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International Journal for Multiscale Computational Engineering
Factor de Impacto: 1.016 Factor de Impacto de 5 años: 1.194 SJR: 0.554 SNIP: 0.68 CiteScore™: 1.18

ISSN Imprimir: 1543-1649
ISSN En Línea: 1940-4352

International Journal for Multiscale Computational Engineering

DOI: 10.1615/IntJMultCompEng.2012002766
pages 295-305


Iman Mehdipour
Department of Mechanical Engineering, Semnan Branch, Islamic Azad University, Semnan, Iran ; Young Researcher Club, Semnan Branch, Islamic Azad University, Semnan, Iran
Amin Barari
Aalborg University
Ganji Domairry
Department of Mechanical Engineering, Babol University of Technology, Babol, Iran


In this study, based on continuum mechanics and an elastic beam model, nonlinear free vibration of embedded single-walled carbon nanotube considering the effects of rippling deformation and midplane stretching on nonlinear frequency is investigated. By utilizing He's energy balance method, the relationship of nonlinear amplitude and frequency for the single-walled carbon nanotube is expressed. The amplitude frequency response curves of the nonlinear free vibration for the single-walled carbon nanotube are obtained and the effects of rippling deformation, midplane stretching, and surrounding elastic medium on the amplitude frequency response characteristics are discussed. In addition, the rippling instability of carbon nanotubes and the effective parameters on their behavior are briefly discussed.


  1. Ansari, R., Hemmatnezhad, M., and Ramezannezhad, H., Application of HPM to the nonlinear vibrations of multiwalled carbon nanotubes. DOI: 10.1002/num.20499

  2. Barari, A., Omidvar, M., Ghotbi, A. R., and Ganji, D. D., Application of homotopy perturbation method and variational iteration method to nonlinear oscillator differential equations. DOI: 10.1007/s10440-008-9248-9

  3. Barari, A., Kaliji, H. D., Ghadimi, M., and Domairry, G., Non-linear vibration of Euler–Bernoulli beams. DOI: 10.1590/S1679-78252011000200002

  4. Bayat, M., Shahidi, M., Barari, A., and Domairry, G., Numerical analysis of the nonlinear vibration of coupled oscillator systems.

  5. Bayat, M., Barari, A., Shahidi, M., and Domairry, G., On the approximate analytical solution of Euler-Bernoulli beams.

  6. Fereidoon, A., Ghadimi, M., Barari, A., Kaliji, H. D., and Domairry, G., Nonlinear vibration of oscillation systems using frequencyamplitude formulation. DOI: 10.3233/SAV-2011-0633

  7. Fu, Y. M., Hong, J. W., and Wang, X. Q., Analysis of nonlinear vibration for embedded carbon nanotubes. DOI: 10.1016/j.jsv.2006.02.024

  8. Ganji, S. S., Ganji, D. D., Ganji, Z. Z., and Karimpour, S., Periodic solution for strongly nonlinear vibration system by He's energy balance method. DOI: 10.1007/s10440-008-9283-6

  9. Ganji, S. S., Barari, A., Ibsen, L. B., and Domairry, G., Differential transform method for mathematical modeling of jamming transition problem in traffic congestion flow. DOI: 10.1007/s10100-010-0154-7

  10. Ganji, S. S., Barari, A., and Ganji, D. D., Approximate analyses of two mass-spring systems and buckling of a column. DOI: 10.1016/j.camwa.2010.12.059

  11. Gibson, R. F., Ayorinde, E. O., andWen, Y., Vibrations of carbon nanotubes and their composites: A review. DOI: 10.1016/j.compscitech.2006.03.031

  12. He, J. H., Preliminary report on the energy balance for nonlinear oscillations. DOI: 10.1016/S0093-6413(02)00237-9

  13. He, J. H., Determination of limit cycles for strongly nonlinear oscillators. DOI: 10.1103/PhysRevLett.90.174301

  14. He, J.-H., Hamiltonian approach to nonlinear oscillators. DOI: 10.1016/j.physleta.2010.03.064

  15. Ho, X., Ye, L., Rotkin, S. V., Xie, X., Du, F., Dunham, S., Zaumseil, J., and Rogers, J. A., Theoretical and experimental studies of Schottky diodes that use aligned arrays of single-walled carbon nanotubes. DOI: 10.1007/s12274-010-0004-x

  16. Ibsen, L. B., Barari, A., and Kimiaeifar, A., Analysis of highly nonlinear oscillation systems using He’s max-min method and comparison with homotopy analysis and energy balance methods. DOI: 10.1007/s12046-010-0024-y

  17. Iijima, S., Helical microtubes of graphitic carbon. DOI: 10.1038/354056a0

  18. Jiao, L., Zhang, L. D., Liu, J., and Dai, H., Aligned graphene nanoribbons and crossbars from unzipped carbon nanotubes. DOI: 10.1007/s12274-010-1043-z

  19. Liu, J. Z., Zheng, Q., and Jiang, Q., Effect of a rippling mode on resonances of carbon nanotubes. DOI: 10.1103/PhysRevLett.86.4843

