VIBRATION ANALYSIS OF SIZE-DEPENDENT NANOBEAMS BASED ON NONLOCAL TIMOSHENKO BEAM THEORY

In the present paper, the semi-analytical differential transformation method (DTM) is employed for vibration analysis of size-dependent nanobeams based on nonlocal Timoshenko beam theory (TBT). The governing motion equations of nanobeam with different edge conditions are derived by the Hamilton’s principle. DTM is applied to discretize the governing equations and boundary conditions, which are then solved to obtain the frequency parameters of nanobeam. In the numerical examples, the good agreements between the present results and existing literature verified the validity and accuracy of the present solution method. The detailed mathematical derivations are presented and numerical investigations are performed while the emphasis is placed on investigating the effect of small scale parameters, mode number, aspect ratios and edge conditions on the normalized natural frequencies of the nanobeams. It is explicitly shown that the vibration of a nanobeam is significantly influenced by these effects.