Nonlinear Flow-Induced Flutter Instability of Double CNTs Using Reddy Beam Theory

Document Type: Research Paper


1 Professor, Faculty of Mechanical Engineering, University of Kashan, Kashan, Iran

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

3 MS Graduate, Faculty of Mechanical Engineering, University of Kashan, Kashan, Iran


In this study, nonlocal nonlinear instability and the vibration of a double carbon nanotube (CNT) system have been investigated. The Visco-Pasternak model is used to simulate the elastic medium between nanotubes, on which the effect of the spring, shear and damping of the elastic medium is considered. Both of the CNTs convey a viscose fluid and a uniform longitudinal magnetic field is applied to them. The fluid velocity is modified by small-size effects on the bulk viscosity and the slip boundary conditions of nano flow through the Knudsen number (Kn). Using von Kármán geometric nonlinearity, Hamilton’s principle and considering longitudinal magnetic field, the nonlinear higher order governing equations for Reddy beam (RB) theory are derived. The differential quadrature method (DQM) is used to obtain the nonlinear frequency and critical fluid velocity (CFV) of the fluid conveying a coupled system. A detailed parametric study is conducted, focusing on the effects of parameters such as magnetic field strength, Knudsen number, aspect ratio, small scale and elastic foundation on the in-phase and out-of-phase vibration of the nanotube. The results indicate that the natural frequency and the critical fluid velocity of double bonded Reddy beams increase with an increase in the longitudinal magnetic field and elastic medium module. Furthermore, the results of this study can be useful for designing and manufacturing micro/nano- double-mechanical systems in advanced mechanics applications by controlling nonlinear frequency with an applied magnetic field.


Main Subjects

[1].Reddy J.N., 2007, Nonlocal theories for bending, buckling and vibration of beams, Int. J. Sci. Technol. 45: 288-307.
[2].Reddy J. N., Wang C. M., 2004, Dynamics of fluid-conveying beams, Centre for Offshore Research and Engineering, National University of Singapore, CORE Report: 1-21.
[3].Wang L., Ni Q., 2008, On vibration and instability of carbon nanotubes conveying fluid, Comput. Mater. Sci. 43: 399-402.
[4].Chang T.P., 2012, Thermal-mechanical vibration and instability of a fluid-conveying single-walled carbon nanotubes embedded in an elastic medium based on nonlocal elasticity theory, Appl. Math. Modell. 36: 1964-1973.
[5].Ghorbanpour Arani A., Zarei M. Sh., Amir S., Khoddami Maraghi Z., 2013, nonlinear nonlocal vibration embedded DWCNT conveying fluid using shell model, Physica B. 410: 188-196.
[6].GhorbanpourArani A., Amir S., 2014, Electro-thermal vibration of visco-elastically coupled BNNT systems conveying fluid embedded on elastic foundation via strain gradient theory, Physica B. 419: 1–6.
[7].Murmu T., Adhikari S., 2011, Axial instability of double-nanobeam-systems, Phys. Lett. A. 375: 601-608.
[8].Simsek M., 2011, Nonlocal effects in the forced vibration of an elastically connected double-carbon nanotube system under a moving nanoparticle, Comput. Mater. Sci. 50: 2112-2123.
[9].Murmu T., Adhikari S., 2012, Nonlocal elasticity based vibration of initially pre-stressed coupled nanobeam systems, Eur. J. Mech. A. Solids 34: 52-62.
[10]. Kuang Y.D., He X.Q., Chen C.Y., Li G.Q., 2009, Analysis of nonlinear vibrations of double-walled carbon nanotubes conveying fluid, Comput. Mater. Sci. 45: 745-756.
[11]. 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, Appl. Math. Modell. 34: 878-889.
[12]. Wang L., Ni Q, 2009, A reappraisal of the computational modelling of carbon nanotubes conveying viscose fluid, Mech. Res. Commun. 36: 833-837.
[13]. Beskok A., Karniadakis G.E., 1999, A model for flows in channels, pipes and ducts at micro and nano scale, Microscale Thermophys. Eng. 3: 43-77.
[14]. Rashidi V., Mirdamadi H.R., Shirani E., 2012, A novel model for vibrations of nanotubes conveying nanoflow, Comput. Mater. Sci. 51: 347-352.
[15]. Eringen A.C., 1983, On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves, J. Appl. Phys. 54: 4703- 4710.
[16]. Ke L.L., Wang Y.Sh., 2011, Flow-induced vibration and instability of embedded double-walled carbon nanotubes based on a modified couple stress theory, Physica E. 43: 1031-1039.
[17]. Karami G., Malekzadeh P., 2002, A new differential quadrature methodology for beam analysis and the associated differential quadrature element method, Comput. Methods Appl. Mech. Eng. 191: 3509-3526.
[18]. Ke L.L., Xiang Y., Yang J., Kitipornchai S., 2009, Nonlinear free vibration of embedded double-walled carbon nanotubes based on nonlocal Timoshenko beam theory, Comput. Mater.Sci. 47: 409-417.
[19]. Chang W. J., Lee H. L., 2009, Free vibration of a single-walled carbon nanotube containing a fluid flow using the Timoshenko beam model, Phys. Lett. A. 373: 982-985.