A hybrid modeling approach integrating lumped mass and finite element methods is developed to establish the coupled dynamic model of a multispan flexible rotor system. The hollow shaft is discretized using Timoshenko beam elements to account for shear deformation, gyroscopic moments, and rotational inertia. A nonlinear dynamic ball bearing model incorporating time‐varying stiffness and radial clearance effects is formulated based on Hertzian contact theory and piecewise Heaviside functions. Analytical derivations and finite element simulations determine the stiffness matrices of laminated couplings, with a 9.95% discrepancy observed between theoretical and numerical angular stiffness values. Viscoelastic rubber damping rings are characterized through a Mooney–Rivlin hyperelastic model combined with a Prony series formulation. Experimental validation on a multispan rotor test platform demonstrates critical speed predictions with less than 4.3% error relative to measured data. Following that, the numerical approach is used to examine how the ball bearing, laminated coupling, and rubber damping ring affect the system’s dynamic behavior. The results demonstrate that the time‐varying stiffness effect of the ball bearing is noticeable at low speeds and diminishes with increasing speed; the laminated coupling lessens the mutual dynamic effect between the system’s rotors and makes each rotor comparatively independent. The natural frequency of the system could be changed by varying the angular stiffness of the laminated coupling since it is more susceptible to it. The rubber damping rings shift the system’s critical speed and reduce resonance traversal amplitudes, while lowering bearing acceleration peaks to mitigate fatigue and extend operational lifespan. This work provides a theoretical framework for designing complex rotor systems with optimized dynamic performance.
Zhu et al. (Wed,) studied this question.