Thermal vibration of a simply supported single-walled carbon nanotube with thermal stress

The thermally induced vibration of a simply supported single-walled carbon nanotube (SWCNT) subject to thermal stress is investigated by using the models of planar and non-planar nonlinear beams with initial stress, respectively. The dynamic equations of nonlinear stochastic vibration of the SWCNT are established, with the geometric nonlinearity of the large deformation taken into account. The thermal vibration of SWCNT is predicted by numerically integrating both the dynamic equations of the nonlinear beam models via the Runge–Kutta algorithm of fourth order. The root-mean-square (RMS) amplitude and the stationary probability density of the thermal vibration of the SWCNT are obtained via the planar and non-planar nonlinear beam models with simply supported boundary conditions for both pre-buckling case and post-buckling case. The RMS amplitude of the thermal vibration of the SWCNT is given by using the numerical integration of probability density function. The RMS amplitude of thermal vibration of a SWCNT predicted via the non-planar nonlinear model with thermal stress is lower than that predicted via the planar nonlinear beam model, but higher than that predicted via the planar linear model.