Variational Principle of Carbon Nanotubes with Temperature Changes Based on Nonlocal Euler-Bernoulli Beam Model
In this paper, the CNTS are considered as the Euler-Bernoulli beams which have been used in many references about the CNTS. Taken the thermal-mechanical coupling and small scale effect into account, the variational principle for the CNTS is presented by the variational integral method. With the derivation of the varitional principle, the vibration governing equation is illustrated, which will be benefit for the numerical simulation with finite element method in further investigations. From the stationary value conditions deduced by the variational principle, the influences of the temperature changes and the thermal expansion coefficients based on nonlocal Euler-Bernoulli beam model are presented.
A. Saimoto and M.H. Aliabadi
T. Fan "Variational Principle of Carbon Nanotubes with Temperature Changes Based on Nonlocal Euler-Bernoulli Beam Model", Key Engineering Materials, Vols. 452-453, pp. 785-788, 2011