Stability of Rotating Pretwisted, Tapered Beams With Randomly Varying Speeds

Abstract

This paper presents a study of stability of coupled bending-bending vibration of pretwisted, tapered beams rotating at randomly varying speeds. The rotating speed is characterized as a wide-band, stationary random process with a zero mean and small intensity superimposed on a constant speed. This randomly varying speed may result in the existence of parametric random instability of the beam. The stochastic averaging method is used to derive Ito’s equation for an approximation solution, and expressions for stability boundaries of the system are obtained by the second-moment and sample stability criteria, respectively. It is observed that those system parameters which will raise the first natural frequency but not enhance the centrifugal force of the beam tend to stabilize the system.