THERMO-FLUIDIC PARAMETERS EFFECTS ON NONLINEAR VIBRATION OF FLUID-CONVEYING NANOTUBE RESTING ON ELASTIC FOUNDATIONS USING HOMOTOPY PERTURBATION METHOD

Abstract

In this paper, effects of thermo-fluidic parameters on the nonlinear dynamic behaviours of single-walled carbon nanotube conveying fluid with slip boundary conditions and resting on linear and nonlinear elastic foundations under external applied tension and global pressure is studied using homotopy perturbation method.  From the result, it is observed that increase in the Knudsen number, the slip parameter,  leads to decrease in the frequency of vibration and the critical velocity while natural frequency and the critical fluid velocity increase as the in stretching effect increases.  Also, as the Knudsen number increases, the bending stiffness of the nanotube decreases and in consequent, the critical continuum flow velocity decreases as the curves shift to the lowest frequency zone. As the change in temperature increases, the natural frequencies and the critical flow velocity of the structure increase for the low or room temperature while at high temperature, increase in temperature change, decreases the natural frequencies and the critical flow velocity of the structure. Further, it is established that the alteration of nonlinear flow-induced frequency from linear frequency is significant as the amplitude, flow velocity and axial tension increase. The developed analytical solutions can be used as starting points for better understanding of the relationship between the physical quantities of the problem.

Keywords

• Thermo-Fluidic Effects,Non-Linear Vibration,Slip Boundary Condition,Fluid-Conveying Nanotube,Homotopy Perturbation Method

References

1. [1] Iijima, S. (1991). Helical microtubules of graphitic carbon”, Nature, London, 354, 6348, 56–58.
2. [2] Yoon, C., Ru, C. Q. and Mioduchowski, A. (2005). Vibration and instability of carbon nanotubes conveying fluid”, Journal of Applied Mechanics, Transactions of the ASME, 65(9), 1326–1336.
3. [3] Yan, Y, Wang, W. Q. and Zhang, L. X. (2010). Nonlocal effect on axially compressed buckling of triple-walled carbon nanotubes under temperature field. Journal of Applied Math and Modelling, 34, 3422–3429.
4. [4] Murmu, T. and Pradhan, S. C. (2009). Thermo-mechanical vibration of Single-walled carbon nanotube embedded in an elastic medium based on nonlocal elasticity theory”, Computational Material Science, 46, 854–859.
5. [5] Yang, H. K. and Wang, X. (2006). Bending stability of multi-wall carbon nanotubes embedded in an elastic medium”, Modeling and Simulation in Materials Sciences and Engineering, 14, 99–116.
6. [6] Yoon, J., Ru, C. Q and Mioduchowski, A. (2003). Vibration of an embedded multiwall carbon nanotube”, Composites Science and Technology, 63(11), 1533–1542.
7. [7] Ghorbanpour, Arani, A. Dashti, P., Amir, S. and Yousefi, M. (2005). Nonlinear vibration of coupled nano- and microstructures conveying fluid based on Timoshenko beam model under two-dimensional magnetic field. Acta Mechanica, 226, 2729-2760.
8. [8] Choi, J., Song, O. and Kim, S. (2013). Nonlinear stability characteristics of carbon nanotubes conveying fluids, Acta Mechanica, 224, 1383-1396.

