Vibration Analysis of Nano Beam Using Differential Transform Method Including Thermal Effect

In this paper, based on nonlocal Euler- Bernoulli beam model with arbitrary boundary conditions a simulation method called the Differential Transform Method (DTM) is employed to predict and to analysis the vibration of a single-walled carbon nanotube embedded in an elastic medium under thermal effect. A Winkler type elastic foundation is employed to model the interaction of carbon nanotube and the surrounding elastic medium. Ferstly, the Differential Transform Method is introduced. The research work reveals the significance of the small-scale coefficient, the vibrational mode number and the elastic medium on the non-dimensional natural frequency.