# Dynamic Response of Dual-Disk Rotor System with Uncertainties Based on Chebyshev Convex Method  
[PERSON]  
1 Institute of Vibration Engineering, Northwestern Polytechnical University, Xi'an 710072, China; [EMAIL_ADDRESS] (0.W.); [EMAIL_ADDRESS] (Q.Z.); [PERSON]IL_ADDRESS] (C.F.)  
[PERSON]  
1 Institute of Vibration Engineering, Northwestern Polytechnical University, Xi'an 710072, China; [EMAIL_ADDRESS] (0.W.); [EMAIL_ADDRESS] (Q.Z.); [PERSON]IL_ADDRESS] (C.F.)  
[PERSON]  
1 Institute of Vibration Engineering, Northwestern Polytechnical University, Xi'an 710072, China; [EMAIL_ADDRESS] (0.W.); [EMAIL_ADDRESS] (Q.Z.); [PERSON]IL_ADDRESS] (C.F.)  
[PERSON]  
1 Institute of Vibration Engineering, Northwestern Polytechnical University, Xi'an 710072, China; [EMAIL_ADDRESS] (0.W.); [EMAIL_ADDRESS] (Q.Z.); [PERSON]IL_ADDRESS] (C.F.)  
[PERSON]  
1 Institute of Vibration Engineering, Northwestern Polytechnical University, Xi'an 710072, China; [EMAIL_ADDRESS] (Q.W.); [EMAIL_ADDRESS] (Q.Z.); [PERSON]IL_ADDRESS] (C.F.)  
[PERSON]  
1 Institute of Vibration Engineering, Northwestern Polytechnical University, Xi'an 710072, China; [EMAIL_ADDRESS] (0.W.); [EMAIL_ADDRESS] (Q.Z.); [PERSON]IL_ADDRESS] (C.F.)  
[PERSON]  
1 Institute of Vibration Engineering, Northwestern Polytechnical University, Xi'an 710072, China; [EMAIL_ADDRESS] (Q.Z.); [PERSON]IL_ADDRESS] (C.F.)  
[PERSON]  
1 Institute of Vibration Engineering, Northwestern Polytechnical University, Xi'an 710072, China; [EMAIL_ADDRESS] (Q.Z.); C.  
of the unbalanced response of the flexible rotor. The non-parametric modeling technology is discussed by [PERSON] [16] on the unbalanced response and dynamic balance of the flexible rotor.  
The probability density distribution of uncertainty is important to the dynamic research of rotor system with uncertainty. Whereas, for aero-engine rotor systems it is often difficult to obtain an accurate probability distribution of system uncertainty. In order to avoid the inability, scholars have proposed the concept of cognitive uncertainty and establish a variable probability model [17]. A series of methods such as evidence theory, interval theory, and convex model are established by [PERSON] [18; 19; 20] and [PERSON] [21]. To quantify the uncertainty of dynamic systems with non-probabilistic interval numbers, [PERSON] [22] proposes Chebyshev inclusion function method by interval theory. The improved nonlinear Chebyshev method is applied by [PERSON] [23; 24] to carry out theoretical and experimental analyses on the bolted rotor system. [PERSON] [25] proposes a stable non-embedded interval method based on orthogonal polynomial approximation theory and precise integration method. Transient dynamics on the accelerating start process of the rotor system with interval uncertainty is studied, and vibration characteristics with cognitive uncertainties is obtained. [PERSON] [26] investigates the non-probabilistic steady-state dynamics of a dual-rotor system with parametric uncertainties under two-frequency excitations. However, the problem of uncertain rotor dynamics remains to be further studied, especially in the case of small samples. In addition, the calculation burden also needs to be reduced.  
This paper introduces a convex model to describe the correlated interval variables of a dual-disk rotor system. And a non-probabilistic Chebyshev convex method is applied to obtain dynamic responses of dual-disk rotor system. The rest of the content is organized as follows. First, the finite element method for dual-disk rotor model and deterministic equations of motion will be described in Section 2. Then, in Section 3, the Chebyshev convex method (CCM) for dynamic analysis of uncertain rotors is explained. In Section 4, the dynamic responses with uncertainty are achieved by CCM as well as experimental verification is carried out. Finally, the concluding remarks are drawn in Section 5.