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In this work, a continuum model is proposed to simulate and interpret the coupling vibration characteristics of a rotating disk-beam system with the dovetail interfaces. The dovetail interface feature is represented by a macroslip dry friction model. The present study also derives a new mode function to simulate the vibration of a rotating beam with loosely assembled dovetail attachment. The new proposed mode function is validated by comparing the natural characteristics and vibration response with those obtained from a finite element (FE) model. At last, based on the nonlinear response results obtained by the Newmark-β method, the effects of different parameters on the nonlinear dynamics of the coupling system are discussed. The following interesting phenomena have been revealed: the flexible disk can impose different influences on the response characteristics of the rotating beam. The effects of dry friction on the beam’s energy dissipation are significant, especially at a low rotational speed. Further analysis yields that the excitation level and friction coefficient also exhibit a significant impact on the damping effect of dry friction. Consequently, it should be noted that the optimal values of the contact surface’s parameters allow achieving a better damping effect in the engineering practice.