Thermo-mechanical vibration of rotating axially functionally graded nonlocal Timoshenko beam

The free vibration analysis of rotating axially functionally graded nanobeams under an in-plane nonlinear thermal loading is provided for the first time in this paper. The formulations are based on Timoshenko beam theory through Hamilton's principle. The small-scale effect has been considered using the nonlocal Eringen's elasticity theory. Then, the governing equations are solved by generalized differential quadrature method. It is supposed that the thermal distribution is considered as nonlinear, material properties are temperature dependent, and the power-law form is the basis of the variation of the material properties through the axial of beam. Free vibration frequencies obtained are cantilever type of boundary conditions. Presented numerical results are validated by comparing the obtained results with the published results in the literature. The influences of the nonlocal small-scale parameter, angular velocity, hub radius, FG index and also thermal effects on the frequencies of the FG nanobeams are investigated in detail.