Crack induced vibration localization in simplified bladed-disk structures

In this paper, we study the effect of a crack on the vibratory response of a simplified aero-engine bladed-disk model, which consists of cantilevered beams (blades) coupled with springs (inter-blade internal coupling). Our goal is to obtain qualitative understandings of the unique dynamic behavior of such structure with crack, i.e., the occurrence of vibration localization and its level. A fracture mechanics based approach is employed to evaluate the crack induced stiffness loss on a single beam. By taking advantage of the structural periodicity or near-periodicity, using the U-transformation approach we then develop analytical solutions to the free and forced vibrations of the bladed-disk with a single crack. It is identified that, while the stiffness loss on a single beam could be small and may not cause a significant frequency change, it could lead to the free and forced vibration localization in a periodic structure. The intrinsic relation between the response amplitudes and various system parameters such as internal coupling, crack severity, excitation patterns and number of blades is systematically investigated.