Frequency characteristics of a flexible hub-beam system with arbitrary settling position of attached mass

In this article, the frequency characteristics of a flexible hub-beam system with an attached mass in an arbitrary position are investigated using a first-order approximation coupling (FOAC) model. Three kinds of damping are considered in the model: Damping located at the hub bearing, structural damping caused by the beam material, and damping caused by the air. Cases with both known and unknown large motion of the system are considered. First, the FOAC model is presented with an unknown large motion, using the Hamilton principle and finite element discretization method. Then the dynamic equation for a noninertial system is presented by neglecting the large motion of the system, and the frequency characteristics of the system are studied using numerical simulations. Simulation results indicate that, for the case with a known large motion, the response frequency of the beam is degressive as the settling position of the mass moves from the fixed end to the free end of the beam. The response frequency of the beam decreases with increasing inertia of the hub. Damping affects only the dynamical equilibrium position of the flexible beam and has little effect on the response frequency of the beam. For the case with an unknown large motion, the response frequency of the beam does not show an obvious degressive trend as the settling position of the mass moves from the fixed end to the mid-point of the beam, but it becomes degressive when the mass moves from the mid-point to the free end of the beam. Damping affects not only the final position of the system, but also the vibration amplitude of the flexible beam. However, the response frequency of the beam is barely affected by the damping.