A Semi-analytical Method for Vibrational and BucklingAnalysis of Functionally Graded Nanobeams Consideringthe Physical Neutral Axis Position

Abstract

In this paper, a semi-analytical method is presented for free vibration and buckling analysis of functionally graded (FG) size-dependent nanobeams based on the physical neutral axis position. It is the first time that a semi-analytical dif- ferential transform method (DTM) solution is developed for the FG nanobeams vibration and buckling analysis. Material properties of FG nanobeam are supposed to vary continuously along the thickness according to the power-law form. The physical neutral axis position for mentioned FG nanobeams is determined. The small scale effect is taken into consideration based on nonlocal elasticity theory of Eringen. The nonlocal equations of motion are derived through Hamilton's princi- ple and they are solved applying DTM. It is demonstrated that the DTM has high precision and computational efficiency in the vibration analysis of FG nanobeams. The good agreement between the results of this article and those available in liter- ature validated the presented approach. The detailed mathematical derivations are presented and numerical investigations are performed while the emphasis is placed on investigating the effect of the several parameters such as neutral axis position, small scale effects, the material distribution profile, mode number, thickness ratio and boundary conditions on the normalized natural frequencies and dimensionless buckling load of the FG nanobeams in detail. It is explicitly shown that the vibra- tion and buckling behaviour of a FG nanobeams is significantly influenced by these effects.