9. [9] Zhang, D. P., Lei, Y. and Shen, Z. B. (2016). Free transverse vibration of double-walled carbon nanotubes embedded in viscoelastic medium. Acta Mechanica, 227, 3657-3670.
10. [10] Kiani, K. (2013). Characterization of free vibration of elastically supported double-walled carbon nanotubes subjected to a longitudinally varying magnetic field. Acta Mechanica, 224, 3139-3151.
11. [11] Kiani, K. (2011). Application of nonlocal beam models to double-walled carbon nanotubes under a moving nanoparticle. Part I: theoretical formulations Acta Mechanica, 216, 165-195.
12. [12] Fakhrabadi, M. M. S., Rastgoo, A. and Ahmadian, M. T. (2014). Dynamic analysis of carbon nanotubes under electrostatic actuation using modified couple stress theory. Acta Mechanica, 225, 1523-1535.
13. [13] Lu, P., Lee, H. P., Lu, P. C. and Zhang, P. Q. (2007). Application of nonlocal beam models for carbon nanotubes, International Journal of Solids and Structures, 44, 16, 5289–5300.
14. [14] Zhang, Y. G. Liu, G. and Han, X. (2005). Transverse vibration of double-walled carbon nanotubes under compressive axial load”, Applied Physics Letter A, 340(1-4), 258–266.
15. [15] GhorbanpourArani, M.S. Zarei, M. Mohammadimehr, A. Arefmanesh, M.R. Mozdianfard. M. R. (2011).The thermal effect on buckling analysis of a DWCNT embedded on the Pasternak foundation”, Physica E, 43, 1642–1648.
16. [16] He. J. H. (1999). Homotopy Perturbation Technique. Computer Methods in Applied Mechanics and Engineering, 178, 257-262.
17. [17] He, J. H. (2006). New Interpretation of Homotopy Perturbation Method. International Journal of Modern Physics B, 20, 2561-2568.
18. [18] He, J. H. (2000). A Coupling Method of Homotopy Technique and Perturbation Technique for Nonlinear Problems. International Journal of Non-Linear Mechanics, 35, 37-43.
19. [19] He, J. H. (2006). Some Asymptotic Methods for Strongly Nonlinear Equations. International Journal of Modern Physics B, 20, 1141-1199.
20. [20] He, J. H. (2000). New Perturbation Technique Which Is Also Valid for Large Parameters. Journal of Sound and Vibration, 229, 1257-1263.
21. [21] Rafei., M. and Ganji, D. D., Daniali, H. and Pashaei, H. (2007). The variational iteration method for nonlinear oscillators with discontinuities. J. Sound Vib, 305, 614–620.
22. [22] Ganji, S. S., Ganji, D. D., H. Babazadeh and Karimpour, S. (2008). Variational approach method for nonlinear oscillations of the motion of a rigid rod rocking back and cubic-quintic duffing oscillators. Prog. Electromagn. Res. M, 4, 23–32.
23. [23] Liao, S. J. (1992). The Proposed Homotopy Analysis Technique for the Solution of Nonlinear Problems,Ph. D. dissertation, Shanghai Jiao Tong University.
24. [24] Zhou, J. K. (1986). Differential Transformation and its Applications for Electrical Circuits. Huazhong University Press: Wuhan, China.
25. [25] Sobhan Mosayebidorcheh, O.D. Makinde , D.D. Ganji , and M. A. Chermahini. (2017). DTM-FDM hybrid approach to unsteady MHD Couette flow and heat transfer of dusty fluid with variable properties. Thermal Science and Engineering Progress, 2, 57-63.
26. [26] Mosayebidorcheh, S.Vatani, M. Ganji, D. D. and Mosayebidorcheh, T. (2014). Investigation of the viscoelastic flow and species diffusion in a porous channel with high permeability. Alexandria Engineering Journal, 53, 779–785.
27. [27] Mosayebidorcheh, S., Mosayebidorcheh, T. and Rashidi, M. M. (2014). Analytical solution of the steady state condensation film on the inclined rotating disk by a new hybrid method, Scientific Research and Essays, 9 (12), 557-565.
28. [28] Mosayebidorcheh, S., Rahimi-Gorji, M., Ganji, D. D. , Moayebidorcheh, T., Pourmehran, O. and Biglarian, M. (2017). Transient thermal behavior of radial fins of rectangular, triangular and hyperbolic profiles with temperature-dependent properties using DTM-FDM, Journal of Central South University, 24 (3), 675-682.
29. [29] Hatami, M., Mosayebidorcheh, S. Jing, D. (2017). Two-phase nanofluid condensation and heat transfer modeling using least square method (LSM) for industrial applications, Heat and Mass Transfer, 53 (6), 2061-2072.
30. [30] Fernandez, A. (2009). On some approximate methods for nonlinear models. Appl Math Comput, 215, 168-174.
31. [31] Sobamowo, M. G. (2016). Thermal analysis of longitudinal fin with temperature-dependent properties and internal heat generation using Galerkin’s method of weighted residual. Applied Thermal Engineering, 99, 1316–1330.
32. [32] Eringen, A. C. (1983). On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves”, Journal of Applied Physics, vol. 54(9), 4703–4710.
33. [33] Eringen, A. C. (1972). Linear theory of nonlocal elasticity and dispersion of plane waves”, International Journal of Engineering Science, 10(5), 425–435.
34. [34] Eringen, A. C. and Edelen, D. G. B. (1972). On nonlocal elasticity”, International Journal of Engineering Science, 10(3), 233–248.
35. [35] Sobamowo, M. G., Adeleye, O., Yinusa, A. A. (2017). Analysis of convective-radiative porous fin With temperature-dependent internal heat Generation and magnetic field using Homotopy Perturbation method, Journal of Computational and Applied Mechanics, Vol. 12., No. 2., pp. 127-145
36. [36] Sobamowo, M. G. Nonlinear vibration analysis of single-walled carbon nanotube conveying fluid with slip boundary conditions using variational iterative method, Journal of Applied and Computational Mechanics, 2016, 2(4), 208-221.
37. [37] Ali-Asgari, M., Mirdamadi, H. R. and Ghayour, M. (2013). Coupled effects of nano-size, stretching, and slip boundary conditions on nonlinear vibrations of nano-tube conveying fluid by the homotopy analysis method. Physica E, 52, 77–85
38. [38] Shokouhmand, H., Isfahani, A. H. M. and Shirani, E. (2010). Friction and heat transfer coefficient in micro and nano channels with porous media for wide range of Knudsen number”, International Communication in Heat and Mass Transfer, 37, 890-894.