Stability and Response of Rotating Pretwisted Tapered Blades

Abstract

The dynamic stability and response of a spinning tapered blade under the effect of gyroscopic forces induced by precession of the rotor spin axis is investigated. The stability of the system is studied using a perturbation method as well as the Floquet theory. For the constant precession case, the increase of the taper effect will destabilize the system. For the harmonic precession case, the increase of the initial condition will stabilize the taper‐blade system and does not affect the stability of the uniform straight‐blade system very much. The stability results are shown to be in good agreement with both methods. A technique based on the Floquet theory and periodicity condition is presented to find the initial condition for steady‐state periodic response by only one period of integration. By proper choice of initial condition, the steady‐state periodic response can be obtained by integrating through only one period. The results show that the blade‐tip displacement is monotonically dependent on the gyroscopic effect.