Variational Principle of Carbon Nanotubes with Temperature Changes

摘要

In this paper, the CNS are considered as the Euler-Bernoulli beams which have been used in many references about the CNS. Taken the thermal-mechanical coupling into account, the variational principle for the CNS is presented by the variational integral method. With the derivation of the varitional principle, the stationary value conditions are obtained. At last, 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, it can be observed that the vibration characteristics of the CNS can be influenced by the temperature changes. It is expected to be useful for the design and application of the nano scale devices.