Stability of forced torsional vibrations of an equipped rod

A model of an equipped elastic rod is considered. In the average sense, this model shows the properties of the one-dimensional Cosserat continuum during longitudinal and torsional motions. Natural and forced torsional vibrations are studied in the case of flow loading. Several conditions for vibration stability and for the end of vibrations are formulated. The following distinctive features of motion are found: each vibration mode has two different shapes and two different frequencies and the onset of the divergence regime is observed when the external loads become more intensive.