Stochastic Torsional Vibration of Single-Walled Carbon Nanotubes Under Random Excitation

In this paper, randomly torsional forced vibration of a single-walled carbon nanotube (SWCNTs) is investigated. The pointwise and nonstationary random force in time domain acts on the beam in a fixed point which results to its torsional vibration. The statistical properties of the response are described in terms of covariance and variance of the random excitation. The mean-square amplitude is computed via Fourier transform, while stochastic averaging yields the stationary probability density function for oscillation amplitude. The effect of position of the random force as well the geometry along with chirality of the nanotube on the standard deviation of the torsional displacement of the tube has been numerically investigated. Mean square displacement is calculated in a nanotube with distributed external viscous damping for several types of random excitations and boundary conditions. It was shown that the scale parameter and chirality have significant impact on the standard deviation of displacement in random loading. Method validation involves comparing analytical outcomes with numerical simulations, achieving good correlation.