Hostname: page-component-76fb5796d-vfjqv Total loading time: 0 Render date: 2024-04-25T20:55:24.027Z Has data issue: false hasContentIssue false
  • English
  • Français

Application of Modified Couple Stress Theory and Homotopy Perturbation Method in Investigation of Electromechanical Behaviors of Carbon Nanotubes

Part of: Equations of mathematical physics and other areas of application

Published online by Cambridge University Press:  11 October 2016

Mir Masoud Seyyed Fakhrabadi
Mir Masoud Seyyed Fakhrabadi*
Affiliation:
School of Mechanical Engineering, College of Engineering, University of Tehran, Tehran, Iran
*
*Corresponding author. Email:mfakhrabadi@ut.ac.ir, msfakhrabadi@gmail.com (M. M. S. Fakhrabadi)
Get access

Abstract

The paper presents the size-dependant behaviors of the carbon nanotubes under electrostatic actuation using the modified couple stress theory and homotopy perturbation method. Due to the less accuracy of the classical elasticity theorems, the modified couple stress theory is applied in order to capture the size-dependant properties of the carbon nanotubes. Both of the static and dynamic behaviors under static DC and step DC voltages are discussed. The effects of various dimensions and boundary conditions on the deflection and pull-in voltages of the carbon nanotubes are to be investigated in detail via application of the homotopy perturbation method to solve the nonlinear governing equations semi-analytically.

Keywords

Carbon nanotubesmodified couple stress theoryhomotopy perturbation methodelectrostatic actuation

