Using Green Function Method to Dynamic Analysis of Nanotubes Conveying Fluid Under Moving Load

Document Type : Research Article

Authors

Department of Mechanical Engineering, Sirjan University of Technology, Sirjan, Iran

Abstract

ABSTRACT: In this paper, the dynamic response of carbon nanotubes (CNT) conveying fluid under moving
harmonic load by using the Green function method is investigated. The results of this analysis are obtained for four
different boundary conditions, namely fixed- fixed, fixed- pinned, pinned- fixed and pinned -pinned. The harmonic
load is assumed to travel with uniform velocity, accelerating and decelerating types of motion and the internal fluid
flow is moved with uniform velocity. The Green function and Laplace transform method is implemented to analysis
of force vibrations for achieving exact solutions of dynamic response. In the present work, the effects of various
parameters such as viscoelastic coefficient, moving load and fluid flow velocity, length scale parameter, boundary
conditions, viscous damping and types of the load motion on the dynamic displacement of the CNT are elucidated.
However, the results show that these parameters are vital in investigation of the dynamic displacement of CNT. It is
obvious that the dynamic deflection is very sensitive to the material length scale parameter in which structural stiffness
of CNT and the dimensionless dynamic displacements, respectively, is decreased and increased with increases in the
length scale parameter.

Keywords

Main Subjects


[1] S. Iijima, Helical microtubules of graphitic carbon, nature, 354(6348) (1991) 56-58.
[2] E. Asadi, M. Farhadi Nia, Vibrational study of laminated composite plates reinforced by carbon nanotubes, Modares Mechanical Engineering, 14(3) (2014) 7-16.
[3] T.W. Ebbesen, Carbon nanotubes: preparation and properties, CRC press, 1996.
[4] 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 Letters A,371(5) (2007) 499-503.
[5] M. Zakeri, M. Shayanmehr, M. Shokrieh, Interface modeling of nanotube reinforced nanocomposites by using multi-scale modeling method, Modares Mechanical Engineering, 12(5) (2013) 1-11.
[6] E.V. Dirote, Trends in nanotechnology research, Nova Publishers, 2004.
[7] R. Rafiee, Analysis of Nonlinear Vibrations of a Carbon Nanotube Using Perturbation Technique, Modares Mechanical Engineering, 12(3) (2012) 60-67.
[8] M. Foldvari, M. Bagonluri, Carbon nanotubes as functional excipients for nanomedicines: II. Drug delivery and biocompatibility issues, Nanomedicine:Nanotechnology, Biology and Medicine, 4(3) (2008)183-200.
[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(27) (2008) 275703.
[10] R. Ansari, B. Arash, Nonlocal Flügge Shell Model for Vibrations of Double-Walled Carbon Nanotubes With Different Boundary Conditions, Journal of Applied Mechanics, 80(2) (2013) 021006.
[11] L. Wang, Vibration and instability analysis of tubular nano-and micro-beams conveying fluid using nonlocal elastic theory, Physica E: Low-dimensional Systems and Nanostructures, 41(10) (2009) 1835-1840.
[12] J. Yoon, C. Ru, A. Mioduchowski, Vibration and instability of carbon nanotubes conveying fluid, Composites Science and Technology, 65(9) (2005) 1326- 1336.
[13] L. Wang, Q. Ni, M. Li, Buckling instability of doublewall carbon nanotubes conveying fluid, Computational Materials Science, 44(2) (2008) 821-825.
[14] L. Wang, Q. Ni, A reappraisal of the computational modelling of carbon nanotubes conveying viscous fluid, Mechanics Research Communications, 36(7) (2009)833-837.
[15] Y.-X. Zhen, B. Fang, Y. Tang, Thermal–mechanical vibration and instability analysis of fluid-conveying double walled carbon nanotubes embedded in viscoelastic medium, Physica E: Low-dimensional Systems and Nanostructures, 44(2) (2011) 379-385.
[16] A. Ghorbanpourarani, M. Mohammadimehr, A.Arefmanesh, A. Ghasemi, Transverse vibration of short carbon nanotubes using cylindrical shell and beam models, Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 224(3) (2010) 745-756.
[17] M. Kargarnovin, D. Younesian, Dynamics of Timoshenko beams on Pasternak foundation under moving load, Mechanics research communications, 31(6) (2004) 713-723.
[18] B. Biondi, G. Muscolino, A. Sidoti, Methods for calculating bending moment and shear force in the moving mass problem, Journal of vibration and acoustics, 126(4)(2004) 542-552.
[19] H. Bulut, O. Kelesoglu, Comparing numerical methods for response of beams with moving mass, Advances in Engineering Software, 41(7) (2010) 976-980.
[20] E. Sharbati, W. Szyszkowski, A new FEM approach for analysis of beams with relative movements of masses, Finite Elements in Analysis and Design, 47(9) (2011)1047-1057.
[21] M.H. Sadeghi, M.H. Karimi-Dona, Dynamic behavior of a fluid conveying pipe subjected to a moving sprung mass–an FEM-state space approach, International Journal of Pressure Vessels and Piping, 88(4) (2011) 123-131.  
[22] D. Yu, J. Wen, H. Shen, X. Wen, Propagation of steadystate vibration in periodic pipes conveying fluid on elastic foundations with external moving loads, Physics Letters A, 376(45) (2012) 3417-3422.
[23] M.H. Kargarnovin, M.T. Ahmadian, R.-A. Jafari-Talookolaei, Dynamics of a delaminated Timoshenkobeam subjected to a moving oscillatory mass, Mechanics based design of structures and machines, 40(2) (2012) 218-240.
[24] S.E. Azam, M. Mofid, R.A. Khoraskani, Dynamic response of Timoshenko beam under moving mass, Scientia Iranica, 20(1) (2013) 50-56.
[25] K. Misiurek, P. Śniady, Vibrations of sandwich beam due to a moving force, Composite Structures, 104 (2013)85-93.
[26] M. Şimşek, Vibration analysis of a functionally graded beam under a moving mass by using different beam theories, Composite Structures, 92(4) (2010) 904-917.
[27] M. Şimşek, Dynamic analysis of an embedded microbeam carrying a moving microparticle based on the modified couple stress theory, International Journal of Engineering Science, 48(12) (2010) 1721-1732.
[28] Y.-d. Li, Y.-r. Yang, Forced vibration of pipe conveying fluid by the Green function method, Archive of Applied Mechanics, 84(12) (2014) 1811-1823.
[29] Z.K. Maraghi, A.G. Arani, R. Kolahchi, S. Amir, M. Bagheri, Nonlocal vibration and instability of embedded DWBNNT conveying viscose fluid, Composites Part B:Engineering, 45(1) (2013) 423-432.
[30] M. Abu-Hilal, M. Mohsen, Vibration of beams with general boundary conditions due to a moving harmonic load, Journal of Sound and Vibration, 232(4) (2000) 703-717.
[31] D.G. Duffy, Green’s functions with applications, CRC Press, 2015.
[32] D. Poole, Linear algebra: A modern introduction, Cengage Learning, 2014.
[33] M.P. Paidoussis, Fluid-structure interactions: slender structures and axial flow, Academic press, 1998.