Abstract:

The primary, subharmonic, and superharmonic resonances of an Euler–Bernoulli beam subjected to harmonic excitations are studied with damping and spring delayed-feedback controllers. By method of multiple scales, the non-linear governing partial differential equation is transformed into linear differential equations directly. Effects of the feedback gains and time-delays on the steady state responses are investigated. The velocity and displacement delayed-feedback controllers are employed to suppress the primary and superharmonic resonances of the forced nonlinear oscillator. The stable vibration regions of the feedback gains and time-delays are worked out based on stablility conditions of the resonances. It is found that proper selection of feedback gains and time-delays can enhance the control performance of beam’s nonlinear vibration. Position of the bifurcation point can be changed or the bifurcation can be eliminated.

Keywords: