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.