# Study on the Coupled Vibration Characteristics of a Two-Stage Bladed Disk Rotor System
## 1 Introduction
[PERSON] et al. [14] analyzed the effects of blade stagger angles on the blade rubbing-induced responses of a rotational shaft-disk-blade system. [PERSON] et al. [15] analyzed the nonlinear dynamic behavior of a rotor-bearing system with interaction between the blades and rotor. [PERSON] et al. [16] investigated the natural frequency of the free transverse vibration of blades in rotating disks to examine the relationship of the natural frequencies, blade stiffness, and nodal diameters, to study how neighboring blades react upon each other and affect the blade's natural frequency. [PERSON] et al. [17] adopted the forced vibration analysis method and considered the influence of multistage coupling on the dynamic characteristics of an octave-disc rotor on a solid shaft. The results show that multi-level coupling must be considered in the design of rotor blades and discs to avoid the resonance caused by low-frequency flow excitation. [PERSON] et al. [18] studied the influence of interstage coupling on the dynamic performance of harmonic and detuned multistage blade-disk structures and pointed out that the dynamic performance of a single-stage rotor depends on the selection of the interstage coupled boundary conditions. Based on sector mistuning, [PERSON] et al. [19] established a reduced order model for the dynamic analysis of mistuned bladed disks. Sector frequency mistuning is preferable to capture blade-to-disk irregularities. [PERSON] et al. [20] proposed an efficient method for analysis of nonlinear vibrations of mistuned bladed disk assemblies. For a practical high-pressure bladed turbine disk, considering several types of nonlinear forced response, the analysis of nonlinear forced response for simplified and realistic models of mistuned bladed disks has been performed. [PERSON] et al. [21] studied the forced vibration of eight detuned blade discs on a solid shaft and found that when the blade disc was on the shaft, detuning had little influence on the blade stress. [PERSON] et al. [22] studied the coupling vibration characteristics of a flexible shaft-disk-blade system with detuning characteristics. Due to the detuning characteristics, the natural frequency and coupling mode types will change accordingly. [PERSON] et al. [23] used a disk comprising of periodically shrouded blades to simulate the weakly coupled periodic structure. The effects of Coriolis force and the magnitude of disorder on the localization phenomenon of a rotating blade-disk system were investigated numerically. [PERSON] et al. [24; 25; 26; 27; 28; 29; 30; 31; 32; 33; 34] studied the vibration characteristics of a graphene nanoplatelet (GPL)-reinforced blade-disk rotor system by the experimental method and the finite element (FE) method, and studied the parallel intelligent algorithm based on a computed unified device architecture. The genetic particle swarm optimization algorithm is used for optimization arrangement on mistuned blades. The above works are mainly based on the finite element method to study the coupled modes and responses of the shaft-disk-blades system under the tuned and mistuned bladed disk. The coupled modes of the multi-stage blade-disc system have not been studied, and the coupled model is greatly simplified compared with the actual structure. In this paper, respectively using the substructure modal synthesis super-element method and the cyclic symmetry analysis method, two kinds of accurate finite element model for two-stage bladed disk were established. The accuracy of the substructure modal synthesis super-element method was verified by the cyclic symmetry analysis method. The interstage coupled vibration of the two-stage bladed disk was analyzed. This research fills in the blanks regarding the interstage coupled vibration of a complex bladed disk and lays a foundation for further research on the effect of a mistuned bladed disk on interstage coupled vibration.