In this article, the thermal effects on buckling and free vibrational characteristics of functionally graded (FG) size-dependent nanobeams subjected to various types of thermal loading are investigated by presenting a Navier-type solution for the first time. Temperature-dependent material properties of FG nanobeams vary continuously along the thickness according to the power-law form. The small-scale effect is taken into consideration based on Eringen's nonlocal elasticity theory. The nonlocal equations of motion are derived through Hamilton's principle and they are solved applying an analytical solution. It is revealed that the proposed modeling can provide accurate frequency results of the FG nanobeams.

In the present study, thermo-electrical buckling characteristics of functionally graded piezoelectric (FGP) Timoshenko nanobeams subjected to in-plane thermal loads and applied electric voltage are carried out by presenting a Navier type solution for the first time. Three kinds of thermal loading, namely, uniform, linear and nonlinear temperature rises through the thickness direction are considered. Thermo-electro-mechanical properties of FGP nanobeam are supposed to vary smoothly and continuously throughout the thickness based on power-law model. Eringen’s nonlocal elasticity theory is exploited to describe the size dependency of nanobeam. Using Hamilton’s principle, the nonlocal governing equations together with corresponding boundary conditions based on Timoshenko beam theory are obtained for the thermal buckling analysis of graded piezoelectric nanobeams including size effect and they are solved applying analytical solution. According to the numerical results, it is revealed that the proposed modeling can provide accurate critical buckling temperature results of the FG nanobeams as compared some cases in the literature. In following a parametric study is accompanied to examine the effects of the several parameters such as various temperature distributions, external electric voltage, power-law index, nonlocal parameter and aspect ratio on the critical buckling temperature difference of the size-dependent FGP nanobeams in detail. It is found that the small scale effect and electrical loading have a significant effect on buckling temperatures of FGP nanobeams.