Dynamic Instability of Visco-SWCNTs Conveying Pulsating Fluid Based on Sinusoidal Surface Couple Stress Theory

Document Type : Research Paper


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

2 Faculty of Mechanical Engineering, University of Kashan, Kashan, Iran


In this study, a realistic model for dynamic instability of embedded single-walled nanotubes (SWCNTs) conveying pulsating fluid is presented considering the viscoelastic property of the nanotubes using Kelvin–Voigt model. SWCNTs are placed in longitudinal magnetic fields and modeled by sinusoidal shear deformation beam theory (SSDBT) as well as modified couple stress theory. The effect of slip boundary condition and small size effect of nano flow are considered using Knudsen number. The Gurtin–Murdoch elasticity theory is applied for incorporation the surface stress effects. The surrounding elastic medium is described by a visco-Pasternak foundation model, which accounts for normal, transverse shear and damping loads. The motion equations are derived based on the Hamilton's principle. The differential quadrature method (DQM) in conjunction with Bolotin method is used in order to calculate the dynamic instability region (DIR) of visco-SWCNTs induced by pulsating fluid. The detailed parametric study is conducted, focusing on the combined effects of the nonlocal parameter, magnetic field, visco-Pasternak foundation, Knudsen number, surface stress and fluid velocity on the dynamic instability of SWCNTs. The results depict that increasing magnetic field and considering surface effect shift DIR to right. The results presented in this paper would be helpful in design and manufacturing of nano/micro mechanical systems.  


[1] Wang X., Li Q., Xie J., Jin Z., Wang J., Li Y., Jiang K., Fan S., 2009, Fabrication of ultralong and electrically uniform single-walled carbon nanotubes on clean substrates, Nano Letters 9: 3137-3141.
[2] Wong M., Gullapalli S., 2011, Nanotechnology: A Guide to Nano-Objects, Chemical Engineering Progress.
[3] Şimşek M., Reddy J.N., 2013, Bending and vibration of functionally graded microbeams using a new higher order beam theory and the modified couple stress theory, International Journal of Engineering Science 64: 37-53.
[4] Wang L., Xu Y.Y., Ni Q., 2013, Size-dependent vibration analysis of three-dimensional cylindrical microbeams based on modified couple stress theory: A unified treatment, International Journal of Engineering Science 68: 1-10.
[5] Thai H-T., Vo T.P., 2012, A nonlocal sinusoidal shear deformation beam theory with application to bending, buckling, and vibration of nanobeams, International Journal of Engineering Science 54: 58-66.
[6] Kiani K., 2013, Vibration behavior of simply supported inclined single-walled carbon nanotubes conveying viscous fluids flow using nonlocal Rayleigh beam model, Applied Mathematical Modelling 37: 1836-1850.
[7] 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: 423-432.
[8] Murmu T., Pradhan S.C., 2009, Buckling analysis of a single-walled carbon nanotube embedded in an elastic medium based on nonlocal elasticity and Timoshenko beam theory and using DQM, Physica E: Low-Dimensional Systems and Nanostructures 41: 1232-1239.
[9] Ghorbanpour Arani A., Kolahchi R., Hashemian M., 2014, Nonlocal surface piezoelasticity theory for dynamic stability of double-walled boron nitride nanotube conveying viscose fluid based on different theories, Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science.
[10] 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.
[11] Mirramezani M., Mirdamadi H.R., Ghayour M., 2013, Innovative coupled fluid–structure interaction model for carbon nano-tubes conveying fluid by considering the size effects of nano-flow and nano-structure, Computational Materials Science 77: 161-171.
[12] Kaviani F., Mirdamadi H.R., 2013, Wave propagation analysis of carbon nano-tube conveying fluid including slip boundary condition and strain/inertial gradient theory, Computers & Structures 116: 75-87.
[13] Lee H.L., Chang W.J., 2010, Surface effects on frequency analysis of nanotubes using nonlocal Timoshenko beam theory, Journal of Applied Physics 108: 093503.
[14] Gheshlaghi B., Hasheminejad S.M., 2011, Surface effects on nonlinear free vibration of nanobeams, Composites Part B: Engineering 42: 934-937.
[15] Malekzadeh P., Shojaee M., 2013, Surface and nonlocal effects on the nonlinear free vibration of non-uniform nanobeams, Composites Part B: Engineering 52: 84-92.
[16] Kiani K., 2014, Vibration and instability of a single-walled carbon nanotube in a three-dimensional magnetic field, Journal of Physics and Chemistry of Solids 75: 15-22.
[17] Wang H., Dong K., Men F., Yan Y.J., Wang X., 2010, Influences of longitudinal magnetic field on wave propagation in carbon nanotubes embedded in elastic matrix, Applied Mathematical Modelling 34: 878-889.
[18] Ghorbanpour Arani A., Amir S., Dashti P., Yousefi M., 2014, Flow-induced vibration of double bonded visco-CNTs under magnetic fields considering surface effect, Computational Materials Science 86: 144-154.
[19] Lei Y., Adhikari S., Friswell M.I., 2013, Vibration of nonlocal Kelvin–Voigt viscoelastic damped Timoshenko beams, International Journal of Engineering Science 66: 1-13.
[20] 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: Condensed Matter 419: 1-6.
[21] Lei Y., Murmu T., Adhikari S., Friswell M.I., 2013, Dynamic characteristics of damped viscoelastic nonlocal Euler–Bernoulli beams, European Journal of Mechanics - A/Solids 42: 125-136.
[22] Gurtin M., Ian Murdoch A., 1975, A continuum theory of elastic material surfaces, Archive for Rational Mechanics and Analysis 57: 291-323.
[23] Gurtin M., Ian Murdoch A., 1978, Surface stress in solids, International Journal of Solids and Structures 14: 431-440.
[24] Ansari R., Ashrafi M.A., Pourashraf T., Sahmani S., 2015, Vibration and buckling characteristics of functionally graded nanoplates subjected to thermal loading based on surface elasticity theory, Acta Astronautica 109: 42-51.
[25] Shaat M., Mohamed S.A., 2014, Nonlinear-electrostatic analysis of micro-actuated beams based on couple stress and surface elasticity theories, International Journal of Mechanical Sciences 84: 208-217.
[26] Ansari R., Sahmani S., 2011, Bending behavior and buckling of nanobeams including surface stress effects corresponding to different beam theories, International Journal of Engineering Science 49: 1244-1255.
[27] Bolotin V.V., 1964, The Dynamic Stability of Elastic Systems, Holden-Day, San Francisco.
[28] Lanhe W., Hongjun W., Daobin W., 2007, Dynamic stability analysis of FGM plates by the moving least squares differential quadrature method, Composite Structures 77: 383-394.
[29] 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: Engineering 43: 64-69.