  20. Liu, J. Z., Zheng, Q., and Jiang, Q., Effect of bending instabilities on the measurements of mechanical properties of multiwall carbon nanotubes. DOI: 10.1103/PhysRevB.67.075414

  21. Ma, X., Anand, D., Zhang, X., Tsige, M., and Talapatra, S., Carbon nanotube-textured sand for controlling bioavailability of contaminated sediments. DOI: 10.1007/s12274-010-1046-9

  22. Mahdavi, M. H., Jiang, L. Y., and Sun, X., Nonlinear vibration of a single-walled carbon nanotube embedded in a polymer matrix aroused by interfacial van der Waals forces. DOI: 10.1063/1.3266174

  23. Mehdipour, I., Ganj, D. D., and Mozaffari, M., Application of the energy balance method to nonlinear vibrating equations. DOI: 10.1016/j.cap.2009.05.016

  24. Mehdipour, I., Barari, A., and Domairry, G., Application of a cantilevered SWCNT with mass at the tip as a nanomechanical sensor. DOI: 10.1016/j.commatsci.2011.01.025

  25. Miansari, Mo., Miansari, Me., Barari, A., and Domairry, G., Analysis of Blasius equation for flat-plate flow with infinite boundary value. DOI: 10.1080/15502280903563541

  26. Mirgolbabaei, H., Barari, A., Ibsen, L. B., and Esfahani, M. G., Analytical solution of forced-convective boundary-layer flow over a flat plate. DOI: 10.1016/S1644-9665(12)60049-1

  27. Momeni, M., Jamshidi, N., Barari, A., and Ganji, D. D., Application of He's energy balance method to Duffing harmonic oscillators. DOI: 10.1080/00207160903337239

  28. Omidvar, M., Barari, A., Momeni, M., and Ganji, D. D., New class of solutions for water infiltration problems in unsaturated soils. DOI: 10.1080/17486020903294333

  29. Poncharal, P., Wang, Z. L., Ugarte, D., and de Heer, W. A., Electrostatic deflections and electromechanical resonances of carbon nanotubes. DOI: 10.1126/science.283.5407.1513

  30. Ranjbartoreh, A. R., Ghorbanpour, A., and Soltani, B., Double-walled carbon nanotube with surrounding elastic medium under axial pressure. DOI: 10.1016/j.physe.2007.04.010

  31. Rasekh, M. and Khadem, S. E., Nonlinear vibration and stability analysis of axially loaded embedded carbon nanotubes conveying fluid. DOI: 10.1088/0022-3727/42/13/135112

  32. Sfahani, M. G., Ganji, S. S., Barari, A., Mirgolbabae, H., and Domairry, G., Analytical solutions to nonlinear conservative oscillator with fifth-order non-linearity. DOI: 10.1007/s11803-010-0021-5

  33. Sfahani, M. G., Barari, A., Omidvar, M., Ganji, S. S., and Domairry, G., Dynamic response of inextensible beams by improved energy balance method. DOI: 10.1177/2041306810392113

  34. Shokrieh, M. M. and Rafiee, R., Prediction of mechanical properties of an embedded carbon nanotube in polymer matrix based on developing an equivalent long fiber. DOI: 10.1016/j.mechrescom.2009.12.002

  35. Wan, H., Delale, F., and Shen, L., Effect of CNT length and CNT-matrix interphase in carbon nanotube (CNT) reinforced composites. DOI: 10.1016/j.mechrescom.2004.10.011

  36. Wang, X. Y. andWang, X., Numerical simulation for bending modulus of carbon nanotubes and some explanations for experiment. DOI: 10.1016/S1359-8368(03)00084-2

  37. Wang, X., Zhang, Y. C., Xia, X. H., and Huang, C. H., Effective bending modulus of carbon nanotubes with rippling deformation. DOI: 10.1016/j.ijsolstr.2004.04.038

  38. Wang, X.,Wang, X. Y., and Xiao, J., A non-linear analysis of the bending modulus of carbon nanotubes with rippling deformations. DOI: 10.1016/j.compstruct.2004.07.009

  39. Yaghmaei, K. and Rafii-Tabar, H., Observation of fluid layering and reverse motion in double-walled carbon nanotubes. DOI: 10.1016/j.cap.2009.03.015

  40. Younesian, D., Askari, H., Saadatnia, Z., and KalamiYazdi, M., Frequency analysis of strongly nonlinear generalized Duffing oscillators using He's frequency–amplitude formulation and He's energy balance method. DOI: 10.1016/j.camwa.2010.03.013

  41. Zhang, H. W., Zhang, Z. Q., and Wang, L., Molecular dynamics simulations of electrowetting in double-walled carbon nanotubes. DOI: 10.1016/j.cap.2008.07.010

  42. Zhang, H. L., Periodic solutions for some strongly nonlinear oscillations by He's energy balance method. DOI: 10.1016/j.camwa.2009.03.068

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