Thermal buckling and free vibration analysis of size dependent Timoshenko FG nanobeams in thermal environments

In this paper, the thermal effect on buckling and free vibration characteristics of functionally graded (FG) size-dependent Timoshenko nanobeams subjected to an in-plane thermal loading are investigated by presenting a Navier type solution for the first time. Material properties of FG nanobeam are supposed to be temperature-dependent and vary continuously along the thickness according to the power-law form. The small scale effect is taken into consideration based on nonlocal elasticity theory of Eringen. The nonlocal equations of motion are derived based on Timoshenko beam theory through Hamilton’s principle and they are solved applying analytical solution. According to the numerical results, it is revealed that the proposed modeling can provide accurate frequency results of the FG nanobeams as compared to some cases in the literature. 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 thermal effect, material distribution profile, small scale effects, beam thickness and mode number on the critical buckling temperature and normalized natural frequencies of the temperature-dependent FG nanobeams in detail. It is explicitly shown that the thermal buckling and vibration behavior of a FG nanobeams is significantly influenced by these effects.