Vibration of wavy single-walled carbon nanotubes based on nonlocal Euler Bernoulli and Timoshenko models

International Journal of Advanced Structural Engineering

Volumn 4, Issue 1, 2012, Pages

  Soltani, Payam ^a,b   Kassaei, Amir ^a   Taherian, Mohammad Mehdi ^a   Farshidianfar, Anooshiravan ^b  

^a ISLAMIC AZAD UNIVERSITY   (Iran)

^b FERDOWSI UNIVERSITY OF MASHHAD   (Iran)

Author keywords

Curved single walled carbon nanotubes; Nonlocal elasticity theory; Timoshenko beam model; Vibration

Indexed keywords

EID: 84975292462     PISSN: 20083556     EISSN: 20086695     Source Type: Journal    
DOI: 10.1186/2008-6695-4-3     Document Type: Article

References (40)

1. Iijima S: Helical microtubes of graphitic carbon. Nature 1991, 354: 56–58. 10.1038/354056a0
2. Dresselhaus MS, et al.: Electronic, thermal and mechanical properties of carbon nanotubes. Philosophical Transactions of the Royal Society of London. Ser A Math Phys Eng Sci 2004,362(1823):2065–2098.
3. Treacy MMJ, Ebbesen TW, Gibson JM: Exceptionally high Young's modulus observed for individual carbon nanotubes. Nature 1996,381(6584):678–680. 10.1038/381678a0
4. Walgraef D: On the mechanics of deformation instabilities in carbon nanotubes. Eur Phys J Spec Top 2007,146(1):443–457. 10.1140/epjst/e2007-00198-3
5. Chen L, et al.: Single-Walled Carbon Nanotube AFM Probes: Optimal Imaging Resolution of Nanoclusters and Biomolecules in Ambient and Fluid Environments. Nano Lett 2004,4(9):1725–1731. 10.1021/nl048986o
6. Hafner JH, Cheung CL, Lieber CM: Growth of nanotubes for probe microscopy tips. Nature 1999,398(6730):761–762. 10.1038/19658
7. Nishide D, et al.: High-yield production of single-wall carbon nanotubes in nitrogen gas. Chem Phys Lett 2003,372(1–2):45–50.
8. Tsukagoshi K, et al.: Carbon nanotube devices for nanoelectronics. Physica B 2002,323(1–4):107.
9. Lau K-T, et al.: On the effective elastic moduli of carbon nanotubes for nanocomposite structures. Compos Part B Eng 2004,35(2):95–101. 10.1016/j.compositesb.2003.08.008
10. Liew KM, He XQ, Wong CH: On the study of elastic and plastic properties of multi-walled carbon nanotubes under axial tension using molecular dynamics simulation. Acta Mater 2004,52(9):2521–2527. 10.1016/j.actamat.2004.01.043
11. Yoon J, Ru CQ, Mioduchowski A: Vibration and instability of carbon nanotubes conveying fluid. Compos Sci Technol 2005,65(9 SPEC. ISS):1326–1336.
12. Zhang YY, Wang CM, Tan VBC: Effect of omitting terms involving tube radii difference in shell models on buckling solutions of DWNTs. Comput Mater Sci 2006,37(4):578–581. 10.1016/j.commatsci.2005.10.007
13. Wang L, et al.: The thermal effect on vibration and instability of carbon nanotubes conveying fluid. Phys E 2008,40(10):3179–3182. 10.1016/j.physe.2008.05.009
14. Kuang YD, et al.: Analysis of nonlinear vibrations of double-walled carbon nanotubes conveying fluid. Comput Mater Sci 2009,45(4):875–880. 10.1016/j.commatsci.2008.12.007
15. Yakobson BI, et al.: High strain rate fracture and C-chain unraveling in carbon nanotubes. Comput Mater Sci 1997,8(4):341–348. 10.1016/S0927-0256(97)00047-5
16. Nguyen HLT, Elishakoff I, Nguyen VT: Buckling under the external pressure of cylindrical shells with variable thickness. Int J Solid Struct 2009,46(24):4163–4168. 10.1016/j.ijsolstr.2009.07.025
17. Yan Y, Wang WQ, Zhang LX: Dynamical behaviors of fluid-conveyed multi-walled carbon nanotubes. Appl Math Model 2009,33(3):1430–1440. 10.1016/j.apm.2008.02.010
18. Liew KM, Wang Q: Analysis of wave propagation in carbon nanotubes via elastic shell theories. Int J Eng Sci 2007,45(2–8):227–241.
