Free vibration analysis of rotating functionally graded double-tapered beam including porosities

This paper presents a semi-analytical model for free vibration analysis of rotating functionally graded material (FGM) beams with porosities and double-tapered cross section. The modified rule of mixture is adopted to describe material properties of FGM beams with even and uneven distributions of the porosity phases. A general mathematical formulation is constructed based on the order truncation principle of the fully geometrically nonlinear beam theory. The governing equations of motion are then derived by using the modified variational method and multidomain mixed approximations. The developed model enables one to expediently take into consideration the Coriolis effects and nonlinear effects arising from the interaction among various vibration modes, such as bending-stretching, bending-twist and twist-stretching couplings. Comparisons with the results obtained from the existing literature are provided to verify the present procedure. Parametric studies are also carried out to investigate the effects of material property distribution, porosity volume fraction, rotation speed and various geometric parameters upon the free vibration behaviors of the porous rotating FGM beam. The results reveal that these parameters have remarkable effects in the dynamics of the rotating porous FGM beams, and variations of the volume fraction of porosity and material property distribution may result in stretching-bending and twist-bending vibration couplings of rotating porous FGM beams.