higherorder mathematical modeling for dynamic behavior of protein microtubule shell structures including shear deformation and small-scale effects, / Mathematical Biosciences (2014) In Press.
  15. J. L. Tsai and J. F. Tu, Characterizing mechanical properties of graphite using molecular dynamics simulation, / Mater Des, 31 (1) (2010) 194-. CrossRef
  16. K. I. Tserpes, Role of intertube spacing in the pullout forces of double-walled carbon nanotubes, / Mater Des, 28 (7) (2007) 2197-01. CrossRef
  17. M. Desquenes, S. V. Rotkin and N. R. Alaru, Calculation of pull-in voltages for carbonnanotube based nanoelectromechanical switches, / Nanotechnology, 13 (2002) 120-1. CrossRef
  18. R. C. Batra and A. Sears, Continuum models of multiwalled carbon nanotubes, / Int. J. Solids Struct., 44 (2007) 7577-6. CrossRef
  19. S. S. Gupta and R. C. Batra, Continuum structures equivalent in normal mode vibrations to single-walled carbon nanotubes, / Comput. Mater. Sci., 43 (2008) 715-3. CrossRef
  20. L. A. Girifalco, M. Hodak and R. S. Lee, Carbon nanotubes, buckyballs, ropes, and a universal graphitic potential, / Phys Rev: B, 62 (19) (2000) 13104-0. CrossRef
  21. 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, 37 (2013) 1096-107. CrossRef
  22. H. Zeighampour and Y. Tadi Beni, Size-dependent vibration of fluid-conveying double-walled carbon nanotubes using couple stress shell theory, / Physica E: Low-dimensional Systems and Nanostructures, 61 (2014) 28-9. CrossRef
  23. S. Narendar and S. Gopalakrishnan, Nonlocal continuum mechanics formulation for axial, flexural, shear and contraction coupled wave propagation in single walled carbon nanotubes, / Latin American Journal of Solids and Structures, 9 (2012) 497-13. CrossRef
  24. K. Kiani, Vibration and instability of a single-walled carbon nanotube in a three-dimensional magnetic field, / Journal of Physics and Chemistry of Solids, 75 (1) (2014) 15-2. CrossRef
  25. S. Bagheri, A. Nikkar and H. Ghaffarzadeh, Study of nonlinear vibration of Euler-Bernoulli beams by using analytical approximate techniques, / Latin American Journal of Solids and Structures, 11 (1) (2014) 157-68. CrossRef
  26. H. M. Sedighi and K. H. Shirazi, A new approach to analytical solution of cantilever beam vibration with nonlinear boundary condition, / Journal of Computational and Nonlinear Dynamics, 7 (3) (2012) 034502. CrossRef
  27. H. M. Sedighi, K. H. Shirazi and J. Zare, Novel equivalent function for deadzone nonlinearity: Applied to analytical solution of beam vibration using he’s parameter expanding method, / Latin American Journal of Solids and Structures, 9 (2012) 443-51. CrossRef
  28. J. H. He, Max-min approach to nonlinear oscillators, / International Journal of Nonlinear Sciences and Numerical Simulation, 9 (2008) 207-10.
  29. H. M. Sedighi and K. H. Shirazi, Asymptotic approach for nonlinear vibrating beams with saturation type boundary condition, / Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 227 (11) (2013) 2479-486.
  30. M. Ghadimi, A. Barari, H. D. Kaliji and G. Domairry, Periodic solutions for highly nonlinear oscillation systems, / Archives of Civil and Mechanical Engineering, 12 (3) (2012) 389-95. CrossRef
  31. H. M. Sedighi, K. H. Shirazi and M. A. Attarzadeh, A study on the quintic nonlinear beam vibrations using asymptotic approximate approaches, / Acta Astronautica, 91 (2013) 245-50. CrossRef
  32. H. M. Sedighi, Size-dependent dynamic pull-in instability of vibrating electrically actuated microbeams based on the strain gradient elasticity theory, / Acta Astronautica, 95 (2014) 111-23. CrossRef
  33. H. Ghaffarzadeh and A. Nikkar, Explicit solution to the large deformation of a cantilever beam under point load at the free tip using the variational iteration method-II, / Journal of Mechanical Science and Technology, 27(11) (2013) 3433-438. CrossRef
  34. H. 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, 6 (3) (2014) 1450030, doi: 10.1142/S1758825114500306 . CrossRef
  35. J. H. He, Hamiltonian approach to nonlinear oscillators, / Physics Letters A, 374 (23) (2010) 2312-314. CrossRef
  36. J. H. He, Iteration perturbation method for strongly nonlinear oscillations, / Journal of Vibration and Control, 7 (2001) 631-42. CrossRef
  37. J. H. He, Some asymptotic methods for strongly nonlinear equations, / International Journal of Modern Physics B, 20 (10) (2006) 1141-199. CrossRef
  38. J. H. He, Asymptotic methods for solitary solutions and compactons, / Abstract and Applied Analysis, 916793 (2012) doi:10.1155/2012/916793 .
  39. S. J. Liao, / Beyond perturbation, CRC Press, Boca Raton (2003). CrossRef
  40. A. Koochi, A. Kazemi and M. Abadyan, Simulating deflection and determining stable length of freestanding carbon nanotube probe/sensor in the vicinity of grapheme layers using a nanoscale continuum model, / Nano, 06 (2011) 419 DOI: 10.1142/S1793292011002731 . CrossRef
  41. A. Koochi, A. Noghrehabadi and M. Abadyan, Approximating the effect of van der waals force on the instability of electrostatic nano-cantilevers, / International Journal of Modern Physics B, 25 (29) (2011) 3965-976. CrossRef
  42. R. Soroush, A. Koochi, A. S. Kazemi and M. Abadyan, Modeling the effect of van der Waals attraction on the instability of electrostatic cantilever and doubly-supported nanobeams using modified adomian method, / International Journal of Structural Stability and Dynamics, 12 (05) (2012) 1250036. CrossRef
  43. J. H. He, Homotopy perturbation method with two expanding parameters, / Indian J. Phys., 88 (2) (2014) 193-96. CrossRef
  
