Influence of Temperature Change on Modal Analysis of Rotary Functionally Graded Nano-beam in Thermal Environment

The free vibration analysis of rotating functionally graded (FG) nano-beams under an in-plane thermal loading is provided for the first time in this paper. The formulation used is based on Euler-Bernoulli beam theory through Hamilton’s principle and the small scale effect has been formulated using the Eringen elasticity theory. Then, they are solved by a generalized differential quadrature method (GDQM). It is supposed that, according to the power-law form (P-FGM), the thermal distribution is non-linear and material properties are dependent to temperature and are changing continuously through the thickness. Free vibration frequencies are obtained for two types of boundary conditions; cantilever and propped cantilever. The novelty of this work is related to vibration analysis of rotating FG nano-beam under different distributions of temperature with different boundary conditions using nonlocal Euler-Bernoulli beam theory. Presented theoretical results are validated by comparing the obtained results with literature. Numerical results are presented in both cantilever and propped cantilever nano-beams and the influences of the thermal, nonlocal small-scale, angular velocity, hub radius, FG index and higher modes number on the natural frequencies of the FG nano-beams are investigated in detail.