Nonlocal beam theories for vibration of the nanobeam with various boundary condition using Differential transformationmethod

Employing of Euler-Bernoulli and Timoshenko beam theories and the Eringen’s nonlocal elasticity theory, the governing equation for nanobeam with different boundary condition is derived by the Hamilton’s principle. The Differential Transform method (DTM) is applied to discretize the governing equations and boundary conditions, which are then solved to shows the various frequency of nanobeam. The results are compared with the works that has been done in the past and shows the good agreements in the numerical examples. Parametric study is applied in details. The effects of the small scale parameter, aspect ratio and different boundary condition on the vibrational response of the system are investigated.

Keywords:

Nonlocal elasticity , Beam theories , Vibration , Differential transformation method