A finite element dynamic modeling method considering the bolt non-uniform connection effect for the vibration characteristics of the disk–drum–shaft coupled structure is proposed. This structure consists of disks, drums, and hollow shafts, with significant differences in their geometric structures, which poses a challenge to modeling efficiency. A universal element with four nodes and 60 degrees of freedom is created in this paper. Based solely on the universal element and first-order shear theory, a universal expression for the stiffness matrix and mass matrix applicable to disk, drum, and shaft structures is derived to improve modeling efficiency. A dynamic model of the coupled structure is established by simulating the non-uniform connection effect of bolts and boundary conditions through the construction of an eight-degree-of-freedom spring-damping element. The effectiveness of the modeling method is verified through experiments, and the results showed good consistency between the natural frequency and vibration response of the simulation and those of the experiment. Finally, the influence of changes in bolt pre-tightening torque on the vibration characteristics of coupled structures is studied.