Considering stiffness mistuning, position mistuning, and arc-length mistuning, a unified modeling approach is presented for the first time to investigate the traveling wave vibration of double thin-walled cylindrical shells coupled structure with multi-ring hard coating in a rotation state. Initially, a discontinuous arc connection is constructed to simulate a fault of bolt connection mistuning by improving the whole-circumference continuous artificial spring method. The elastic boundary conditions are simulated by using the artificial spring method. Meanwhile, a hard coating multi-ring strategy is more suitable for vibration suppression compared to the full coating strategy in practical applications, so the parametric multi-partitioning approach is utilized to model the multi-ring hard coating. Then, the dynamical equation is derived according to Sanders' shell theory and the Rayleigh-Ritz method. Finally, an efficient state space method is adopted to solve the traveling wave frequencies, and the validity of the theoretical method is verified through the literature. Furthermore, the influences of the mistuning Model, mistuning degree, and mistuning number on the traveling wave frequencies are analyzed. The analysis reveals that the influences of mistuning Models on the traveling wave frequencies are significantly different among the three mistuning types. The increase in mistuning degree and mistuning number leads to a decrease in traveling wave frequency, and the decrease range in the forward traveling wave frequency is greater compared to the backward traveling wave frequency.

Modeling and traveling wave vibration analysis of rotating multi-ring hard coating double thin-walled cylindrical shells coupled structure considering connection mistuning