Wave propagation in double-walled carbon nanotubes on a novel analytically nonlocal Timoshenko-beam model

Journal of Sound and Vibration

Volumn 330, Issue 8, 2011, Pages 1704-1717

  Yang, Yang ^a,b   Zhang, Lixiang ^a   Lim, C W ^b  

^a KUNMING UNIVERSITY OF SCIENCE AND TECHNOLOGY   (China)

^b CITY UNIVERSITY OF HONG KONG   (Hong Kong)

Author keywords

[No Author keywords available]

Indexed keywords

ANT MODEL; BEAM MODEL; CONTINUUM ELASTICITY THEORY; DOUBLE-WALLED CARBON NANOTUBES; GOVERNING EQUATIONS; HIGH-ORDER; NANO SCALE; NON-LOCAL EFFECT; NONLOCAL; NONLOCALITIES; STIFFNESS ENHANCEMENT; TIMOSHENKO BEAM MODEL; VAN DER WAALS INTERACTIONS; VARIATIONAL PRINCIPLES;

CARBON NANOTUBES; CRACK PROPAGATION; MULTIWALLED CARBON NANOTUBES (MWCN); VAN DER WAALS FORCES; VARIATIONAL TECHNIQUES; WAVE PROPAGATION;

COMPUTER SIMULATION;

EID: 79751538505     PISSN: 0022460X     EISSN: 10958568     Source Type: Journal    
DOI: 10.1016/j.jsv.2010.10.028     Document Type: Article

References (54)