• 作者单位：Hamid M. Sedighi (1)
  Farhang Daneshmand (2) (3) (4)
  
  1. Mechanical Engineering Department, Faculty of Engineering, Shahid Chamran University of Ahvaz, Ahvaz, 61357-43337, Iran
  2. Department of Mechanical Engineering, McGill University, 817 Sherbrooke Street West, Montreal, Quebec, H3A 2K6, Canada
  3. Department of Bioresource Engineering, McGill University, 21111 Lakeshore Road, Sainte-Anne-de-Bellevue, Quebec, H9X 3V9, Canada
  4. School of Mechanical Engineering, Shiraz University, Shiraz, Iran
  
• ISSN：1976-3824

文摘

A continuum model is utilized to extract the nonlinear governing equation for Carbon nanotube (CNT) probes near graphite sheets. The van der Waals (vdW) intermolecular force and electrostatic actuation are included in the equation of motion. Static and dynamic pull-in behavior of the system is investigated in this paper. To this end, a new asymptotic procedure is presented to predict the pull-in instability of electrically actuated CNTs by employing an analytic approach namely He’s iteration perturbation method (IPM). The effects of basic non-dimensional parameters such as initial amplitude, intermolecular force, geometrical parameter and actuation voltage on the pull-in instability as well as the fundamental frequency are studied. The obtained results from numerical simulations by employing three mode assumptions verify the strength of the analytical procedure. The qualitative analysis of the system dynamics shows that the equilibrium points of the autonomous system include stable center points and unstable saddle nodes. The phase portraits of the carbon nanotube actuator exhibit periodic and homoclinic orbits.