Dynamics of a pretwisted blade under nonconstant rotating speed

An analytical model is presented to investigate the vibration and stability of a pretwisted blade under nonconstant rotating speed which is characterized by a periodic perturbation. The time-dependent rotating speed leads to a system with six parametric instability regions in primary and combination resonances. Each instability is predicted using the multiple scale method and validated by the numerical results of a more detailed model. The analyses show that the combination resonance at about twice the fundamental frequency is the most critical aspect and is sensitive to system parameter variation. This instability can be minimized by either increasing the pretwist angle or decreasing the stagger angle.