1. S. Iijima Helical microtubules of graphitic carbon Nature 354 1991 56 58 (Pubitemid 21896780)
2. M.M.J. Treacy, T.W. Ebbesen, and J.M. Gibson Exceptionally high Young's modulus observed for individual carbon nanotubes Nature 381 1996 680 687
3. M. Ajayan, and O.Z. Zhou Applications of carbon nanotubes Topics in Applied Physics 80 2001 391 425
4. Ball Roll up for the revolution Nature 414 2001 142 144 (Pubitemid 33051202)
5. R.H. Baughman, A.A. Zakhidov, and W.A. de Heer Carbon nanotubesthe route toward applications Science 297 2002 787 792 (Pubitemid 34845917)
6. D.W. Brenner, O.A. Shenderova, J.A. Harrison, S.J. Stuart, B. Ni, and S.B. Sinnott A second-generation reactive empirical bond order (REBO) potential energy expression for hydrocarbons Journal of Physics: Condensed Matter 14 2002 783 802 (Pubitemid 34153770)
7. K.M. Liew, C.H. Wong, and M.J. Tan Buckling properties of carbon nanotube bundles Applied Physics Letters 87 2005 041901
8. S. Kitipornchai, X.Q. He, and K.M. Liew Buckling analysis of triple-walled carbon nanotubes embedded in an elastic matrix Journal of Applied Physics 97 2005 114318
9. B.I. Yakobson, C.J. Brabec, and J. Bernholc Nanomechanics of carbon tubes: instabilities beyond linear range Physical Review Letters 76 1996 2511 2514
10. C.Q. Ru Effective bending stiffness of carbon nanotubes Physical Review B 62 2000 9973 9976 (Pubitemid 32332459)
11. C.Q. Ru Elastic buckling of single-walled carbon nanotube ropes under high pressure Physical Review B 62 2000 10405 10408 (Pubitemid 32332505)
12. U. Lee, and H. Oh Evaluation of the structural properties of single-walled carbon nanotubes by using a dynamic continuum modeling method Mechanics of Advanced Materials and Structures 15 2 2008 79 87 (Pubitemid 351222572)
13. J. Yoon, C.Q. Ru, and A. Mioduchowski Terahertz vibration of short carbon nanotubes modeled as Timoshenko-beams Journal of Applied Mechanics-Transactions of the ASME 72 2005 10 17 (Pubitemid 40308590)
14. C.Y. Wang, C.Q. Ru, and A. Mioduchowski Vibration of microtubules as orthotropic elastic shells Physica E 35 2006 48 56 (Pubitemid 44437004)
15. Q. Wang, and V.K. Varadan Wave characteristics of carbon nanotubes International Journal of Solids and Structures 43 2006 254 265 (Pubitemid 41691416)
16. T. Natsuki, T. Hayashi, and M. Endo Wave propagation of carbon nanotubes embedded in an elastic medium Journal of Applied Physics 97 2005 044307
17. M. Mitra, and S. Gopalakrishnan Wave propagation in multiple-walled carbon nanotube Computional Material Science 45 2009 411 418
18. A. Chakraborty Shell element based model for wave propagation analysis in multiple-walled carbon nanotubes International Journal of Solids and Structures 44 2007 1628 1642 (Pubitemid 46072860)
19. Y. Yan, X.Q. He, and L.X. Zhang Flow-induced instability of double-walled carbon nanotubes based on an elastic shell model Journal of Applied Physics 102 2007 044307
20. Y. Yan, L.X. Zhang, and W.Q. Wang Dynamical mode transitions of simply supported double-walled carbon nanotubes based on an elastic shell model Journal of Applied Physic 103 2008 113523
21. Y. Yan, L.X. Zhang, and W.Q. Wang Dynamical properties of multi-walled carbon nanotubes based on a nonlocal elasticity model International Journal of Modern Physics B 22 2008 4975 4986
22. Y. Yan, X.Q. He, L.X. Zhang, and C.M. Wang Dynamic behavior of triple-walled carbon nanotubes conveying fluid Journal of Sound and Vibration 319 2009 1003 1018
23. Y. Yan, W.Q. Wang, and L.X. Zhang Dynamical behaviors of fluid-conveyed multi-walled carbon nanotubes Applied Mathematical Modelling 33 2009 1430 1440
24. Y. Yan, W.Q. Wang, and L.X. Zhang Dynamical properties of multi-walled carbon nanotubes based on nonlocal Timoshenko beam theory Modern Physics Letter B 23 2009 2625 2636
25. Y. Yan, W.Q. Wang, and L.X. Zhang Noncoaxial vibration of fluid-filled multi-walled carbon nanotubes Applied Mathematical Modelling 34 2010 122 128
26. A.C. Eringen Nonlocal Continuum Field Theories 2002 Springer US
27. J. Peddieson, G.R. Buchanan, and R.P. McNitt Application of nonlocal continuum models to nanotechnology International Journal of Engineering Science 4 2003 305 312
28. L.F. Wang, and H.Y. Hu Flexural wave propagation in single-walled carbon nanotubes Physical Review B 71 2005 195412
29. Q. Wang Wave propagation in carbon nanotubes via nonlocal continuum mechanics Journal of Applied Physics 98 2005 124301
30. Q. Wang, G.Y. Zhou, and K.C. Lin Scale effect on wave propagation of double-walled carbon nanotubes International Journal of Solids and Structures 43 2006 6071 6084 (Pubitemid 46059261)
