Vibration power flow and dynamic interactions in nonlinear mistuned bladed disk system

This study investigates vibration characteristics and energy transfer in linear and nonlinear mistuned bladed disk system. The power flow analysis (PFA) method is developed to reveal the dynamic interactions and energy distribution patterns. Power flow equations based on a lumped parameter model (LPM) considering the cubic stiffness and dry friction nonlinearities are derived. The harmonic balance (HB) method with the alternating frequency time (AFT) scheme is used to solve analytical solutions of steady-state frequency response of both linear and nonlinear cases. Numerical time marching method is used to obtain reliable time-domain responses for comparisons with analytical solutions. The results show that energy transfer from the blades to the disk is affected by the cubic coupling stiffness, resulting in bending of the second resonance peaks in disk-dominant modes at higher frequencies with out-of-phase motion. The dry friction primarily contributes to reducing vibration amplitudes by dissipating more energy. Mistuning effects on the dynamic interactions between sectors are also investigated, and it is shown that mistuning of blade stiffness causes intense vibration energy localization and uneven energy distribution within the system. It is shown that power flow can serve as an indicator of mistuning conditions. Also, power flow-based indicators such as the Stress Amplification Indicator (SAI) and the tuned Coupling Power Indicator (tCPI) are used to effectively quantify mistuning sensitivity. The effects of single blade mistuning on the dynamics are experimentally investigated, demonstrating that mass and stiffness mistuning induce distinct changes in both natural frequencies and response amplitudes of bladed disk system. These results contribute to better design and performance optimization for the dynamics behaviour of nonlinear bladed disk systems.