Critical buckling temperature of single-walled carbon nanotubes embedded in a one-parameter elastic medium based on nonlocal continuum mechanics

In this paper, the critical buckling temperature of single-walled carbon nanotubes (SWCNTs), which are embedded in one-parameter elastic medium (Winkler foundation) is estimated under the umbrella of continuum mechanics theory. Nonlocal continuum theory is incorporated into Timoshenko beam model and the governing differential equations of motion are derived. An explicit expression for the non-dimensional critical buckling temperature is also derived in this work. The effect of the nonlocal small scale coefficient, the Winkler foundation parameter and the ratio of the length to the diameter on the critical buckling temperature is investigated in detail. It can be observed that the effects of nonlocal small scale parameter and the Winkler foundation parameter are significant and should be considered for thermal analysis of SWCNTs. The results presented in this paper can provide useful guidance for the study and design of the next generation of nanodevices that make use of the thermal buckling properties of embedded single-walled carbon nanotubes.

Graphical abstractThe critical buckling temperature of single-walled carbon nanotubes (SWCNTs), which are embedded in one-parameter elastic medium (Winkler foundation) is estimated under the umbrella of nonlocal continuum mechanics theory. Figure optionsDownload full-size imageDownload as PowerPoint slideResearch highlights► Critical buckling temperatures of embedded carbon nanotubes are captured. ► Nonlocal continuum theory is incorporated into Timoshenko beam model. ► Nonlocal scale and Winkler parameter are significant on thermal analysis of SWCNTs. ► Critical buckling temperature of SWCNT becomes negative at lower mode numbers. ► Scale effects on thermal buckling are not obvious for slender SWCNTs.