Multi-mode vibration attenuation of mistuned bladed disks by frictional tuned mass dampers array

An effective method is presented for multi-mode vibration attenuation of mistuned bladed disk (blisk) by employing ring-like array structure composed of multiple frictional tuned mass dampers (FTMDs). The multi-mode vibration attenuation is realized by arranging multiple series of FTMDs. A novel design scheme of the FTMD array is presented. 3D finite element method is employed for quantitative modelling of the blisk-FTMD array system, and the rotordynamic effects of Coriolis forces, spin softening and centrifugal stiffening are taken into account to reach better tuning in natural frequencies in the rotating conditions. The free-interface component mode synthesis method is used to reduce the order of the model. An efficient technique, which combines the harmonic balance method, the analytical formulation of Jacobian matrix and the parameterized Newton-Raphson method, is employed to solve the nonlinear equations. Finally, a blisk, with its first 4ND and 5ND modes being targeted, is employed as an example to illustrate the effectiveness of the presented method. Numerical results show that the method can obviously mitigate the multi-mode vibration of blisk with wide levels of mistuning and is robust against the small tuning deviations of the oscillators.