Stability analysis of rotating blade vibration due to torsional excitation

This paper presents an approximate analysis of the vibration stability of a rotating blade due to shaft torsional vibration excitation. The governing equation adopted in the study is a Hill's type linear second order ordinary differential equation with multiple harmonically variable coefficient terms. The strained parameters method, a perturbation technique, is utilized in developing the stability transition curves in the plane of parameters related to the rotor speed, the torsional vibration excitation frequency and the blade natural frequency. The stable and unstable regions obtained by perturbations are contrasted to those obtained by numerical stability analysis performed using Floquet theory and an excellent match is observed for small torsional vibration amplitudes. Numerical integration of the original equation at selected points in the predicted stable and unstable regions showed that the predicted behavior of the responses is correct, wherein the unstable regions growing blade vibration is exhibited.