A precessing and nutating beam with a tip mass

Abstract Stability analysis of elastic vibration of a simultaneously precessing and nutating beam with a tip mass is attempted here. A simple two-degree of freedom model is considered to have an understanding of the terms appearing in the parametric equations with precession softening and centrifugal stiffening. The stability margin is determined using a variant of Hill's method using precession and nutation speeds as parameters. It is found that the stability of an only precessing beam depends on the inclination of the beam-centerline with the axis of precession. A precessing beam with very slow nutation is unstable because of its passage through a particular range of nutation angle.