Iranian Journal of Mechanical Engineering Transactions of ISME

Iranian Journal of Mechanical Engineering Transactions of ISME

Free vibration and instability study of conveying fluid carbon nanotubes based on the Donnel-cylindrical shell theory

Authors
Abstract
In this paper, a novel model is proposed to study free vibration and instability of the single walled carbon nanotubes conveying fluid based on the Donnell-cylindrical shell model and the modified couple stress theory. This new model include only one material length scale parameter in which it ables to capture the effect of carbon tube size in the nano scale. Governing dynamical constitutive relations as well as the boundary conditions have obtained via the Hamilton principle. The mentioned constitutive relations have been solved using differential quadrature method (DQM). Moreover, the effect of internal fluid and its velocity have been investigated on the frequency changes and instability of the nanotube, the effect of material length scale parameter, temperature changes as well as surrounding elastic medium and different boundary condition have been studied too.
Keywords

[1] Iijima, S., "Helical Microtubules of Graphitic Carbon", Nature, Vol. 354, pp. 56–58, (1991).
 
[2] Wang, Q., Liew, K.M., and Duan, W.H., "Modeling of the Mechanical Instability of Carbon Nanotubes", Carbon, Vol. 46, pp. 285–290, (2008).
 
[3] Yan, Y., He, X.Q., Zhang, L.X., and Wang, C.M., "Dynamic behavior of Triple-walled Carbon Nanotubes Conveying Fluid ", Journal of Sound and Vibration, Vol. 319, pp. 1003–1018, (2009).
 
[4] Natsuki, T., Lei, X.W., Ni, Q.Q., and Endo, M., "Free Vibration Characteristics of Double-walled Carbon Nanotubes Embedded in an Wlastic Medium", Physics Letters A, Vol. 374, pp. 2670–2674, (2010).
 
[5] Foldvari, M., and Bagonluri, M. "Carbon Nanotubes as Functional Excipients for Nanomedicines: II. Drug Delivery and Biocompatibility Issues", Nanomedicine: Nanotechnology, Biology, and Medicine, Vol. 4, pp. 183-200, (2008).
 
[6] Khosravian, N., and Rafii-Tabar, H., "Computational Modelling of a Non-viscous Fluid Flow in a Multi-walled Carbon Nanotube Modelled as a Timoshenko Beam", Nanotechnology, Vol. 19, pp. 275703, (2008).
 
[7] Yoon, J., Ru, C.Q., and Mioduchowski, A., "Vibration and Instability of Carbon Nanotubes Conveying Fluid", Composite Science and Technology, Vol. 65, pp. 1326–1336, (2005).
 
[8] Yoon, C.Q., Ru, A., and Mioduchowski, A., "Flow-induced Flutter Instability of Cantilever Carbon Nanotubes", Journal of Solids and Structures, Vol. 43, pp. 3337–3349, (2006).
 
[9] Wang, X.Y., Wang, X., and Sheng, G.G., "The Coupling Vibration of Fluid-filled Carbon Nanotubes", Journal of Physics Letters D: Apply Physics, Vol. 40, pp. 2563-2572, (2007).
 
[10] Wong, E.W., Sheehan, P.E., and Lieber, C.M., "Nanobeam Mechanics: Elasticity, Strength and Toughness of Nano-rods and Nanotubes", Science, Vol. 277, pp. 1971–1974, (1997).
 
[11] Zhang, Y.Q., Liu, X., and Zhao, J.H., "Influence of Temperature Change on Column Buckling of Multi Walled Carbon Nanotubes", Physics Letters A, Vol. 372, pp. 1676–1681, (2008).
 
[12] Yang, Y., Zhang, L., and Lim, C.W., "Wave Propagation in Double-walled Carbon Nanotubes on a Novel Analytically Nonlocal Timoshenko-beam Model", Journal of Sound and Vibration, Vol. 330., pp. 1704–1717, (2011).
 
[13] Elishakoff, I., and Pentaras, D., "Rapid Communication Fundamental Natural Frequencies of Double-walled Carbon Nanotubes", Journal of Sound and Vibration, Vol. 322, pp. 652–664, (2009).
 
[14] Yoon, J., Ru, C.Q., and Mioduchowski, A., "Vibration and Instability of Carbon Nanotubes Conveying Fluid", Composites Science and Technology, Vol. 65, pp. 1326–1336, (2005).
 
[15] Ahangar, S., Rezazadeh, G.h., Shabani, R., Ahmadi, G., and Toloei, A., "On the Stability of a Microbeam Conveying Fluid Considering Modified Couple Stress Theory", International Journal of Mechanics and Materials in Design, Vol. 7, pp. 327–342, (2011).
 
[16] Zhen, Y., and Fang, B., "Thermal–mechanical and Nonlocal Elastic Vibration of Single-walled Carbon Nanotubes Conveying Fluid", Computational Materials Science, Vol. 49, pp. 276–282, (2010).
 
[17] Wang, L., "Size-dependent Vibration Characteristics of Fluid-conveying Microtubes"Journal of Fluid Structure, Vol. 26, pp. 675-684, (2010).
 
