At present, the vibrational coupling mechanism of the rotor system with a double-disk magnetic coupler has not been sufficiently studied. Based on the mechanical impedance theory, the patterns of structural mass and stiffness distribution were quantitatively described, to establish the model for the vibrational coupling mechanism. Methods were proposed to determine the vibrational coupling point and to simulate the transient response to the interacting excitations, so as to analyze the potential vibrational coupling point and the dynamic response characteristics. Then, the Campbell diagram of the shared support-dual rotor system was combined with the mechanical impedance characteristics of the shared support. As a result, it was found that although the base vibration of the shared support was significantly amplified, the single-axis trajectory showed that both the output and input rotors were synchronized with the forward vortex motion, with almost no coupling between them. A double-disk magnetic coupler test bench with a rated power of 55 kW was designed to verify the experiments. The results showed that the vibration displacement occurred in a periodic variation pattern. Moreover, the maximum errors between the theoretical, simulated, and experimental values of the vibration displacement at different input speeds were less than 5%. The experiments verified the validity of the model for the vibrational coupling mechanism and the simulation of the transient response to the interacting excitation. The results of the study could be used as a basis for calculating the vibration of the rotor system with a double-disk magnetic coupler.