Free vibration analysis of rotating FG-CNT reinforced composite beams in thermal environments with general boundary conditions

The linear free vibration of rotating FG-CNTRC Timoshenko beams in the thermal environments with general boundary conditions is investigated. The classical and non-classical boundary conditions of the rotating beams are simulated by the artificial spring technique. The first order shear deformation theory is employed to establish the governing equations and the temperature depended material properties of the FG-CNTRC are considered. By adopting the Rayleigh-Ritz method together with the artificial technique, a unified solution for the free vibration of rotating beams is carried out. The allowance displacement functions of the rotating beams with different boundary conditions are unified expanded in the form of Jacobi polynomials. The results obtained by the present solution are compared with those in the existing literature to evaluate the accuracy of the proposed approach. The effects of volume fraction and distribution types of carbon nanotubes, rotating speed, temperature, slenderness ratio and hub ratio on the vibration behaviors of the beams are investigated. The stable regions of rotating FG-CNTRC beams in thermal environment are achieved. Furthermore, a general and effective solution for the vibration analysis of rotating FG-CNTRC beams with classic and non-classic boundary conditions is proposed. The main advantage of the proposed solution is that there is no need to change the displacement trial function and solution equations for the beams with different boundary conditions and it can be also applied to analyze the vibration behaviors of other structures.