19. Fu YM, Hong JW, Wang XQ: Analysis of nonlinear vibration for embedded carbon nanotubes. J Sound Vib 2006,296(4–5):746–756.
20. Chaterjee S, Pohit G: A large deflection model for the pull-in analysis of electrostatically actuated microcantilever beams. J Sound Vib 2009,322(4–5):969–986.
21. Chowdhury R, Adhikari S, Mitchell J: Vibrating carbon nanotube based bio-sensors. Phys E 2009,42(2):104–109. 10.1016/j.physe.2009.09.007
22. Hsu J-C, Chang R-P, Chang W-J: Resonance frequency of chiral single-walled carbon nanotubes using Timoshenko beam theory. Phys Lett A 2008,372(16):2757–2759. 10.1016/j.physleta.2008.01.007
23. Wang CM, Tan VBC, Zhang YY: Timoshenko beam model for vibration analysis of multi-walled carbon nanotubes. J Sound Vib 2006,294(4–5):1060–1072.
24. Lee H-L, Chang W-J: A closed-form solution for critical buckling temperature of a single-walled carbon nanotube. Phys E 2009,41(8):1492–1494. 10.1016/j.physe.2009.04.022
25. Mahdavi MH, Jiang LY, Sun X: Nonlinear vibration of a double-walled carbon nanotube embedded in a polymer matrix. Phys E 2011,43(10):1813–1819. 10.1016/j.physe.2011.06.017
26. Rao S: Vibration of continuous systems. Wiley, Hoboken, New Jersey; 2007.
27. Eringen AC: On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves. J Appl Phys 1983,54(9):4703–4710. 10.1063/1.332803
28. Murmu T, Pradhan SC: Thermo-mechanical vibration of a single-walled carbon nanotube embedded in an elastic medium based on nonlocal elasticity theory. Comput Mater Sci 2009,46(4):854–859. 10.1016/j.commatsci.2009.04.019
29. Şimşek M: Vibration analysis of a single-walled carbon nanotube under action of a moving harmonic load based on nonlocal elasticity theory. Phys E 2011, 50: 2112–2123.
30. Mehdipour I, Barari A, Domairry G: Application of a cantilevered SWCNT with mass at the tip as a nanomechanical sensor. Comput Mater Sci 2011, 50: 1830–1833. 10.1016/j.commatsci.2011.01.025
31. Wang L, Ni Q: On vibration and instability of carbon nanotubes conveying fluid. Comput Mater Sci 2008,43(2):399–402. 10.1016/j.commatsci.2008.01.004
32. Yang J, Ke LL, Kitipornchai S: Nonlinear free vibration of single-walled carbon nanotubes using nonlocal Timoshenko beam theory. Phys E 2010,42(5):1727–1735. 10.1016/j.physe.2010.01.035
33. Murmu T, Pradhan SC: Buckling analysis of a single-walled carbon nanotube embedded in an elastic medium based on nonlocal elasticity and Timoshenko beam theory and using DQM. Phys E 2009,41(7):1232–1239. 10.1016/j.physe.2009.02.004
34. Joshi AY, Sharma SC, Harsha SP: Dynamic Analysis of a Clamped Wavy Single Walled Carbon Nanotube Based Nanomechanical Sensors. J Nanotechnol Eng Med 2010,1(3):031007–7.
35. Hawwa MA, Mayoof FN: Nonlinear oscillations of a carbon nanotube resonator. International Symposium on Mechatronics and its Applications, Sharjah; 2009.
36. Eringen AC: Nonlocal continuum field theories. Springer Verlag; 2002.
37. Gupta SS, Bosco FG, Batra RC: Wall thickness and elastic moduli of single-walled carbon nanotubes from frequencies of axial, torsional and inextensional modes of vibration. Comput Mater Sci 2010,47(4):1049–1059. 10.1016/j.commatsci.2009.12.007
38. Mayoof FN, Hawwa MA: Chaotic behavior of a curved carbon nanotube under harmonic excitation. Chaos Solitons Fractals 2009,42(3):1860–1867. 10.1016/j.chaos.2009.03.104
39. Yoon J, Ru CQ, Mioduchowski A: Vibration of an embedded multiwall carbon nanotube. Compos Sci Technol 2003,63(11):1533–1542. 10.1016/S0266-3538(03)00058-7
40. Lanir Y, Fung YCB: Errata on "Fiber Composite Columns Under Compression" J. COMPOSITE MATERIALS, Vol. 6 (July 1972), pp. 387–401. J Compos Mater 1972,6(4):533–535.