MSC classification

Secondary: 35Q70: PDEs in connection with mechanics of particles and systems
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 9 , Issue 1 , February 2017 , pp. 23 - 42
Copyright
Copyright © Global-Science Press 2017 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1] Iijima, S., Helical microtubules of graphitic carbon, Nature, 354(6348) (1991), pp. 56–58.CrossRefGoogle Scholar
[2] Sung, M., Paek, S.-U., Ahn, S.-H. and Lee, J. H., A study of carbon-nanotube-based nanoelectromechanical resonators tuned by shear strain, Comput. Mater. Sci., 51(1) (2012), pp. 360–364.CrossRefGoogle Scholar
[3] Loh, O., Wei, X., Sullivan, J., Ocola, L. E., Divan, R. and Espinosa, H. D., Carbon-carbon contacts for robust nanoelectromechanical switches, Adv. Mater., 24(18) (2012), pp. 2463–2468.CrossRefGoogle ScholarPubMed
[4] Cheng, C. L. and Zhao, G. J., Steered molecular dynamics simulation study on dynamic self-assembly of single-stranded DNA with double-walled carbon nanotube and graphene, Nanoscale, 4(7) (2012), pp. 2301–2305.CrossRefGoogle Scholar
[5] Adhikari, S. and Chowdhury, R., The calibration of carbon nanotube based bionanosensors, J. Appl. Phys., 107(12) (2010), pp. 124322–124322.CrossRefGoogle Scholar
[6] Koochi, A., Kazemi, A. S., Noghrehabadi, A., Yekrangi, A. and Abadyan, M., New approach to model the buckling and stable length of multi walled carbon nanotube probes near graphite sheets, Mater. Design, 32(5) (2011), pp. 2949–2955.CrossRefGoogle Scholar
[7] Fakhrabadi, M. M. S., Samadzadeh, M., Rastgoo, A., Yazdi, M. H. and Mashhadi, M. M., Vibrational analysis of carbon nanotubes using molecular mechanics and artificial neural network, Physica E: Low-Dimensional Systems and Nanostructures, 44(3) (2011), pp. 565–578.CrossRefGoogle Scholar
[8] Fakhrabadi, M. M. S., Amini, A., Reshadi, F., Khani, N. and Rastgoo, A., Investigation of buckling and vibration properties of hetero-junctioned and coiled carbon nanotubes, Comput. Mater. Sci., 73 (2013), pp. 93–112.CrossRefGoogle Scholar
[9] Huang, X., Yuan, H., Liang, W. and Zhang, S., Mechanical properties and deformation morphologies of covalently bridged multi-walled carbon nanotubes: multiscale modeling, J. Mech. Phys. Solids, 58(11) (2010), pp. 1847–1862.CrossRefGoogle Scholar
[10] Pradhan, S. C. and Murmu, T., Small-scale effect on vibration analysis of single-walled carbon nanotubes embedded in an elastic medium using nonlocal elasticity theory, J. Appl. Phys., 105(12) (2009), pp. 124306–124306.CrossRefGoogle Scholar
[11] Ansola, R., Veguería, E., Canales, J. and Alonso, C., Evolutionary optimization of compliant mechanisms subjected to non-uniform thermal effects, J. Finite. Elements. Anal. Design, 57 (2012), pp. 1–14.CrossRefGoogle Scholar
[12] Tayyaba, S., Afzulpurkar, N. and Ashraf, M. W., Simulation and design optimization of piezoelectricaly actuated valveless blood pump for hemofiltration system, J. Sens. Transducers., 139 (2012), pp. 63–78.Google Scholar
[13] Zand, M. M., The dynamic pull-in instability and snap-through behavior of initially curved microbeams, J. Mech. Adv. Mat. Struct., 19 (2012), pp. 485–491.CrossRefGoogle Scholar
[14] Stölken, J. S. and Evans, A. G., A microbend test method for measuring the plasticity length scale, Acta Materialia, 46(14) (1998), pp. 5109–5115.CrossRefGoogle Scholar
[15] Mindlin, R. and Tiersten, H., Effects of couple-stresses in linear elasticity, Archive Rat. Mech. Anal., 11(1) (1962), pp. 415–448.CrossRefGoogle Scholar
[16] Yang, F., Chong, A. C. M., Lam, D. C. C. and Tong, P., Couple stress based strain gradient theory for elasticity, Int. J. Solids Structures, 39(10) (2002), pp. 2731–2743.CrossRefGoogle Scholar
[17] Koiter, W. T., Couple stresses in the theory of elasticity, I and II, Nederl. Akad. Wetensch. Proc. Ser. B, 67 (1964), pp. 17–29.Google Scholar
[18] Toupin, R. A., Elastic materials with couple-stresses, Archive Rat. Mech. Anal., 11(1) (1962), pp. 385–414.CrossRefGoogle Scholar
[19] Mindlin, R. D., Influence of couple-stresses on stress concentrations, Exp. Mech., 3(1) (1963), pp. 1–7.CrossRefGoogle Scholar
[20] Mindlin, R. D. and Tiersten, H. F., Effects of couple-stresses in linear elasticity, Archive Rat. Mech. Anal., 11(1) (1962), pp. 415–448.CrossRefGoogle Scholar
[21] Dequesnes, M., Rotkin, S. V. and Aluru, N. R., Calculation of pull-in voltages for nanoelectromechanical switches, J. Nanotech., 13 (2002), pp. 120–131.CrossRefGoogle Scholar
[22] Ke, C. and Espinosa, H. D., Numerical analysis of nanotube based NEMS devices–part I: electrostatic charge distribution on multiwalled nanotubes, J. Appl. Mech., 72 (2005), pp. 721–725.CrossRefGoogle Scholar
[23] Ke, C., Espinosa, H. D. and Pugno, N., Numerical analysis of nanotube based NEMS devices– part II: role of finite kinematics, stretching and charge concentration, J. Appl.Mech., 72 (2005), pp. 726–731.CrossRefGoogle Scholar
[24] Ouakad, H. M. and Younis, M. I., Nonlinear dynamics of electrically actuated carbon nanotube resonators, J. Comput. Nonlinear Dyn., 5 (2010), pp. 1–13.Google Scholar
[25] Soroush, R., Koochi, A., Kazemi, A. S., Noghrehabadi, A., Haddadpour, H. and Abadyan, M., Investigating the effect of Casimir and van der Waals attractions on the electrostatic pull-in instability of nano actuators, J. Phys. Scr., 82 (2010), 045801.CrossRefGoogle Scholar
[26] Koochi, A., Kazemi, A., Khandani, F. and Abadyan, M., Influence of surface effects on size-dependent instability of nano-actuators in the presence of quantum vacuum fluctuations, J. Phys. Scr., 85 (2012), 035804.CrossRefGoogle Scholar
[27] Abadyan, M., Novinzadeh, A. and Kazemi, A., Approximating the effect of the Casimir force on the instability of electrostatic nano-cantilevers, J. Phys. Scr., 81 (2010), 015801.CrossRefGoogle Scholar
[28] Koochi, A., Noghrehabadi, A., Abadyan, M. and Roohi, E., Approximating the effect of van der Waals force on the instability of electrostatic nano-cantilevers, Int. J. Modern Phys. B, 25(29) (2011), pp. 3965–3976.CrossRefGoogle Scholar
[29] Abdi, J., Koochi, A., Kazemi, A. S. and Abadyan, M., Modeling the effects of size dependence and dispersion forces on the pull-in instability of electrostatic cantilever NEMS using modified couple stress theory, Smart Mater. Struct., 20 (2011), 055011.CrossRefGoogle Scholar
[30] He, J. H., Homotopy perturbation technique, Comput. Methods Appl. Mech. Eng., 178(3) (1999), pp. 257–262.CrossRefGoogle Scholar
[31] Yang, F., Chong, A. C. M., Lam, D. C. C. and Tong, P., Couple stress based strain gradient theory for elasticity, Int. J. Solids Struct., 39(10) (2002), pp. 2731–2743.CrossRefGoogle Scholar
[32] Ke, C. H., Pugno, N., Peng, B. and Espinosa, H. D., Experiments and modeling of carbon nanotube-based NEMS devices, J. Mech. Phys. Solids, 53(6) (2005), pp. 1314–1333.CrossRefGoogle Scholar
[33] Fakhrabadi, M. M. S., Rastgoo, A. and Ahmadian, M. T., Analysis of pull-in instability of electrostatically actuated carbon nanotubes using the homotopy perturbation method, J. Mech. Mater. Struct., 8(8) (2013), pp. 385–401.CrossRefGoogle Scholar
[34] Mojahedi, M., Zand, M. M. and Ahmadian, M. T., J. Appl. Math. Model., 34 (2010), pp. 1032–1041.CrossRefGoogle Scholar
[35] Zand, M. Moghimi and Ahmadian, M. T., Application of homotopy analysis method in studying dynamic pull-in instability of microsystems, Mech. Res. Commun., 36(7) (2009), pp. 851–858.CrossRefGoogle Scholar