Analysis of Crack Induced Vibration Localization in Simplified Bladed-Disk Structures

In this paper, we study the effect of crack on the vibratory response of a simplified bladed-disk model. A mono-coupled cyclically periodic structure consisting of cantilevered beams coupled with springs is used to emulate the dynamic response of bladed-disk in aero-engines. A fracture mechanics based approach is employed to evaluate the stiffness loss due to the occurrence of crack on single beam. Then, by taking advantage of the unique property of periodic structures, using the U-transform approach we develop analytical solutions to the free and forced vibrations of the structure with a single crack. It is identified that, while the stiffness loss on a single beam could be small and may not cause significant frequency change, it could lead to 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, and excitation patterns is explored.