A precessing and nutating beam with a tip mass

•The paper constructs the stability borderline for a uniformly precessing and nutating beam with tip mass.•A simple two degree of freedom model with centrifugal stiffening is considered.•It is found that an only nutating beam is always stable.•An only precessing beam is unstable within a range of constant nutation angles.

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.