Application of HPM to the nonlinear vibration of multlwalled carbon nanotubes

Numerical Methods for Partial Differential Equations

Volumn 26, Issue 2, 2010, Pages 490-500

  Ansari, R ^a   Hemmatnezhad, M ^a   Ramezannezhad, H ^a  

^a UNIVERSITY OF GUILAN   (Iran)

Author keywords

Carbon nanotubes; Elastic medium; Homotopy perturbation method; Nonlinear vibration

Indexed keywords

EID: 76649107972     PISSN: 0749159X     EISSN: 10982426     Source Type: Journal    
DOI: 10.1002/num.20499     Document Type: Article

References (29)

1. 1 S. Iijima, Helica microtubes of graphitic carbon, Nature 354 ( 1991), 56–58.
2. 2 C. Q. Ru, Intrinsic vibration of multiwalled carbon nanotubes, Int J Nonlinear Sci Numer Simul 3 ( 2002), 735–746.
3. 3 J. Yoon, C. Q. Ru, and A. Mioduchowski, Noncoaxial resonance of an isolated multiwall carbon nanotube, Phys Rev B 66 ( 2002), 233402–233414.
4. 4 Y. Zhang, G. Liu, and X. Han, Transverse vibrations of double‐walled carbon nanotubes under compressive axial load, Phys Lett A 340 ( 2005), 258–266.
5. 5 J. Yoon, C. Q. Ru, and A. Mioduchowski, Vibration of an embedded multiwall carbon nanotube, Compos Sci Technol 63 ( 2003), 1533–1542.
6. 6 I. Elishakoff and D. Pentaras, Fundamental natural frequencies of double‐walled carbon nanotubes, J Sound Vibr 322 ( 2009), 652–664.
7. 7 S. B. Ye, R. P. S. Han, and L. H. Wang, Oscillatory response of a capped double‐walled carbon nanotube, Int J Nonlinear Sci Numer Simul 9 ( 2008), 339–346.
8. 8 Y. M. Fu, J. W. Hong, and X. Q. Wang, Analysis of nonlinear vibration for embedded carbon nanotubes, J Sound Vibr 296 ( 2006), 746–756.
9. 9 J. N. Ding, B. Kan, G. G. Cheng, Z. Fan, N. Y. Yuan, and Z. Y. Ling, Numerical approach to torsion deformation of armchair single walled carbon nanotubes, Int J Nonlinear Sci Numer Simul 9 ( 2008), 309–314.
10. 10 S. Adali, Variational principles for multi‐walled carbon nanotubes undergoing buckling based on nonlocal elasticity theory, Phys Lett A 372 ( 2008), 5701–5705.
11. 11 J. H. He, An elementary introduction to recently developed asymptotic methods and nanomechanics in textile engineering, Int J Mod Phys B 22 ( 2008), 3487–3578.
12. 12 J. H. He, The homotopy perturbation method for nonlinear oscillators with discontinuities, Appl Math Comput 151 ( 2004), 287–292.
13. 13 J. H. He, Application of homotopy perturbation method to nonlinear wave equations, Chaos Solitons Fractals 26 ( 2005), 695–700.
14. 14 J. H. He, Homotopy perturbation method for solving boundary value problems, Phys Lett A 350 ( 2006), 87–88.
15. 15 J. H. He, Limit cycle and bifurcation of nonlinear problems, Chaos Solitons Fractals 26 ( 2005), 827–833.
16. 16 J. H. He, Homotopy perturbation technique, Comput Methods Appl Mech Eng 178 ( 1999), 257–262.
17. 17 J. H. He, A coupling method of homotopy technique and perturbation technique for nonlinear problems, Int J Nonlinear Mech 35 ( 2000), 37–43.
18. 18 J. H. He, Comparison of homotopy perturbation method and homotopy analysis method, Appl Math Comput 156 ( 2004), 527–539.
19. 19 J. H. He, Homotopy perturbation method: a new nonlinear analytical technique, Appl Math Comput 135 ( 2003), 73–79.
20. 20 J. H. He, Some asymptotic methods for strongly nonlinear equations, Int J Mod Phys B 20 ( 2006), 1141–1199.
21. 21 A. Rajabi and D. D. Ganji, Application of homotopy perturbation method in nonlinear heat conduction and convection equations, Phys Lett A 360 ( 2007), 570–573.
22. 22 D. D. Ganji and A. Sadighi, Application of homotopy perturbation and variational iteration methods to nonlinear heat transfer and porous media equations, J Comput Appl Math 207 ( 2007), 24–34.
23. 23 D. D. Ganji, The application of Hes homotopy perturbation method to nonlinear equations arising in heat transfer, Phys Lett A 355 ( 2006), 337–341.
24. 24 S. Abbasbandy, A numerical solution of Blasius equation by Adomians decomposition method and comparison with homotopy perturbation method, Chaos Solitons Fractals 31 ( 2007), 257–260.
25. 25 J. Biazar and H. Ghazvini, Exact solutions for nonlinear Schrödinger equations by Hes homotopy perturbation method, Phys Lett A 366 ( 2007), 79–84.
26. 26 S. Abbasbandy, Numerical solutions of the integral equations: homotopy perturbation and Adomians decomposition method, Appl Math Comput 173 ( 2006), 493–500.
27. 27 V. Marinca, Application of modified homotopy perturbation method to nonlinear oscillations, Arch Mech 58 ( 2006), 241–256.
28. 28 J. H. He, Recent development of the homotopy perturbation method, Topol Methods Nonlinear Anal 31 ( 2008), 205–209.
29. 29 J. Biazar and H. Ghazvini, Convergence of the homotopy perturbation method for partial differential equations, Nonlinear Anal: Real World Appl 10 ( 2009), 2633–2640.