Optimal Reduction of the Vibration of the Flexible-Shaft-Disk-Blades System Using a Set of Nonlinear Energy Sinks on the Disk

Recently, modern turbines are designed close to their critical operating points with lower stability margin. Therefore, accurate dynamic analysis and using advanced vibration control systems are required. In this paper, the application of nonlinear energy sinks (NESs) for indirect vibration reduction of the blades in a flexible shaft-disk-blades system of a real steam turbine is conducted. 37 packets of seven-connected blades are mounted on the perimeter of the disk. The cyclic finite element analysis is employed to obtain mode shapes and frequency diagram. For the second combined mode of system, which is a combination of the second bending mode of shaft and the third bending mode of disk-blades, a two degrees of freedom (2DOFs) reduced order model (ROM) is identified for each sector. The cyclic symmetry of ROM reduces the size of the studied model to 2 DOFs. NESs with a small mass, an essential nonlinear stiffness and a linear damping are installed on the ROM in the antinode position of desired mode. The Runge-Kutta method is used to solve the nonlinear equations numerically. Optimum stiffness and damping of the NESs are determined to minimize the vibration amplitude of the blades.The results show the occurrence of strongly modulated response around the resonance, and hence, the desired vibration reduction of the blades is take placed. If the NESs have large nonlinear stiffness or low damping, a saddle-node bifurcation and a large island form near the resonance, and the blades could experience large amplitude periodic motion in the negative detuning frequencies.