[18] Lee, H.L., and Chang, W.J., "Free Transverse Vibration of the Fluid-conveying Single-walled Carbon Nanotube using Nonlocal Elastic Theory", Journal of Apply Physics, Vol. 103, pp. 024302, (2008).
 
[19] Ke, L.L., and Wang, Y.S., "Flow-induced Vibration and Instability of Embedded Double-walled Carbon Nanotubes Based on a Modified Couple Stress Theory", Physica E, Vol. 43, pp. 1031–1039, (2011).
 
[20] Yang, F., Chong, A.C.M., Lam, D.C.C., and Tong, P., "Couple Stress Based Strain Gradient Theory for Elasticity", International Journal of Solids Structure, Vol. 39, pp. 2731–2743, (2002).
 
[21] Ma, H.M., Gao, X.L., and Reddy, J.N, "A Microstructure-dependent Timoshenko Beam Model Based on a Modified Couple Stress Theory", Journal of the Mechanics and Physics of Solids, Vol. 56, pp. 3379-3391, (2008).
 
[22] Chong, A.C.M., Yang, F., Lam, D.C.C., and Tong, P., "Torsion and Bending of Micron-scaled Structures", Journal of Materials Research, Vol. 16, pp. 1052-1058, (2001).
 
[23] Stolken, J.S., and Evans, A.G., "A Microbend Test Method for Measuring the Plasticity Length Scale", Acta Materialia, Vol. 46, pp. 5109-5115, (1998).
 
[24] Paliwal, D.N., Pandey, R.K., and Nath, T., "Free Vibrations of Circular Cylindrical Shell on Winkler and Pasternak Foundations",International Journal of Pressure Vessels and PipingVol. 69, pp. 79–89, (1996).
 
[25] Amabili, M., "Nonlinear Vibrations and Stability of Shells and Plates", Cambridge University Press, New York, (2008).
 
[26] Bakhtiari-Nejad, F., and Mousavi-Bideleh, M., "Nonlinear Free Vibration Analysis of Prestressed Circular Cylindrical Shells on the Winkler/Pasternak Foundation", Thin Walled Structures, Vol. 53, pp. 26–39, (2012).
 
[27] Karagiozis, K.N., Amabili, M., Padoussis, M.P., and Misra, A.K., "Nonlinear Vibrations of Fluid-filled Clamped Circular Cylindrical Shells", Journal of Fluids and Structures, Vol. 21, pp. 579–595, (2005).
 
[28] Ghorbanpour Arani, A., Amir, S., Shajari, A.R., and Mozdianfard, M.R., "Electro-thermo-mechanical Buckling of DWBNNTs Embedded in Bundle of CNTs using Nonlocal Piezoelasticity Cylindrical Shell Theory", Composites: Part B, Vol. 43, pp. 195–203, (2012).
 
[29] Bellman, R., Kashef, B.G., and Casti, J., "Differential Guadrature: a Technique for the Rapid Solution of Nonlinear Partial Differential Equations", Journal of Computational Physic, Vol. 10, pp. 40–52, (1972).
 
[30] Shu, C., "Differential Quadrature and its Application in Engineering", Springer-verlag, London, (2000).
 
[31] Shu, C., and Richards, B.E., "Application of Generalized Differential Quadrature to Solve Two Dimensional Incompressible Navier-Stokes Equations", International Journal for Numerical, Methods in Fluids, Vol. 15, pp. 791-798, (1992).
 
[32] Bert, C.W., and Malik, M., "Free Vibration Analysis of Thin Cylindrical Shells by the Differential Quadrature Method", ASME Journal Pressure Vessel Tech, Vol. 118, pp. 1-12, (1996).
 
[33] Wang, C.Y., Ru, C.Q., and Mioduchowski A., "Applicability and Limitations of Simplified Elastic Shell Equations for Carbon Nanotubes", Journal of Apply Mechanic, Vol. 71, pp. 622–631, (2004).
 
[34] Fazelzadeh, S.A., and Ghavanloo, E., "Nonlocal Anisotropic Elastic Shell Model for Vibrations of Single-walled Carbon Nanotubes with Arbitrary Chirality", Composite Structures, Vol. 94, pp. 1016-1022, (2012).
 
[35] Yakobson, B.I., Brabec, C.J., and Bernholc, J., "Nanomechanics of Carbon Tubes: Instabilities Beyond Linear Response", Physical Review Letters, Vol. 76, pp. 2511-2514,  (1996).
 
[36] Wang, L.F., Zheng, Q.S., Liu, J.Z., and Jiang, Q., "Size Dependence of the Thin-shell Model for Carbon Nanotubes", Physical Review Letters, Vol. 95, pp. 105501, (2005).
 
[37] Ghorbanpour Arani, A., Mohammadimehr, M., Saidi, A.R., Shogaei, S., and Arefmanesh, A., "Thermal Buckling Analysis of Double-walled Carbon Nanotubes Considering the Small-scale Length Effect", Journal of Mechanical Engineering Science Part C, Vol. 225, pp. 248-256,(2010).
Volume 15, Issue 3 - Serial Number 32
System Dyanamics and Solid Mechanics
Autumn 2013
Pages 73-99

  • Receive Date 22 November 2013