Ghorbanpour Arani, A., Zarei, M. (2014). Nonlinear Nonlocal Vibration of an Embedded Viscoelastic Y-SWCNT Conveying Viscous Fluid Under Magnetic Field Using Homotopy Analysis Method. Journal of Solid Mechanics, 6(2), 173-193.

A Ghorbanpour Arani; M.Sh Zarei. "Nonlinear Nonlocal Vibration of an Embedded Viscoelastic Y-SWCNT Conveying Viscous Fluid Under Magnetic Field Using Homotopy Analysis Method". Journal of Solid Mechanics, 6, 2, 2014, 173-193.

Ghorbanpour Arani, A., Zarei, M. (2014). 'Nonlinear Nonlocal Vibration of an Embedded Viscoelastic Y-SWCNT Conveying Viscous Fluid Under Magnetic Field Using Homotopy Analysis Method', Journal of Solid Mechanics, 6(2), pp. 173-193.

Ghorbanpour Arani, A., Zarei, M. Nonlinear Nonlocal Vibration of an Embedded Viscoelastic Y-SWCNT Conveying Viscous Fluid Under Magnetic Field Using Homotopy Analysis Method. Journal of Solid Mechanics, 2014; 6(2): 173-193.

Nonlinear Nonlocal Vibration of an Embedded Viscoelastic Y-SWCNT Conveying Viscous Fluid Under Magnetic Field Using Homotopy Analysis Method

^{1}Faculty of Mechanical Engineering, University of Kashan--- Institute of Nanoscience & Nanotechnology, University of Kashan

^{2}Faculty of Mechanical Engineering, University of Kashan

Abstract

In the present work, effect of von Karman geometric nonlinearity on the vibration characteristics of a Y-shaped single walled carbon nanotube (Y-SWCNT) conveying viscose fluid is investigated based on Euler Bernoulli beam (EBB) model. The Y-SWCNT is also subjected to a longitudinal magnetic field which produces Lorentz force in transverse direction. In order to consider the small scale effects, nonlocal elasticity theory is applied due to its simplicity and accuracy. The small-size effects and slip boundary conditions of nano-flow are taken into account through Knudsen number (Kn). The Y-SWCNT is surrounded by elastic medium which is simulated as nonlinear Visco-Pasternak foundation. Using energy method and Hamilton’s principle, the nonlinear governing motion equation is obtained. The governing motion equation is solved using both Galerkin procedure and Homotopy analysis method (HAM). Numerical results indicate the significant effects of the mass and velocity of the fluid flow, strength of longitudinally magnetic field, (Kn), angle between the centerline of carbon nanotube and the downstream elbows, nonlocal parameter and nonlinear Visco-Pasternak elastic medium. The results of this work is hoped to be of use in design and manufacturing of nano-devices in which Y-shaped nanotubes act as basic elements.

