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

Based on the nonlocal bernoullieuler and timoshenko beam theories, the dynamic stability ofembedded single-walled carbon nanotubes (swcnts) under axial compression is studied in a thermalenvironment. 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 thesurrounding elastic medium. the free vibration and axial buckling of swcnts are discussed as subsetproblems. 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 elasticmedium on the dynamic stability characteristics of the swcnts, with simply-supported boundaryconditions. it is found that the difference between instability regions predicted by local and nonlocal beamtheories is significant for nanotubes with lower aspect ratios. moreover, it is observed that in contrastto high temperature environments, at low temperatures, increasing the temperature change moves theorigins of the instability regions to higher excitation frequencies and leads to further stability of the systemat lower excitation frequencies.