Stability Analysis and Control of a Rotary Flexible Beam.

This paper addresses the stability analysis and control of a two degree of freedom flexible rotary beam with a flexible joint. The beam has been modelled as a lumped mass system with flexibility in two planes represented by torsional springs. The nonlinear equations of the system are coupled and contain gyroscopic terms. It is shown that the system can exhibit both divergence and flutter instabilities as the rotational speed andor the beam and joint stiffnesses vary. It is demonstrated that the stabilization of the system is possible by adjusting the joint flexibility, via position feedback. Furthermore, addition of damping to the joint through velocity feedback, could remove the oscillations in one direction and significantly reduce the vibrations in the other, once the joint stiffness is properly tuned at internal resonance.