Dynamic Model of Functionally Graded Flexible Beams Based on Neutral Axis and Setting Position

Due to the asymmetry of material properties under certain graded index, the neutral axis of the functionally graded material beam no longer coincides with the central axis which passes through the geometric center of the cross section. The effects of the neutral axis position and setting position (the contact point of the hub and beam) on the nonlinear dynamic characteristics of a rotating hub-functionally graded materials beam are studied here. To achieve this goal, the classical central axis model, the neutral axis model, and the neutral axis/setting position model are respectively established. The nonlinear rigid–flexible coupling term, which is the longitudinal shortening caused by the transverse bending deformation of the flexible beam, is also considered in the above three models and can’t be ignored when the large overall motion of the system is at high speed. Results show that the neutral axis and the setting position affect the dynamic behavior of the beam system with the large overall motion. The length of the rotating FGM beam is shortened under the action of the centrifugal force in the CA model which is not considered the NA influence. The results of this paper can be helpful to the research of the composite structures that undergo the large overall rotating motion.