The connection conditions and vibration suppression methods of coupled shell structures have received much attention, particularly as these structures play a crucial role in aero-engine components. In this paper, the vibration characteristics of a rotating hard coating damping double-thin-walled cylindrical shell coupled structure under bolt connection conditions are studied. First, a discontinuous arc connection is constructed to simulate actual bolt connection conditions by improving the artificial spring distribution method of the continuous entire circumference. And the artificial spring technique is used to define the boundary conditions of the shell structure. Next, the strain energy of the hard-coating shell structure is determined based on Sander's shell theory. The effect of rotational speed is considered, and the Rayleigh-Ritz method is used to derive the dynamic equations of the shell structure. In addition, the efficient state space method is used for calculation. The rationality and accuracy of the theoretical methods are validated through literature comparisons and finite element analysis. Additionally, the effects of rotational speed, connection stiffness, hard-coating thickness, and boundary conditions on the traveling wave vibration characteristics of the shell structure are analyzed. The results show that the traveling wave frequency increases significantly when the connection stiffness is in the range of 10⁸～10¹⁰. Besides, the rotation leads to a separation phenomenon and an overall increasing trend in the traveling wave frequency. A greater hard coating thickness notably impacts the traveling wave frequency, exhibiting a maximum increase of 5.87% in the traveling wave frequency when the hard-coating thickness rises from 0 to 0.85 mm. These findings provide valuable theoretical insights and data support for the engineering design of hard-coating coupled double-thin-walled cylindrical shell structures.