Bifurcation control of a flexible beam under principal parametric excitation

A new approach is proposed in this paper for the nonlinear control of a flexible cantilever beam which is excited under a principal parametric vibration. The approach is based on a bifurcation control principle that combines linear and nonlinear feedback control strategies. A simplified nonlinear vibration model that accounts for the beam´s flexibility and the control feedback, is first derived by using the method of multiple scales. The analysis of stability based on Krasovskii´s theorem is then applied to the above system. Simulation results show that the proposed approach is effective for use in the case of parametric vibration control