dynamic stability of embedded single walled carbon nanotubes including thermal effects

a nonlocal beam model based on the bernoulli–euler beam theory is presented to investigate the dynamic stability of embedded single-walled carbon nanotubes (swcnts) in thermal environment under combined static and periodic axial loads. the dynamic stability analysis is carried out by including the effects of small-scale parameter, temperature change and elastic medium. the equation of motion is reduced to the extended mathieu-hill equation, the stability of which is analyzed through the floquet-lyapunov theory as well as bounded and unbounded solution theory. the instability regions obtained from both theories are examined and compared with each other. also, the effects of the small-scale parameter, temperature change, elastic medium, compressive static axial load and excitation frequency on the dynamic stability of swcnts are discussed in detail. the prediction of dynamic instability of carbon nanotubes enables one to eliminate this phenomenon in cases that may fall within the range of practical significance.