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2014 | Vol. 66, nr 4 | 217--244
Tytuł artykułu

Vibration analysis of single-walled carbon nanotubes conveying nanoflow embedded in a viscoelastic medium using modified nonlocal beam model

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Języki publikacji
In this study, the vibration and stability analysis of a single-walled carbon nanotube (SWCNT) coveying nanoflow embedded in biological soft tissue are performed. The effects of nano-size of both fluid flow and nanotube are considered, simultaneously. Nonlocal beam model is used to investigate flow-induced vibration of the SWCNT while the small-size effects on the flow field are formulated through a Knudsen number (Kn), as a discriminant parameter. Pursuant to the viscoelastic behavior of biological soft tissues, the SWCNT is assumed to be embedded in a Kelvin–Voigt foundation. Hamilton’s principle is applied to the energy expressions to obtain the higher-order governing differential equations of motion and the corresponding higher-order boundary conditions. The differential transformation method (DTM) is employed to solve the differential equations of motion. The effects of main parameters including Kn, nonlocal parameter and mechanical behaviors of the surrounding biological medium on the vibrational properties of the SWCNT are examined.

Opis fizyczny
Bibliogr. 47 poz., rys., wykr.
  • Department of Mechanical Engineering Sirjan University of Technology 78137-33385 Sirjan, I.R., Iran,
  • Department of Mechanical Engineering College of Technology of Sirjan Shahid Bahonar University of Kerman 76169-14111 Kerman, I.R., Iran,
  • Department of Mechanical Engineering Isfahan University of Technology 84156-83111 Isfahan, I.R., Iran,
  • 1. S. Iijima, Helical microtubules of graphitic carbon, Nature, 354, 56–58, 1991.
  • 2. T.W. Ebbesen, Carbon Nanotubes: Preparation and Properties, CRC Press, New York, 1997.
  • 3. S.C. Fang, W.J. Chang, Y.H. Wang, Computation of chirality- and size-dependent surface Young’s moduli for single-walled carbon nanotubes, Physics Letter A, 371, 499–503, 2007.
  • 4. G.E. Gadd, M. Blackford, S. Moricca, N. Webb, P.J. Evans, A.M. Smith, G. Jacobsen, S. Leung, A. Day, Q. Hua, The world’s smallest gas cylinders?, Science, 277, 933–936, 1997.
  • 5. E.V. Dirote, Trends in Nanotechnology Research, Nova Science Publishers, New York, 2004.
  • 6. L. Wang, Q. Ni, M. Li, Buckling instability of double-wall carbon nanotubes conveying fluid, Computational Material Science, 44, 821–825, 2008.
  • 7. M. Foldvari, M. Bagonluri, Carbon nanotubes as functional excipients for nanomedicines: II, Drug delivery and biocompatibility issues, Nanomedicine: Nanotechnology, Biology and Medicine, 4, 183–200, 2008.
  • 8. S. Sawano, T. Arie, S. Akita, Carbon nanotube resonator in liquid, Nano Letters, 10, 3395–3398, 2010.
  • 9. N. Khosravian, H. Rafii-Tabar, Computational modelling of a non-viscous fluid flow in a multi-walled carbon nanotube modelled as a Timoshenko beam, Nanotechnology, 19, 275703, 2008.
  • 10. P. Soltani, M.M. Taherian, A. Farshidianfar, Vibration and instability of a viscousfluid conveying single-walled carbon nanotube embedded in a visco-elastic medium, Journal of Physics D: Applied Physics, 43, 425401, 2010.
  • 11. E. Ghavanloo, M. Rafiei, F. Daneshmand, In-plane vibration analysis of curved carbon nanotubes conveying fluid embedded in viscoelastic medium, Physical Letters A, 375, 1994-1999, 2011.
  • 12. S. Rinaldi, S. Prabhakar, S. Vengallator, M.P. Paidoussis, Dynamics of microscale pipes containing internal flow: damping, frequency shift, and stability, Journal of Sound and Vibration, 329, 1081–1088, 2010.
  • 13. L. Wang, Size-dependent vibration characteristics of fluid-conveying microtubes, Journal of Fluids and Structures, 26, 675–684, 2010.
  • 14. J. Yoon, C.Q. Ru, A. Mioduchowski, Vibration and instability of carbon nano-tubes conveying fluid, Composites Science and Technology, 65, 1326–1336, 2005.
  • 15. N. Khosravian, H. Rafii-Tabar, Computational modelling of the flow of viscous fluids in carbon nanotubes, Journal of Physics D: Applied Physics, 40, 7046–7052, 2007.
  • 16. C.D. Reddy, C. Lu, S. Rajendran, K.M. Liew, Free vibration analysis of fluidconveying single-walled carbon nanotubes, Applied Physics Letters, 90, 133122, 2007.
  • 17. L. Wang, Q. Ni, M. Li, Q. Qian, The thermal effect on vibration and instability of carbon nanotubes conveying fluid, Physica E, 40, 3179–3182, 2008.
  • 18. W. Chang, H. Lee, Free vibration of a single-walled carbon nanotube containing a fluid flow using the Timoshenko beam model, Physical Letters A, 373, 982–985, 2009.
  • 19. T. Natsuki, Q.Q. Ni, M. Endo, Wave propagation in single- and double-walled carbon nanotubes filled with fluids, Journal of Applied Physics, 101, 034319, 2007.
