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Wave Propagation in Fluid-Filled Single-Walled Carbon Nanotube Based on the Nonlocal Strain Gradient Theory

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Abstract

A dynamic Timoshenko beam model is established based on the new nonlocal strain gradient theory and slip boundary theory to study the wave propagation behaviors of fluid-filled carbon nanotubes (CNTs) at nanoscale. The nanoscale effects caused by the CNTs and the inner fluid are simulated by the nonlocal strain gradient effect and the slip boundary effect, respectively. The governing equations of motion are derived and resolved to investigate the wave characteristics in detail. The numerical solution shows that the strain gradient effect leads to the stiffness enhancement of CNTs when the nonlocal stress effect causes the decrease in stiffness. The dynamic properties of CNTs are affected by the coupling of these two scale effects. The flow velocity of fluid inside the CNT is increased due to the slip boundary effect, resulting in the promotion of wave propagation in the dynamic system.

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References

  1. Iijima S. Helical microtubules of graphitic carbon. Nature. 1991;354(6348):56–8.

    Article  Google Scholar 

  2. Treacy MMJ, Ebbesen TW, Gibson JM. Exceptionally high Young’s modulus observed for individual carbon nanotubes. Nature. 1996;381(6584):678–80.

    Article  Google Scholar 

  3. Wong EW, Sheehan PE, Lieber CM. Nanobeam mechanics elasticity, strength and toughness of nanorods and nanotubes. Science. 1997;277(5334):1971–5.

    Article  Google Scholar 

  4. Ball P. Roll up for the revolution. Nature. 2001;414(6860):142–4.

    Article  Google Scholar 

  5. Baughman RH, Zakhidov AA, de Heer WA. Carbon nanotubes-the route toward applications. Science. 2002;297(5582):787–92.

    Article  Google Scholar 

  6. Hauquier F, Pastorin G, Hapiot P, et al. Carbon nanotube-functionalized silicon surfaces with efficient redox communication. Chem Commun. 2006;43(43):4536–8.

    Article  Google Scholar 

  7. Liew KM, Wong CH, Tan MJ. Buckling properties of carbon nanotube bundles. Appl Phys Lett. 2005;87(4):041901–3.

    Article  Google Scholar 

  8. Kitipornchai S, He XQ, Liew KM. Buckling analysis of triple-walled carbon nanotubes embedded in an elastic matrix. J Appl Phys. 2005;97(11):114318–24.

    Article  Google Scholar 

  9. Yan Y, He XQ, Zhang LX, et al. Flow-induced instability of double-walled carbon nanotubes based on an elastic shell model. J Appl Phys. 2007;102(4):044307.

    Article  Google Scholar 

  10. Yan Y, He XQ, Zhang LX, et al. Dynamic behavior of triple-walled carbon nanotubes conveying fluid. J Sound Vib. 2009;319(3–5):1003–18.

    Article  Google Scholar 

  11. Yan Y, Wang WQ, Zhang LX. Dynamical behaviors of fluid-conveyed multi-walled carbon nanotubes. Appl Math Model. 2009;33(3):1430–40.

    Article  MathSciNet  MATH  Google Scholar 

  12. Yoon J, Ru CQ, Mioduchowski A. Vibration and instability of carbon nanotubes conveying fluid. Compos Sci Technol. 2005;65(9):1326–36.

    Article  Google Scholar 

  13. Yoon J, Ru CQ, Mioduchowski A. Flow-induced flutter instability of cantilever carbon nanotubes. Int J Solids Struct. 2006;43(11–12):3337–49.

    Article  MATH  Google Scholar 

  14. Eringen AC. Nonlocal continuum field theories. New York: Springer; 2002.

    MATH  Google Scholar 

  15. Bahaadini R, Hosseini M. Effects of nonlocal elasticity and slip condition on vibration and stability analysis of viscoelastic cantilever carbon nanotubes conveying fluid. Comput Mater Sci. 2016;114:151–9.

