The effect of small scale on the vibrational behavior of single-walled carbon nanotubes with a moving nanoparticle

Document Type : Research Paper


1 Department of Mechanical Engineering, Islamic Azad University, Ahvaz branch, Ahvaz, Iran

2 Mechanical Engineering Department, Faculty of Engineering, Shahid Chamran University of Ahvaz, Ahvaz, Iran


In this paper, free and forced vibration of simply-supported Single-walled carbon nanotube is investigated under the moving nanoparticle by considering nonlocal cylindrical shell model. To validate the theoretical results, modal analysis of nanotube is conducted using ANSYS commercial software. Excellent agreement is exhibited between the results of two different methods. Furthermore, the dynamic response of SWCNT under moving nanoparticle is also studied. It is assumed that the nanoparticle travels along the center of nanotube with constant velocity and the van der Waals force between CNT and particle is taken into account. The dynamic response of the SWCNT under the influence of C60 particle obtained using dynamic Green’s function and modal expansion. The obtained results show that the nonlocal scale effect decreases the natural frequency and dynamic displacement of the CNT.


Main Subjects

[1] Iijima, S., “Helical microtubules of graphitic carbon”, Nature, 354, pp. 56 – 58, 1991.
[2] Yakobson, B. I., Avouris, P., “Mechanical Properties of Carbon Nanotubes”, Topics in Applied Physics, 80, pp. 287-327, 2001.
[3] Akgöz, B., Civalek, Ö., "Deflection of a hyperbolic shear deformable microbeam under a  concentrated load", Journal of Applied and Computational Mechanics, 2(2), pp. 65-73, 2016.
[4] Soroush, R., Yekrangi, A., "Investigation of the vdW Force-Induced Instability in Nano-scale Actuators Fabricated form Cylindrical Nanowires", Journal of Applied and Computational Mechanics, 2(1), pp. 8-20, 2016.       
[5] Cheraghbak, A., Loghman, A., "Magnetic field effects on the elastic behavior of polymeric piezoelectric cylinder reinforced with CNTs", Journal of Applied and Computational Mechanics, 2(4), pp. 222-229, 2016.
[6] Abbondanza, D., Battista, D., Morabito, F., Pallante, C., Barretta, R., Luciano, R., Marotti de Sciarra, F., Ruta, G., "Linear dynamic response of nanobeams accounting for higher gradient effects", Journal of Applied and Computational Mechanics, 2(2), pp. 54-64, 2016.    
[7] Meyyappan, M., “Carbon Nanotubes Science Applications”, New York, U.S.: CRC Press, 2005.
[8] Rao, C. N., Cheetham, A. K., “Science and technology of nanomaterials: current status and future prospects”, Journal of Materials Chemistry, pp. 2887-2894, 2001.
[9] Sawano, T. A., Akita, S. “Carbon nanotube resonator in liquid”, Nano Letters, pp. 3395–3398, 2010.
[10] Eringen, A. C., “on differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves”, J. Appl. Phys., pp. 4703, 1983.
[11] Zhang, Y. Q., Liu, G. R., Xie, X. Y., “Free transverse vibrations of double-walled carbon nanotubes using a theory of nonlocal elasticity”, Phys Rev B, pp. 195404, 2005.
[12] Wang, Q., Varadan, V. K., “Vibration of carbon nanotubes studied using nonlocal continuum mechanics”, Smart Materials and Structures, pp. 659, 2006.
[13] Wang, C. M., Zhang, Y. Y., He, X. Q., “Vibration of nonlocal Timoshenko beams”, Nanotechnology, pp. 105401, 2007.
[14] Ansari, R. and Sahmani, A. S., “Small scale effect on vibrational response of single-walled carbon nanotubes with different boundary conditions based on nonlocal beam models.” Communications in Nonlinear Science and Numerical Simulation, pp. 1965–1979, 2012.
[15] Lee, H. L. and W. J. Chang. “Dynamic modelling of a single-walled carbon nanotube for nanoparticle delivery.” Proc. R. Soc. A, pp. 860–868, 2010.
[16] Kiani, K. and B. Mehri. “Assessment of nanotube structures under a moving nanoparticle using nonlocal beam theories” Journal of Sound and Vibration, pp. 2241-2264, 2010.
[17] Pourseifi, M., O. Rahmani and A. H. Hoseini. “Active vibration control of nanotube structures under a moving nanoparticle based on the nonlocal continuum theories” Meccanica, pp. 1351-1369, 2015.
[18] Soedel, W., “vibration of shells and plates”, New York, USA: Marcel Dekker Inc., 2004.
[19] Cox, B. J. and J. M. Hill. “Mechanics of atoms and fullerenes in single-walled carbon nanotubes. I. Acceptance and suction energies. ” Proceedings of the Royal Society of London A, Mathematical, Physical and Engineering Sciences, pp. 461-477, 2007.