Nonlocal Vibration of Embedded Coupled CNTs Conveying Fluid Under Thermo-Magnetic Fields Via Ritz Method

Subject Areas : Engineering

A Ghorbanpour Arani ¹ , S Amir ²

1 - Faculty of Mechanical Engineering, University of Kashan--- Institute of Nanoscience & Nanotechnology, University of Kashan
2 - Faculty of Mechanical Engineering, University of Kashan

Received: 2013-04-08 Accepted : 2013-05-30 Published : 2013-06-30

Keywords: magnetic field, Vibration, Conveying fluid, Visco-Pasternak medium, Coupled system, Knudsen Number,

Abstract :

In this work, nonlocal vibration of double of carbon nanotubes (CNTs) system conveying fluid coupled by visco-Pasternak medium is carried out based on nonlocal elasticity theory where CNTs are placed in uniform temperature change and magnetic field. Considering Euler-Bernoulli beam (EBB) model and Knudsen number, the governing equations of motion are discretized and Ritz method is applied to obtain the frequency of coupled CNTs system. The detailed parametric study is conducted, focusing on the remarkable effects of the Knudsen number, aspect ratio, small scale, thermo-magnetic fields, velocity of conveying fluid and visco-Pasternak medium on the stability of coupled system. The results indicate that magnetic field has significant effect on stability of coupled system. Also, it is found that trend of figures have good agreement with the previous researches. Results of this investigation could be applied for optimum design of nano/micro mechanical devices for controlling stability of coupled systems conveying fluid under thermo-magnetic fields.

References:

[1] Iijima S., 1991, Helical micro tubes of graphitic carbon, Nature 354: 56-58.

[2] Yan Z., Jiang L.Y., 2011, The vibrational and buckling behaviors of piezoelectric nanobeams with surface effects, Nanotechnology 22(24): 245703-2457010.

[3] Ghorbanpour Arani A., Zarei M.S., Mohammadimehr M., Arefmanesh A., Mozdianfard M.R., 2011, The thermal effect on buckling analysis of a DWCNT embedded on the pasternak foundation, Physica E 43: 1642-1648.

[4] Ghorbanpour Arani A., Mohammadimehr M., Arefmanesh A., Ghasemi A., 2009, Transverse vibration of short carbon nanotube using cylindrical shell and beam models, Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 224: 745-756.

[5] Zhen Y., Fang B., Tang Y., 2011, Thermal-mechanical vibration and instability analysis of fluid-conveying double walled carbon nanotubes embedded in visco-elastic medium, Physica E 44: 379-385.

[6] Kuang Y.D., He X.Q., Chen C.Y., Li G.Q., 2009, Analysis of nonlinear vibrations of double-walled carbon nanotubes conveying fluid, Computation Materials Science 45: 875-880.

[7] Wang L., 2010, Vibration analysis of fluid-conveying nanotubes with consideration of surface effects, Physica E 43: 437-439.

[8] Khosravian N., Rafii-Tabar H., 2007, Computational modelling of the flow of viscous fluids in carbon nanotubes, Journal of Physics D: Applied Physics 40: 7046-7052.

[9] Wang L., Ni Q., Li M., Qian Q., 2008, The thermal effect on vibration and instability of carbon nanotubes conveying fluid, Physica E 40: 3179-3182.

[10] Murmu T., McCarthy M.A., Adhikari S., 2012, Vibration response of double-walled carbon nanotubes subjected to an externally applied longitudinal magnetic field: a nonlocal elasticity approach, Journal of Sound and Vibration 331: 5069-5086.

[11] Murmu T., Pradhan S.C., 2009, Thermo-mechanical vibration of a single-walled carbon nanotube embedded in an elastic medium based on nonlocal elasticity theory, Computation Materials Science 46: 854-859.

[12] Murmu T., Adhikari S., 2011, Nonlocal buckling behavior of bonded double-nanoplate-systems, Journal of Applied Physics 108(8): 084316-084319.

[13] Khodami Maraghi Z., Ghorbanpour Arani A., Kolahchi R., Amir S., Bagheri M.R., 2013, Nonlocal vibration and instability of embedded DWBNNT conveying viscose fluid, Composites Part B Engineering 45(1): 423-432.

[14] Eringen A.C., 1983, On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves, Journal of Applied Physics 54: 4703-4710.

[15] Ghavanloo E., Fazelzadeh S.A., 2011, Flow-thermoelastic vibration and instability analysis of viscoelastic carbon nanotubes embedded in viscous fluid, Physica E 44(1): 17-24.

[16] Karniadakis G., Beskok A., Aluru N., 2005, Microflows and Nanoflows: Fundamentals and Simulation, Springer.

[17] Mirramezani M., Mirdamadi H.R., 2012, The effects of knudsen-dependent flow velocity on vibrations of a nano-pipe conveying fluid, Archive of applied mechanics 82(7): 879-890.

[18] Ghorbanpour Arani A., Shajari A.R., Atabakhshian V., Amir S., Loghman A., 2013, Nonlinear dynamical response of embedded fluid-conveyed micro-tube reinforced by BNNTs, Composites Part B Engineering 44(1): 424-432.

[19] Amabili M., 2008, Nonlinear Vibrations and Stability of Shells and Plates, Italy, Cambridge University Press.

[20] Yang J., Ke L.L., Kitipornchai S., 2010, Nonlinear free vibration of single-walled carbon nanotubes using nonlocal Timoshenko beam theory, Physica E 42(5): 1727-1735.

[21] Mohammadimehr M., Saidi A.R., Ghorbanpour Arani A., Arefmanesh A., Han Q., 2010, Torsional buckling of a DWCNT embedded on winkler and pasternak foundations using nonlocal theory, Journal of Mechanical Science and Technology 24(6): 1289–1299.