<p>To achieve high thrust-to-weight ratio and high efficiency, aero-engines generally adopt the dual-rotor structure design. Among them, due to design dispersion, assembly errors and long-term service, various uncertainties exist throughout the entire service process of dual-rotor systems. Under this circumstance, due to small size design of blade tip clearance, the uncertainties further have a potential influence on the rub-impact fault, which poses greater challenges to the evaluation of dynamic characteristics. This paper aims to investigate the vibration steady-state behaviors of a non-probabilistic uncertain dual-rotor system with/without rub-impact fault between turbine blades and casings. Then the governing equations of motion of deterministic dual-rotor system with rub-impact are theoretical derived based on the finite element theory. The effects of individual uncertain parameters and combinations of multiple uncertain parameters are described by the Chebyshev interval algorithm. After that the response comparisons between deterministic system and uncertain system are conducted at different rotational speeds. Besides, the rub response intervals of dual-rotor system are further determined in terms of time histories, whirling orbit, and impact force. Through sensitivity analysis, the sensitive parameters for the dual-rotor system are further clarified as well. Finally, to verify the effectiveness of theoretical analysis, the beat vibration experiment is performed on a dual-rotor test rig, which proves that the experimental results are exactly within the range of uncertain response intervals.</p>