Bifurcation Control of Parametric Resonance in Axially Excited Cantilever Beam

Bifurcation control of parametric resonance in an axially excited cantilever beam is theoretically and experimentally investigated. In the cases when the excitation frequency is in the neighborhood of twice the natural frequencies, the parametric resonance is produced through the trans-critical bifurcation and the cantilever overcomes also saddle-node bifurcation at the finite amplitude which is a discontinuous bifurcation [

1

] [

2

]. In state of the passage through resonance, jumping phenomena occurs due to the discontinuity of the bifurcation. Our control objectives is to avoid the occurance of the jaump phenomena in the state of the passage throught resonance. We have proposed a bifurcaion control method for parametric resonance in a single degree of freedom system. In this research, the method is expanded to the paremetric resonance produced in the acontinuous system, i.e., cantilever beam. Then, a control method for the avoidance of the paremetric resonance is proposed. Also, the validity of the mehod is experimentally confirmed.