REGULATION OF A LUMPED-PARAMETER CANTILEVER BEAM VIA INTERNAL RESONANCE USING NONLINEAR COUPLING ENHANCEMENT

In this article, we propose a nonlinear control law to enhance the performance of internal resonance (IR) controllers used for the regulation of vibration in flexible structures. Active IR controllers are composed of sliding or rotational actuators attached to the flexible structure, introducing dynamic nonlinearities into the system. The IR control strategy forces a state of internal resonance at which the transfer of oscillatory energy from the structure to the controller mechanism takes place. Once this energy is transferred to the controller it is dissipated via velocity feedback. These controllers are unconventional since they function at a state of resonance. The resonance condition is established upon tuning the controller natural frequency (using position feedback) to twice the fundamental beam frequency which causes the oscillatory energy to be transferred to the controller via the nonlinear coupling terms where it is dissipated. However, the rate of dissipation is limited since the controllers have a limited ''critical'' damping coefficient. In this article we study the effect of the IR controller on a simplified lumped mass model representing a cantilever beam. The nonlinear enhancement technique proposed in this article improves the performance of this type of regulator by increasing the nonlinear coupling effect which is responsible for the energy transfer, and hence, speeding the rate of vibration suppression.