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Nonlinear vibration and instability of fluid-conveying DWBNNT embedded in a visco-Pasternak medium using modified couple stress theory

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Abstract

Nonlinear free vibration and instability of fluid-conveying double-walled boron nitride nanotubes (DWBNNTs) embedded in viscoelastic medium are studied in this paper. The effects of the transverse shear deformation and rotary inertia are considered by utilizing the Timoshenko beam theory. The size effect is applied by the modified couple stress theory and considering a material length scale parameter for beam model. The nonlinear effect is considered by the Von Kármán type geometric nonlinearity. The electromechanical coupling and charge equation are employed to consider the piezoelectric effect. The surrounding viscoelastic medium is described as the linear visco-Pasternak foundation model characterized by the spring and damper. Hamilton’s principle is used to derive the governing equations and boundary conditions. The differential quadrature method (DQM) is employed to discretize the nonlinear higher-order governing equations, which are then solved by a direct iterative method to obtain the nonlinear vibration frequency and critical fluid velocity of fluid-conveying DWBNNTs with clamped-clamped (C-C) boundary conditions. A detailed parametric study is conducted to elucidate the influences of the small scale coefficient, spring and damping constants of surrounding viscoelastic medium and fluid velocity on the nonlinear free vibration, instability and electric potential distribution of DWBNNTs. This study might be useful for the design and smart control of nano devices.

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References

  1. Y. Q. Zhang, G. R. Liu and X. Y. Xie, Free transverse vibrations of doublewalled carbon nanotubes using a theory of nonlocal elasticity, Phy. Review B, 71 (2005) 195404.

    Article  Google Scholar 

  2. Y. Q. Zhang, G. R. Liu and X. Han, Transverse vibrations of double-walled carbon nanotubes under compressive axial load, Phy. Letters A, 340 (2005) 258–66.

    Article  MATH  Google Scholar 

  3. P. J. F. Harris, Carbon nanotubes and related structures, Cambridge University Press, Londen (1999).

    Book  Google Scholar 

  4. C. Q. Ru, Effective bending stiffness of carbon nanotubes, Phy. Review B, 62 (2000) 9973–9976.

    Article  Google Scholar 

  5. C. W. Chen, M. H. Lee and S. J. Clark, Band gap modification of single-walled carbon nanotube and boron nitride nanotube under a transverse electric field, Nanotechnology, 15 (2004) 1837.

    Article  Google Scholar 

  6. A. Salehi-Khojin and N. Jalili, Buckling of boron nitride nanotube reinforced piezoelectric polymeric composites subject to combined electro-thermo-mechanical loadings, Compos. Sci. Tech., 68 (2008) 1489–1501.

    Article  Google Scholar 

  7. C. C. Tang, Y. Bando, T. Sato and K. Kurashima, A novel precursor for synthesis of pure boron nitride nanotubes, Chem. Comm., 12 (2002) 1290–1291.

    Article  Google Scholar 

  8. E. Hernandez, C. Goze, P. Bernier and A. Rubio, Elastic properties of C and BxCyNz composite nanotubes, Phy. Rev. Lett., 80 (1998) 4502–4505.

    Article  Google Scholar 

  9. K. N. Kudin, G. E. Scuseria and B. I. Yakoboson, C2F, BN, and C nanoshell elasticity from ab initio computations, Phy. Review B, 64 (2001) 235406.

    Article  Google Scholar 

  10. N. G. Chopra and A. Zettl, Measurement of the elastic modulus of a multiwall boron nitride nanotube, Solid State Comm., 105 (1998) 297–300.

    Article  Google Scholar 

  11. A. P. Suryavanshi, M. F. Yu, J. G. Wen, C,C, Tang and Y. Bando, Elastic modulus and resonance behavior of boron nitride nanotubes, Appl. Phy. Lett., 84 (2004) 2527–2529.

    Article  Google Scholar 

  12. B. Akdim, R. Pachter, X. F. Duan and W. W. Adams, Comparative theoretical study of single-wall carbon and boron-nitride nanotubes, Phy. Review B, 67 (2003) 245404.

