Investigations of the Transverse Vibrations of a Carbon Nanotube Resting on an Elastic Foundation

The aim of this work is to study the linear free vibrations of a simply supported single-walled carbon nanotube (SWCNT) resting in a linear Winkler–Pasternak foundation. Euler-Bernoulli beam theory and Eringen’s non-local elasticity are used to establish the theoretical model. Once the governing linear equation of motion is determined, by introducing the boundary conditions, an homogeneous system is obtained, where the eigenvalues of this system have been determined using the Newton-Raphson algorithm. To assess the accuracy of this method, the results obtained are compared with those from the existing literature. In this study, the effects of the nanotube’s small scale and the Winkler-Pasternak parameters on the natural frequencies have been taken account.