Transverse Vibrations of Single-Walled Carbon Nanotube Resting in an Elastic Medium
摘要
The aim of this work is to study the linear free vibrations of a simply supported single-walled carbon nanotube (SWCNT) embedded in a Winkler–Pasternak foundation. Based on Eringen’s nonlocal elasticity theory and Euler-Bernoulli’s beam theory, a theoretical model has been established. Once the governing linear equation of motion is determined, the Newton-Raphson algorithm is applied to calculate the natural frequencies. To assess the accuracy of this method, the obtained results are compared with those from the existing literature. The study takes into consideration the effects of the nanotube’s small scale and the Winkler-Pasternak parameters on the natural frequencies.