    Article  Google Scholar 

  13. T. Dumitrica, H. F. Bettinger, G. E. Scuseria and B. I. Yakobson, Thermodynamics of yield in boron nitride nanotubes, Phy. Review B, 68 (2003) 85412.

    Article  Google Scholar 

  14. W. H. Moon and H. J. Hwang, Molecular-dynamics simulation of structure and thermal behavior of boron nitride nanotubes, Nanotechnology, 15 (2004) 431–434.

    Article  Google Scholar 

  15. J. Yoon, C. Q. Ru and A. Mioduchowski, Vibration and instability of carbon nanotubes conveying fluid, Compos. Sci. Tech., 65 (2005) 1326–1343.

    Article  Google Scholar 

  16. N. Khosravian and H. Rafii-Tabar, Computational modelling of a non-viscous fluid flow in a multi-walled carbon nanotube modelled as a Timoshenko beam, Nanotechnology, 19 (2008) 275703.

    Article  Google Scholar 

  17. H. L. Lee and W. J. Chang, Vibration analysis of fluidconveying double-walled carbon nanotubes based on nonlocal elastic theory, J. Phys. Cond. Mat., 21 (2009) 115302.

    Article  Google Scholar 

  18. L. Wang and Q. Ni, A reappraisal of the computational modeling of carbon nanotubes conveying viscous fluid, Mech. Res. Comm., 36 (2009) 833–837.

    Article  MATH  Google Scholar 

  19. W. J. Chang and H. L. Lee, Free vibration of a single-walled carbon nanotube containing a fluid flow using the Timoshenko beam model, Phy. Lett. A, 373 (2009) 982–985.

    Article  MATH  Google Scholar 

  20. Y. M. Fu, J. W. Hong and X. Q. Wang, Analysis of nonlinear vibration for embedded carbon nanotubes, J. Sound and Vib., 296 (2006) 746–756.

    Article  Google Scholar 

  21. D. Walgraef, On the mechanics of deformation instabilities in carbon nanotubes, Eur. Phy. J, 146 (2007) 443–457.

    Google Scholar 

  22. Y. D. Kuang, X. Q. He, C. Y. Chen and G. Q. Li, Analysis of nonlinear vibrations of double-walled carbon nanotubes conveying fluid, Comput. Mat. Sci., 45 (2009) 875–880.

    Article  Google Scholar 

  23. J. Yang, L. L. Ke and S. Kitipornchai, Nonlinear free vibration of single-walled carbon nanotubes using nonlocal Timoshenko beam theory, Physica E, 42 (2010) 1727–1735.

    Article  Google Scholar 

  24. K. Kumar, M. E. Andrews, V. Jayashankar, A. K. Mishra and S. Suresh, Measurement of viscoelastic properties of polyacrylamide-based tissue-mimicking phantoms for ultrasound elastography applications, IEEE Trans. Ins. Meas., 59 (2010) 1224–1232.

    Article  Google Scholar 

  25. P. Soltani, M. M. Taherian and A. Farshidianfar, Vibration and instability of a viscous-fluid-conveying single-walled carbon nanotube embedded in a visco-elastic medium, J. Phys. D: Appl. Phys., 43 (2010) 425401–425409.

    Article  Google Scholar 

  26. A. G. Arani, S. Amir, A. R. Shajari, M. R. Mozdianfard, Z. K. Maraghi and M. Mohammadimehr, Electro-thermal nonlocal vibration analysis of embedded DWBNNTs, Proc. Ins. Mech. Eng. Part C, 224 (2011) 745–756.

    Google Scholar 

  27. A. G. Arani, S. Amir, A. R. Shajari and M. R. Mozdianfard, Electro-thermo-mechanical buckling of DWBNNTs embedded in bundle of CNTs using nonlocal piezoelasticity cylindrical shell theory, Compos. Part B: Eng., 43 (2012) 195–203.

    Article  Google Scholar 

  28. A. G. Arani, M. Shokravi, S. Amir and M. R. Mozdianfard, Nonlocal electro-thermal transverse vibration of embedded fluid-conveying DWBNNTs, J. Mech. Sci. Tech., 26 (2012) 1455–1462.

