Nonlinear Vibration Analysis of Embedded Multiwalled Carbon Nanotubes in Thermal Environment

Document Type : Persian


1 Assistant Professor, Mechanical Engineering Department, Guilan University

2 M.Sc., Mechanical Engineering Department, Guilan University.


In this article, based on the Euler-Bernoulli beam theory, the large-amplitude vibration of multiwalled carbon nanotubes embedded in an elastic medium is investigated. The method of incremental harmonic balance is implemented to solve the set of governing nonlinear equations coupled via the van der Waals (vdW) interlayer force. The influences of number of tube walls, the elastic medium, nanotube aspect ratio and temperature rise on nonlinear frequency are fully examined. The results obtained for single-walled, double-walled and triple-walled carbon nanotubes indicate that with increasing the number of tube walls, coefficient of the surrounding elastic medium, tube aspect ratio and temperature nonlinear frequency tend to the linear counterpart.


[1]  Iijima S.,  Helica microtubes of graphitic carbon, Nature, 354, 1991, 56-58.
[2]  Fu Y.M., Hong J.W., Wang X.Q., Analysis of nonlinear vibration for embedded carbon nanotubes, J. Sound and Vibration, Vol. 296, 2006, pp. 746–756.
[3] Wang C.M., Tan V.B.C., Zhang Y.Y.,
Timoshenko beam model for vibration analysis of multi-walled carbon nanotubes, J. Sound and Vibration, Vol. 294, 2006, pp.1060–1072.
[4]  Lu Y. J., Wang X, 2006, combined torsional buckling of multi-walled carbon nanotubes. J. Phys D, Vol.39, pp. 3380–3387.
[5]  Wang X., Lu G., Lu Y.J., Buckling of embedded multi-walled carbon nanotubes under combined torsion and axial loading, Int J. Solids and Structures, Vol. 44, 2007, 336–351.
[6]   Hsu Jung-Chang, Chang Ruo-Ping, Chang Win-Jin, Resonance frequency of chiral single-walled carbon nanotubes using Timoshenko beam theory, J. Physics Letters A, Vol. 372, 2008, pp.2757–2759
[7]  Wang L., Ni Q., Li M., Qian Q.,The thermal effect on vibration and instability of carbon nanotubes conveying fluid, Physica E, Vol. 40(10), 2008, pp. 3179-3182.
[8]   Hahn H.T., Williams J.G., Compression failure mechanisms in unidirectional composite, J. Composite Materials Testing and Design, Vol.7, 1984, pp.115–139.
[9]   Jones J.E., The determination of molecular from the variation of the viscosity of a gas with temperature, Proc. Roy. Soc. 106A, 1924,441.
[10] Girifalco L.A., Lad R.A., Energy of cohesion,   compressibility, and the potential energy function of graphite system, J. Chemical  Physics, 195,Vol.25, pp.693–697.