[1] Iijima S., 1991, Helical microtubules of graphitic carbon, Nature 354:56-58. [2] Wang B.L., Wang K.F., 2013, Vibration analysis of embedded nanotubes using nonlocal continuum theory, Composites Part B 47:96-101. [3] Fang B., Zhen Y.X., Zhang C.P., Tang Y., 2013, Nonlinear vibration analysis of double-walled carbon nanotubes based on nonlocal elasticity theory, Applied Mathematical Modelling 37:1096-1107. [4] Simsek M., Yurtcu H.H., 2013, Analytical solutions for bending and buckling of functionally graded nanobeams based on the nonlocal Timoshenko beam theory, Composite Structures 97:378-386. [5] Liang F., Su Y., 2013, Stability analysis of a single-walled carbon nanotube conveying pulsating and viscous fluid with nonlocal effect, Applied Mathematical Modelling 37:6821-6828. [6] Ghorbanpour Arani A., Abdollahian M., Kolahchi R., Rahmati A.H., 2013, Electro-thermo-torsional buckling of an embedded armchair DWBNNT using nonlocal shear deformable shell model, Composites Part B 51:291-299. [7] Ke L.L., Wang Y.S., Wang Z.D., 2012, Nonlinear vibration of the piezoelectric nanobeams based on the nonlocal theory Composite Structures 94:2038-2047. [8] Ghorbanpour Arani A., Kolahchi R., Vossough H., 2012, Buckling analysis and smart control of SLGS using elastically coupled PVDF nanoplate based on the nonlocal Mindlin plate theory, Physica B 407:4458-4465. [9] Ghorbanpour Arani A., Kolahchi R., Khoddami Maraghi Z., 2013, Nonlinear vibration and instability of embedded double-walled boron nitride nanotubes based on nonlocal cylindrical shell theory, Applied Mathematical Modelling 37:7685-7707. [10] Ke L.L., Wang Y.S., Yang J., Kitipornchai S., 2012, Nonlinear free vibration of size-dependent functionally graded microbeams, International Journal of Engineering Science 50:256-267. [11] Asghari M., Kahrobaiyan H.H., Ahmadian M.T., 2010, A nonlinear Timoshenko beam formulation based on the modified couple stress theory, International Journal of Engineering Science 48:1749-1761. [12] Reddy J.N., 2011, Microstructure-dependent couple stress theories of functionally graded beams, Journal of the Mechanics and Physics of Solids 59:2383-2399. [13] Chena W., Lili M.X., 2012, A model of composite laminated Reddy plate based on new modified couple stress theory, Composite Structures 94:2143-2156. [14] Zhao J., Zhou S., Wang B., Wang X., 2012, Nonlinear microbeam model based on strain gradient theory, Applied Mathematical Modelling 36:2674-2686. [15] Ramezani S., 2012, A micro scale geometrically non-linear Timoshenko beam model based on strain gradient elasticity theory, International Journal of Non-Linear Mechanics 47:863-873. [16] 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. [17] Wang L., 2009, Dynamical behaviors of double-walled carbon nanotubes conveying fluid accounting for the role of small length scale, Computational Materials Science 45:584-588. [18] Ghavanloo E., Daneshmand F., Rafiei M., 2010, Vibration and instability analysis of carbon nanotubes conveying fluid and resting on a linear viscoelastic Winkler foundation, Physica E 42:2218-2224. [19] Kuang Y.D., He X.Q., Chen C.Y., Li G.Q., 2009, Analysis of nonlinear vibrations of double-walled carbon nanotubes conveying fluid, Computational Materials Science 45:875-880. [20] Xia W., Wang L., 2010, Vibration characteristics of fluid-conveying carbon nanotubes with curved longitudinal shape, Computational Materials Science 49:99-103. [21] Wang L., Ni Q., 2009, A reappraisal of the computational modelling of carbon nanotubes conveying viscous fluid, Mechanics Research Communications 36:833-837. [22] Abdollahian M., Ghorbanpour Arani A., Mosallaie Barzoki A.A., Kolahchi, R., Loghman A., 2013, Non-local wave propagation in embedded armchair TWBNNTs conveying viscous fluid using DQM, Physica B 418:1-15. [23] Lee H.L., Chang W.J., 2009, Vibration analysis of a viscous-fluid-conveying single-walled carbon nanotube embedded in an elastic medium, Physica E 41:529-532. [24] Jannesari H., Emami M.D., Karimpour H., 2012, Investigating the effect of viscosity and nonlocal effects on the stability of SWCNT conveying flowing fluid using nonlinear shell model, Physics Letters A 376:1137-1145. [25] Rashidi V., Mirdamadi H.R., Shirani E., 2012, A novel model for vibrations of nanotubes conveying nanoflow, Computational Materials Science 51:347-352. [26] Mirramezani M., Mirdamadi H.R., 2012, Effects of nonlocal elasticity and Knudsen number on fluid–structure interaction in carbon nanotube conveying fluid, Physica E 44:2005-2015. [27] Lei X.W., Natsuki T., Shi J.X., Ni Q.Q., 2012, Surface effects on the vibrational frequency of double-walled carbon nanotubes using the nonlocal Timoshenko beam model, Composites Part B 43:64-69. [28] Ashgharifard Sharabiani P., Haeri Yazdi M.R., 2013, Nonlinear free vibrations of functionally graded nanobeams with surface effects, Composites Part B 45:581-586. [29] Wang L., 2010, Vibration analysis of fluid-conveying nanotubes with consideration of surface effects, Physica E 43:437-439. [30] Biro L.P., Horvath Z.E., Mark G.I., Osvath Z., Koos A.A., Santucci S., Kenny J.M., 2004, Carbon nanotube Y junctions: growth and properties, Diamond and Related Materials 13:241-249. [31] Lin R.M., 2012, Nanoscale vibration characterization of multi-layered graphene sheets embedded in an elastic medium, Computational Materials Science 53:44-52. [32] Pradhan S.C., Phadikar J.K., 2009, Small scale effect on vibration of embedded multilayered graphene sheets based on nonlocal continuum models, Physics Letters A 373:1062-1069. [33] Ghorbanpour Arani A., Zarei M.Sh., Amir S., Khoddami Maraghi Z., 2013, Nonlinear nonlocal vibration of embedded DWCNT conveying fluid using shell model, Physica B 410:188-196 [34] Ghorbanpour Arani A., Amir S., 2013, Electro-thermal vibration of visco-elastically coupled BNNT systems conveying fluid embedded on elastic foundation via strain gradient theory, Physica B 419:1-6. [35] Eichler A., Moser J., Chaste J., Zdrojek M., Wilson-Rae I., Bachtold A., 2011, Nonlinear damping in mechanical resonators made from carbon nanotubes and grapheme, Nature Nanotechnology 6:339-342. [36] Pirbodaghi T., Ahmadian M.T., Fesanghary M., 2009, On the homotopy analysis method for non-linear vibration of beams, Mechanics Research Communications 36:143-148. [37] Moghimi Zand M., Ahmadian M.T., 2009, Application of homotopy analysis method in studying dynamic pull-in instability of Microsystems, Mechanics Research Communications 36:851-858. [38] Reddy J.N., Wang C.M., 2004, Dynamics of Fluid-Conveying Beams: Governing Equations and Finite Element Models, Centre for Offshore Research and Engineering National University of Singapore. [39] Ghorbanpour Arani A., Amir S., 2013, Nonlocal vibration of embedded coupled CNTs conveying fluid under thermo-magnetic fields via ritz method, Journal of Solid Mechanics 5:206-215. [40] Gurtin M.E., Murdoch A.I., 1975, A continuum theory of elastic material surfaces, Archive for Rational Mechanics and Analysis 57:291-323. [41] Narendar S., Ravinder S., Gopalakrishnan S., 2012, Study of non-local wave properties of nanotubes with surface effects, Computational Materials Science 56:179-184. [42] Paidoussis M.P., 1998, Fluid-Structure Interactions: Slender Structures and Axial Flow, Academic Press, London. [43] Liao S.J., 2003, Beyond Perturbation: Introduction to the Homotopy Analysis Method, Chapman and Hall, CRC Press, Boca Raton. [44] Hosseini S.H., Pirbodaghi T., Asghari M., Farrahi G.H., Ahmadian M.T., 2008, Nonlinear free vibration of conservative oscillators with inertia and static type cubic nonlinearities using homotopy analysis method, Journal of Sound and Vibration 316:263-273.