    Article  Google Scholar 

  29. T. H. Brockmann, Theory of adaptive fiber composites, Springer Science, USA (2009).

    Book  MATH  Google Scholar 

  30. V. Rashidi, H. R. Mirdamadi and E. Shirani, A novel model for vibrations of nanotubes conveying nanoflow, Comput. Mat. Sci., 51 (2012) 347–352.

    Article  Google Scholar 

  31. G. Karniadakis, A. Beskok and N. Aluru, Microflows and Nanoflows: Fundamentals and Simulation, Springer, USA (2005).

    Google Scholar 

  32. L. L. Ke and Y. S. Wang, Flow-induced vibration and instability of embedded double-walled carbon nanotubes based on a modified couple stress theory, Physica E, 10 (2011) 1016–1021.

    Google Scholar 

  33. M. Amabili, Nonlinear vibrations and stability of shells and plates, Cambridge University Press, London (2008).

    Book  MATH  Google Scholar 

  34. L. L. Ke, Y. Xiang, J. Yang and S. Kitipornchai, Nonlinear free vibration of embedded double-walled carbon nanotubes based on nonlocal Timoshenko beam theory, Comput. Mat. Sci., 47 (2009) 409–417.

    Article  Google Scholar 

  35. C. Shu, Differential quadrature and its application in engineering, Springer, London (2000).

    Book  MATH  Google Scholar 

  36. C. M. Wang, V. B. C. Tan and Y. Y. Zhang, Timoshenko beam model for vibration analysis of multi-walled carbon nanotubes, J. Sound Vib., 294 (2006) 1060–1065.

    Article  Google Scholar 

  37. L. L. Ke and Y. S. Wang, Flow-inducedvibration and instability of embedded double-walled carbon nanotubes based on a modified couple stress theory, Physica E, 43 (2011) 1031–1039.

    Article  Google Scholar 

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Authors and Affiliations

  1. Faculty of Mechanical Engineering, University of Kashan, Kashan, Iran

    A. Ghorbanpour Arani, M. R. Bagheri, R. Kolahchi & Z. Khoddami Maraghi

  2. Institute of Nanoscience & Nanotechnology, University of Kashan, Kashan, Iran

    A. Ghorbanpour Arani

Authors
  1. A. Ghorbanpour Arani
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  2. M. R. Bagheri
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  3. R. Kolahchi
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  4. Z. Khoddami Maraghi
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Correspondence to A. Ghorbanpour Arani.

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Recommended by Associate Editor Ohseop Song

Ali Ghorbanpour Arani received his B.Sc. degree from Sharif University of Technology, Tehran, Iran, in 1988. He then received his M.Sc. degree from Amirkabir University of Technology, Tehran, Iran, in 1991 and his Ph.D. degree from the Esfahan University of Technology, Esfahan, Iran, in 2001. Dr Ali Ghorbanpour Arani is a Professor in the Mechanical Engineering Department of University of Kashan, Kashan, Iran. His current research interests are stress analyses, stability and vibration of nanotubes and functionally graded materials. Mohammad Reza Bagheri received his B.Sc. degree from the University of Kashan in Kashan, Iran, in 2008. He then received his M.Sc. degree from University of Kashan in Kashan, Iran, in 2011.

Reza Kolahchi received his B.Sc. degree from the University of Islamic Kashan in Kashan, Iran, in 2009. He then received his M.Sc. degree from University of Kashan in Kashan, Iran, in 2011. He is currently a Ph.D. student at University of Kashan in Kashan, Iran. His research interests are nanomechanics, vibration, buckling and smart materials.

Zahra Khoddami Maraghi received her B.Sc. degree from the University of Kashan in kashan, Iran, in 2008. She then received her M.Sc. degree from University of Kashan in Kashan, Iran, in 2011. She is currently a Ph.D. student at University of Kashan in Kashan, Iran. Her research interests are nanomechanics, vibration, instability and smart materials.

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Ghorbanpour Arani, A., Bagheri, M.R., Kolahchi, R. et al. Nonlinear vibration and instability of fluid-conveying DWBNNT embedded in a visco-Pasternak medium using modified couple stress theory. J Mech Sci Technol 27, 2645–2658 (2013). https://doi.org/10.1007/s12206-013-0709-3

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  • DOI: https://doi.org/10.1007/s12206-013-0709-3

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