On the dynamic stability of embedded single-walled carbon nanotubes including thermal environment effects

Based on the nonlocal Bernoulli–Euler and Timoshenko beam theories, the dynamic stability of embedded single-walled carbon nanotubes (SWCNTs) under axial compression is studied in a thermal environment. The developed nonlocal models have the capability to interpret small scale effects. A Winkler-type elastic foundation is employed to represent the interaction of the SWCNT and the surrounding elastic medium. The free vibration and axial buckling of SWCNTs are discussed as subset problems. A parametric study is conducted to investigate the influences of the static load factor, temperature change, nonlocal elastic parameter, slenderness ratio and spring constant of the elastic medium on the dynamic stability characteristics of the SWCNTs, with simply-supported boundary conditions. It is found that the difference between instability regions predicted by local and nonlocal beam theories is significant for nanotubes with lower aspect ratios. Moreover, it is observed that in contrast to high temperature environments, at low temperatures, increasing the temperature change moves the origins of the instability regions to higher excitation frequencies and leads to further stability of the system at lower excitation frequencies.