Thermomechanical Vibration Behavior of FG Nanobeams Subjected to Linear and Non-Linear Temperature Distributions

Abstract

In this study, thermomechanical vibration analysis of functionally graded (FG) nanobeams subjected to in-plane thermal loads are carried out by presenting a Navier-type solution and employing a semi-analytical differential transform method (DTM) for the first time. Two types of thermal loading, namely, linear and non-linear temperature rises through the thickness direction are considered. Thermomechanical properties of FG nanobeam are supposed to vary smoothly and continuously throughout the thickness based on power-law model and material properties are assumed to be temperature-dependent. Eringen non-local elasticity theory is exploited to describe the size dependency of FG nanobeam. Using Hamilton's principle, the non-local equations of motion together with corresponding boundary conditions are obtained for the free vibration analysis of FG nanobeams including size effect and they are solved applying DTM. According to numerical results, it was revealed that the proposed modeling and semi-analytical approach can provide accurate frequency results of the FG nanobeams as compared to analytical results and also some cases in the literature. A parametric study is included to examine the effects of several parameters, such as temperature rise, gradient index, small-scale parameter and boundary conditions on the normalized natural frequencies of the temperature-dependent FG nanobeams in detail. It is explicitly shown that the vibration behaviour of a FG nanobeams is significantly influenced by these effects. The new results can be used as benchmark solutions for analyses of FG nanobeams.