In this paper, the oil film pressure distribution and fluid-structure coupling dynamic characteristics of the ring squeeze film damper-rotor system are studied and the vibration reduction mechanism of the ring squeeze film damper is revealed, the results of which provide a theoretical basis for the dynamic design of the rotor support system. Based on the theory of hydrodynamic lubrication, the Reynolds equation on the working principle of the floating ring is established. Moreover, the oil film pressure distribution of the inner and outer layers of the floating ring is obtained by adopting the finite difference method. The law of oil film pressure, bearing capacity, and deflection angle with eccentricity and the width-to-diameter ratio is analyzed. Then, the fluid-structure coupling model of a dual-disk over-hung rotor system supported by a floating ring bearing is built by using finite element simulation software. The vibration reduction mechanism and the oil film whirl mechanism of the ring squeeze film damper are revealed according to the analysis of the transient characteristics. The fluid-structure coupling method is used to analyze the influence of oil filling on the dynamic characteristics of the elastic ring. The results of this study show that lubricating oil will make its natural frequency drop.