Thermal-induced nonlocal vibration characteristics of heterogeneous beams

In this paper, thermal vibration behavior of nanoscale beams made of functionally graded (FG) materials subjected to various types of thermal loading are investigated. A Reddy shear deformation beam theory which captures both the microstructural and shear deformation effects without the need for any shear correction factors is employed. Material properties of FG nanobeam are assumed to be temperature-dependent and vary gradually along the thickness according to the power-law form. The influence of small scale is captured based on nonlocal elasticity theory of Eringen. The nonlocal equations of motion are derived through Hamilton\'s principle and they are solved applying analytical solution. The comparison of the obtained results is conducted with those of nonlocal Euler-Bernoulli beam theory and it is demonstrated that the proposed modeling predict correctly the vibration responses of FG nanobeams. The effects of nonlocal parameter, material graduation, mode number, slenderness ratio and thermal loading on vibration behavior of the nanobeams are studied in detail.