31. P. Lu, H.P. Lee, C. Lu, and P.Q. Zhang Application of nonlocal beam models for carbon nanotubes International Journal of Solids and Structures 44 2007 5289 5300 (Pubitemid 46509641)
32. W.H. Duan, C.M. Wang, and Y.Y. Zhang Calibration of nonlocal scaling effect parameter for free vibration of carbon nanotubes by molecular dynamics Journal of Applied Physics 101 2007 024305
33. K.M. Liew, Y.G. Hu, and X.Q. He Flexural wave propagation in single-walled carbon nanotubes Journal of Computational and Theoretical Nanoscience 5 2008 581 586 (Pubitemid 351772260)
34. Y. Yan, W.Q. Wang, and L.X. Zhang Small scale effect on the free vibration of multi-walled carbon nanotubes Modern Physics Letters B 22 2008 2769 2777
35. H. Heireche, A. Tounsi, and A. Benzair Scale effect on wave propagation of double-walled carbon nanotubes with initial axial loading Nanotechnology 19 2008 185703
36. Q. Wang Axi-symmetric wave propagation of carbon nanotubes with non-local elastic shell model International Journal of Solids and Structures 6 2006 285 296 (Pubitemid 43786979)
37. L.F. Wang, H.Y. Hu, and W.L. Guo Validation of the non-local elastic shell model for studying longitudinal waves in single-walled carbon nanotubes Nanotechnology 17 2006 1408 1415
38. Q. Wang, and V.K. Varadan Application of nonlocal elastic shell theory in wave propagation analysis of carbon nanotubes Smart Materials and Structures 16 2007 178 190 (Pubitemid 46485430)
39. L.F. Wang, W.L. Guo, and H.Y. Hu Group velocity of wave propagation in carbon nanotubes Proceedings of the Royal Society AMathematical Physical and Engineering Science 464 2008 1423 1438
40. Y.G. Hu, K.M. Liew, Q. Wang, X.Q. He, and B.I. Yakobson Nonlocal shell model for elastic wave propagation in single- and double-walled carbon nanotubes Journal of the Mechanics and Physics of Solids 56 2008 3475 3485
41. L.F. Wang, and K.M. Liew Using model of strain gradient membrane shell to characterize longitudinal wave dispersion in multi-walled carbon nanotubes Journal of Computational and Theoretical Nanoscience 5 2008 1 9
42. D.C.C. Lam, F. Yang, A.C.M. Chong, J. Wang, and P. Tong Experiments and theory in strain gradient elasticity Journal of the Mechanics and Physics of Solids 51 2003 1477 1508
43. C.W. Lim, and C.M. Wang Exact variational nonlocal stress modeling with asymptotic higher-order strain gradients for nanobeams Journal of Applied Physics 101 2007 054312
44. C.W. Lim Equilibrium and static deflection for bending of a nonlocal nanobeam Advances in Vibration Engineering 8 2009 277 300
45. C.W. Lim, Y. Yang, Nonlocal elasticity for wave propagation in carbon nanotubes: the physics and new prediction of nanoscale in nonlocal stress field, Journal of Computational and Theoretical Nanoscience 7 (2010) 988995
46. C.W. Lim, and Y. Yang Wave propagation in carbon nanotubes: nonlocal elasticity induced stiffness and velocity enhancement effects Journal of Mechanics of Materials and Structures 5 2010 459 476
47. C.W. Lim, C. Li, and J.L. Yu The effects of stiffness strengthening nonlocal stress and axial tension on free vibration of cantilever nanobeams Interaction and Multiscale Mechaniccs 2 2009 223 233
48. C.W. Lim, J.C. Niu, Y.M. Yu, Nonlocal stress theory for buckling instability of nanobeams: new prediction on stiffness strengthening effects of nanoscales, Journal of Computational and Theoretical Nanoscience 7 (2010) 21042111
49. C.W. Lim On the truth of nanoscale for nanobeams based on nonlocal elastic stress field theory: equilibrium, governing equation and static deflection Applied Mathematics and Mechanics 31 2010 37 54
50. P. Hagedorn, and A. Dasgupta Vibration and Waves in Continuous Mechanical System 2007 Wiley UK
51. M. Aydogdu Effects of shear deformation on vibration of doublewalled carbon nanotubes embedded in an elastic medium Archive of Applied Mechanics 78 2008 11 723
52. H.M. Ma, X.L. Gao, and J.N. Reddy A microstructure-dependent Timoshenko beam model based on a modified couple stress theory Journal of the Mechanics and Physics of Solids 56 2008 3379 3391
53. S.K. Park, and X.L. Gao BernoulliEuler beam model based on a modified couple stress theory Journal of Micromechanics and Microengineering 16 2006 2355 2359 (Pubitemid 44679456)
54. S.K. Park, and X.L. Gao Variational formulation of a modified couple stress theory and its application to a simple shear problem Zeitschrift fur Angewandte Mathematik und Physik 59 2008 904 917