Engineering Transactions, 65, 2, pp. 319–333, 2017

Nonlocal Critical Velocities of Fluid Conveying Clamped-Pinned Single-Walled Carbon Nanotubes Subjected to Axial Magnetic Field

Chellapilla Kameswara RAO
Nalla Narsimha Reddy Engineering College

Lokavarapu Bhaskara RAO
VIT University

The problem of stability of fluid conveying carbon nanotubes clamped at one end and pinned at the other end and subjected to an axial magnetic field is investigated in this paper. Non-local continuum mechanics formulation is utilized to derive the governing fourth-order partial differential equations, which takes into consideration the small length scale effects and the axial magnetic field. Galerkin’s technique is used to find the solution of the governing equation for the case of clamped-pinned boundary. Closed-form expressions for the critical flow velocity above which the system becomes unstable, of the fluid conveying carbon nanotubes, are obtained and numerical results for different values of axial magnetic field parameter are presented in this paper for use in industrial dynamic design of such devices. The results obtained from these simple and approximate expressions are compared with those existing in literature, wherever available and an excellent agreement is found between them. Along with extensive results on critical velocities new and interesting results are also reported for varying values of nonlocal length parameter. From the results presented in this paper, it is observed that the non-local length parameter along with axial magnetic field parameter are having considerable influence on the critical velocities of the fluid conveying nanotubes.
Keywords: critical flow velocity; Single-Walled Carbon Nano-Tubes; SWCNT; non-local; axial magnetic field
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Yoon J., Ru C.Q., Mioduchowski A., Vibration and instability of carbon nanotubes conveying fluid, Composites Science and Technology, 65(9): 1326–1336, 2005, doi: 10.1016/j.compscitech.2004.12.002.

Reddy C.D., Lu C., Rajendran S., Liew K.M., Free vibration analysis of fluid-conveying single-walled carbon nanotubes, Applied Physics Letters, 90(13): 133122, 2007, doi:

Chang W.J., Lee H.L., Free vibration of a single-walled carbon nanotube containing a fluid flow using the Timoshenko beam model, Physics Letters A, 373(10): 982–985, 2009.

Cemal Eringen A.C., Edelen G.B., On nonlocal elasticity, International Journal of Engineering Science, 10(3): 233–248, 1972.

Cemal Eringen A.C., Nonlocal continuum field theories, Springer-Verlag, New York 2002.

Lee H. L., Chang W.J., Free transverse vibration of the fluid-conveying single-walled carbon nanotube using nonlocal elastic theory, Journal of Applied Physics, 103(2): 024302, 2008, doi: 10.1063/1.2822099.

Lee H.L., Chang W.J., Vibration analysis of a viscous-fluid-conveying single-walled carbon nanotube embedded in an elastic medium, Physica E: Low-dimensional Systems and Nanostructures, 41(4): 529–532, 2009, doi: 10.1016/j.physe.2008.10.002.

Wang Q., Varadan V.K., Vibration of carbon nanotubes studied using nonlocal continuum mechanics, Smart Materials and Structures, 15(2): 659–666, 2006, doi: 10.1088/0964-1726/15/2/050.

Tounsi A., Heireche H., Bedia E.A.A., Comment on “Free transverse vibration of the fluid-conveying single-walled carbon nanotube using nonlocal elastic theory”, Journal of Applied Physics, 105(12): 126105, 2009, doi: 10.1063/1.3153960.

Wang L., 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): 1835–1840, 2009, doi: 10.1016/j.physe.2009.07.011.

Farshidianfar A., Ghassabi A.A., Farshidianfar M.H., Transverse vibration of fluid conveying carbon nanotubes embedded in two-parameter elastic medium, Proceedings of the 18th International Congress on Sound and Vibration, Rio de Janeiro, Brazil, 2011.

Ghorbanpour Arani A., Amir S., Nonlocal vibration of embedded coupled cnts conveying fluid under thermo-magnetic fields via Ritz method, Journal of Solid Mechanics, 5(2): 206–215, 2013.

Feng Liang, Bao Ridong, Stability Analysis of a Fluid-conveying Carbon Nanotube with consideration of Nonlocal and Surface Effects [in Chinese], Mechanics in Engineering, 36(1): 48–53, 2014.

Kiani K., Vibration and instability of a single-walled carbon nanotube in a three-dimensional magnetic field, Journal of Physics and Chemistry of Solids, 75(1): 15–22, 2014, doi: 10.1016/j.jpcs.2013.07.022.

Ponnusamy P., Amuthalakshmi A., Influence of Thermal and Longitudinal Magnetic Field on Vibration Response of a Fluid Conveying Double Walled Carbon Nanotube Embedded in an Elastic Medium, Journal of Computational and Theoretical Nanoscience, 11(12): 2570–2577, 2014, doi: 10.1166/jctn.2014.3674.

Cajić M.S., Lazarević P.M., Karličić D.Z., Nonlocal frequency analysis of a nanobeam under axial magnetic field using finite element method, 8th GRACM International Congress on Computational Mechanics, Volos, Greece, 2015,

Hosseini M., Sadeghi-Goughari M., Vibration and instability analysis of nanotubes conveying fluid subjected to a longitudinal magnetic field, Applied Mathematical Modeling, 40(4): 2560–2576, 2016, doi: 10.1016/j.apm.2015.09.106.

Rao C.K., Simha H.S., Critical velocity of fluid conveying pipes resting on two-parameter foundation, Journal of Sound and Vibration, 302(1–2): 387–397, 2007, doi: 10.1016/j.jsv.2006.11.007.

Rao S.S., Mechanical vibrations, Addison-Wesley, MA, 1986.

Felgar P., Formulas for integrals containing characteristic functions of a vibrating beam, University of Texas Circular No. 14, Bureau of Engineering Research, Austin, Texas, 1950.

Rao C.K., Simha H.S., Vibrations of fluid-conveying pipes resting on two-parameter foundation, The Open Acoustics Journal, 1(1): 24–33, 2008, doi: 10.2174/1874837600801010024.

Ni Q., Zhang Z.L., Wang L., Application of the differential transformation method to vibration analysis of pipes conveying fluid, Applied Mathematics and Computation, 217(16): 7028–7038, 2011, doi: 10.1016/j.amc.2011.01.116.

Païdoussis M.P., Fluid-structure interactions: slender structures and axial flow, Academic Press, London, 1998.

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