Modeling and dynamic analysis of a full flexible shaft–disk–blades system with nonlinear energy sinks (NESs) using modified SAFE diagram

In this paper, the application of nonlinear energy sinks (NESs) for the vibration suppression of the blades in a flexible shaft–disk–blades system is studied. The system is a simplified model of an industrial steam turbine rotor, which includes a shaft, a disk, and 37 packets of 7-connected blades. A two-level model order reduction is used to obtain the mathematical model of this industrial system. The frequency diagram of the whole system is obtained through the modal analysis of a cyclic symmetric finite element model of a single sector, which is practically the first model reduction. Some new families of flexible shaft–disk–blades system’s natural modes with only two harmonics appear on this diagram that are mostly related to the dynamic of the shaft. Hence, it is nominated for modified SAFE (Singh’s Advanced Frequency Evaluation) diagram in this study. Then, as a second model reduction, a two-degree of freedom reduced-order model of the sector is identified to model the system behavior around the 11th family of natural modes. A strong coupling between rotor components occurs at the first nodal diameter of this mode. The NESs, which consist of a small mass, an essentially nonlinear stiffness, and a linear damping, are mounted on the disk to indirectly suppress the vibration of the blades. Numerical study of system behavior and tuning of NES parameters show that the strongly modulated response occurs near the resonance, and the optimum NESs could effectively reduce the out-of-plane vibration of the blades.