The Stability of a Precessing and Nutating Viscoelastic Beam with a Tip Mass

The present work aims at stability analysis of a uniformly precessing and nutating viscoelastic beam with a tip mass as a simple model of a polymeric mechanical arm. The motion of the beam is described as small deformations superposed on rigid body rotation about a point. The damping in the viscoelastic material is considered to be of non-viscous type. The material is modeled in the time-domain using a Voigt model and Maxwell model in parallel. The resulting parametric equations are derived in a rotating frame and analyzed using a variant of Hill's method. The stability borderlines are generated with precession and nutation speeds as parameters for materials with different frequency versus storage modulus and loss coefficient graphs. It is observed that the beam, which only precesses is also unstable for a certain range of non-zero nutation angles.