  • 20. S. Govindjee, J.L. Sackman, On the use of continuum mechanics to estimate the properties of nanotubes, Solid State Communications, 110, 227–230, 1999.
  • 21. L. Wang, Vibration and instability analysis of tubular nano- and micro-beams conveying fluid using nonlocal elastic theory, Physica E, 41, 1835–1840, 2009.
  • 22. B. Amirian, R. Hosseini-Ara, H. Moosavi, Thermal vibration analysis of carbon nanotubes embedded in two-parameter elastic foundation based on nonlocal Timoshenko’s beam theory, Archives of Mechanics, 64, 581–602, 2012.
  • 23. H. Lee, W. Chang, Free transverse vibration of the fluid-conveying single-walled carbon nanotube using nonlocal elastic theory, Journal of Applied Physics, 103, 024302, 2008.
  • 24. L. Wang, Dynamical behaviors of double-walled carbon nanotubes conveying fluid accounting for the role of small length scale, Computational Material Science, 45, 584–588, 2009.
  • 25. A. Tounsi, H. Heireche, E.A.A. Bedia, Comment on “Free transverse vibration of the fluid-conveying single-walled carbon nanotube using nonlocal elastic theory”, Journal of Applied Physics, 105, 126105, 2009.
  • 26. L. Wang, A modified nonlocal beam model for vibration and stability of nanotubes conveying fluid, Physica E, 44, 25–28, 2011.
  • 27. C.W. Lim, J.C. Niu, Y.M. Yu, Nonlocal stress theory for buckling instability of nanotubes: new predictions on stiffness strengthening effects of nanoscales, Journal of Computational and Theoretical Nanoscience, 7, 2104–2111, 2010.
  • 28. 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 (English Ed.), 31, 37–54, 2010.
  • 29. V. Rashidi, H.R. Mirdamadi, E. Shirani, A novel model for vibrations of nanotubes conveying nanoflow, Computational Material Science, 51, 347–352, 2012.
  • 30. F. Kaviani, H.R. Mirdamadi, Influence of Knudsen number on fluid viscosity for analysis of divergence in fluid conveying nano-tubes, Computational Material Science, 61, 270–277, 2012.
  • 31. M. Mirramezani, H.R Mirdamadi, Effects of nonlocal elasticity and Knudsen number on fluid–structure interaction in carbon nanotube conveying fluid, Physica E, 44, 2005–2015, 2012.
  • 32. M.P. Païdoussis, Fluid-Structure Interactions: Slender Structures and Axial Flow, vol. 1, Academic Press, London, 1998.
  • 33. F. Tornabene, A. Marzani, E. Viola, Critical flow speeds of pipes conveying fluid using the generalized differential quadrature method, Advances in Theoretical and Applied Mechanics, 3, 121–138, 2010.
  • 34. J.K. Zhou, Differential Transformation and Its Applications for Electrical Circuits, Huazhong University Press, Wuhan, China, 1986.
  • 35. C.K. Chen, S.H. Ho, Solving partial differential equations by two-dimensional differential transform method, Applied Mathematics and Computation, 106, 171–179, 1999.
  • 36. S.H. Ho, C.K. Chen, Free transverse vibration of an axially loaded non-uniform spinning twisted Timoshenko beam using differential transform, International Journal of Mechanical Sciences, 48, 1323–1331, 2006.
  • 37. C. Mei, Application of differential transformation technique to free vibration analysis of a centrifugally stiffened beam, Computers and Structures, 86, 1280–1284, 2008.
  • 38. M. Balkaya, M.O. Kaya, A. Saglamer, Analysis of the vibration of an elastic beam supported on elastic soil using the differential transform method, Archive of Applied Mechanics, 79, 135–146, 2009.
  • 39. Q. Ni, Z.L. Zhang, L. Wang, Application of the differential transformation method to vibration analysis of pipes conveying fluid, Applied Mathematics and Computation, 217, 7028–7038, 2011.
  • 40. G. Karniadakis, A. Beskok, N. Aluru, Microflows and Nanoflows: Fundamentals and Simulation, Springer, USA, 2005.
  • 41. A. Beskok, G.E. Karniadaki, A model for flows in channels, pipes, and ducts at micro and nano scales, Microscale Thermophysical Engineering, 3, 43–77, 1999.
  • 42. J. Peddieson, G.R. Buchanan, R.P. McNitt, Application of nonlocal continuum models to nanotechnology, International Journal of Engineering Science, 41, 305–312, 2003.
  • 43. R. Li, G. Kardomateas, Thermal buckling of multi-walled carbon nanotubes by nonlocal elasticity, Journal of Applied Physics, 74, 399, 2007.
  • 44. A.C. Eringen, On differential equations of nonlocal elasticity and solutions of skrew dislocation and surface waves, Journal of Applied Physics, 54, 4703–4710, 1983.
  • 45. A.C. Eringen, Nonlocal Continuum Field Theories, Springer, New York, 2002.
  • 46. C.W. Lim, C.M. Wang, Exact variational nonlocal stress modeling with asymptotic higher-order strain gradients for nanobeams, Journal of Applied Physics, 101, 054312, 2007.
  • 47. W.T. Thomson, Theory of Vibration with Applications, Unwin Hyman Ltd., London, 1988.
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