The Effect of Temperature Change on the Transverse Vibration Frequencies of a Carbon Nanotube

In this paper, we study the free transverse vibrational behaviour of a single-walled nanotube (SWCNT) simply supported when subjected to thermal field. The equation for the nanotube’s transverse motion is determined on the basis of Eringen’s non-local elasticity and Euler-Bernoulli theory. By exploiting this equation and the boundary conditions, we determine a homogeneous system whose eigenvalues have been determined using the Newton-Raphson algorithm. In this study, the effects of the thermal load at high temperatures on the linear natural frequencies are examined and identified numerically and/or graphically. The temperature variation values are taken from the existing literature. The results show that a positive variation in temperature relative to ambient temperature decreases the natural frequencies of the nanotube according to a law that can be approximated by a straight line. Linear regressions were used and the relative percentage errors committed were calculated. The very low values of these errors lead to the conclusion that the variations in the frequencies of each mode as a function of the change in temperature can be approximated by an affine function. This will make it possible to calculate these frequencies with a very high degree of accuracy without going back to the equation for the vibratory motion of the nanotube.

The effect of the non-local parameter is also analysed in this article. The results show that increasing this parameter leads to a decrease in the natural vibration frequencies of the carbon nanotube.