    Article  Google Scholar 

  16. Zhen YX, Fang B. Nonlinear vibration of fluid-conveying single-walled carbon nanotubes under harmonic excitation. Int J Non Linear Mech. 2015;76:48–55.

    Article  Google Scholar 

  17. Deng QT, Yang ZC. Vibration of fluid-filled multi-walled carbon nanotubes seen via nonlocal elasticity theory. Acta Mech Solida Sin. 2014;27(6):568–78.

    Article  Google Scholar 

  18. Filiz S, Aydogdu M. Wave propagation analysis of embedded (coupled) functionally graded nanotubes conveying fluid. Compos Struct. 2015;132:1260–73.

    Article  Google Scholar 

  19. Toupin RA. Elastic materials with couple-stresses. Arch Ration Mech Anal. 1962;11(1):385–414.

    Article  MathSciNet  MATH  Google Scholar 

  20. Lim CW, Zhang G, Reddy JN. A higher-order nonlocal elasticity and strain gradient theory and its applications in wave propagation. J Mech Phys Solids. 2015;78:298–313.

    Article  MathSciNet  MATH  Google Scholar 

  21. Li L, Hu YJ. Buckling analysis of size-dependent nonlinear beams based on a nonlocal strain gradient theory. Int J Eng Sci. 2015;97:84–94.

    Article  MathSciNet  Google Scholar 

  22. Li L, Hu YJ, Ling L. Flexural wave propagation in small-scaled functionally graded beams via a nonlocal strain gradient theory. Compos Struct. 2015;133:1079–92.

    Article  Google Scholar 

  23. Li L, Hu YJ, Ling L. Wave propagation in viscoelastic single-walled carbon nanotubes with surface effect under magneticfield based on nonlocal strain gradient theory. Phys E Low Dimens Syst Nanostruct. 2016;75:118–24.

    Article  Google Scholar 

  24. Paidoussis MP. Fluid-structure interactions slender structures and axial flow. San Diego: Academic Press; 1998.

    Google Scholar 

  25. Aifantis EC. Strain gradient interpretation of size effect. Int J Fract. 1999;95(1–4):299–314.

    Article  Google Scholar 

  26. Aifantis EC. Gradient deformation models at nano, micro, and macro scales. J Eng Mater Technol. 1999;121(2):189–202.

    Article  Google Scholar 

  27. Mindlin RD. Micro-structure in linear elasticity. Arch Ration Mech Anal. 1964;16(1):51–78.

    Article  MathSciNet  MATH  Google Scholar 

  28. Mindlin RD. Second gradient of strain and surface-tension in linear elasticity. Int J Solids Struct. 1965;1(4):417–38.

    Article  Google Scholar 

  29. Hagedorn P, Dasgupta A. Vibration and waves in continuous mechanical system. London: Wiley; 2007.

    Book  MATH  Google Scholar 

  30. Hu L, Zheng LV, Qi L. Flexural wave propagation in fluid-conveying carbon nanotubes with system uncertainties. Microfluid Nanofluidics. 2017;21(8):140.

    Article  Google Scholar 

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Acknowledgements

This project is supported by the National Natural Science Foundation of China (Grant No. 11462010).

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Authors and Affiliations

  1. Department of Engineering Mechanics, Kunming University of Science and Technology, Kunming, 650051, China

    Yang Yang, Jinrui Wang & Yang Yu

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  1. Yang Yang
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  2. Jinrui Wang
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  3. Yang Yu
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Correspondence to Yang Yang.

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Yang, Y., Wang, J. & Yu, Y. Wave Propagation in Fluid-Filled Single-Walled Carbon Nanotube Based on the Nonlocal Strain Gradient Theory. Acta Mech. Solida Sin. 31, 484–492 (2018). https://doi.org/10.1007/s10338-018-0035-5

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  • DOI: https://doi.org/10.1007/s10338-018-0035-5

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