The thermo-mechanical vibration of a single-walled carbon nanotube studied using the Bubnov–Galerkin method

The subject of this study is the application of the Bubnov–Galerkin method to the multi-parameter thermo-mechanical vibration of a single-walled carbon nanotube (SWCNT) embedded in a Winkler-type elastic medium. The studies are carried out on the basis of the nonlocal continuum mechanics modeling of the SWCNT. The independent and combined effects of the small scale coefficient (nonlocal parameter), the thermal loading, and the elastic foundation on the fundamental natural frequencies of the SWCNT are extensively investigated. Different boundary configurations of the SWCNT are considered. Validation of special cases of the model with results available in the literature shows good agreement. It is observed that in the presence of the thermally induced axial force, the variation in the fundamental frequencies with the scale coefficient does not follow the same trend for all the boundary conditions. The results also show that for all the boundary configurations, the influence of the elastic foundation on the natural frequencies of the SWCNT is small when compared to the influence of the thermally induced axial force and the nonlocal parameter.