Stability of forced torsional vibrations of an equipped rod

An equipped elastic rod model demonstrating the one-dimensional Cosserat continuum properties under longitudinal and rotary motion is considered. Natural and forced-by-flow rotary oscillations are studied. Exact conditions of oscillatory stability and instability are obtained. The typical motion features are found: exactly two different forms and two different frequencies in each oscillation mode as well as the onset of a divergence mode with an increase of external load intensity.