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The time-delayed velocity and acceleration feedback control are provided to mitigate the resonances response of a nonlinear dynamic beam. By use of the method of multiple scales, the primary resonance and the 1/3 subharmonic resonance response of the controlled beam are analyzed. The excitation amplitude response peak and critical expression are obtained, and numerical simulations are also given. The effect of the feedback gains and time delayed on the steady-state response of the two types of resonances are investigated. The result show that time-delayed acceleration feedback control can effectively mitigate amplitude, and the main resonance response is affected periodically. Selecting reasonable control gain and time delay quantity can avoid the main resonance region and unstable multi-solutions, and can improve the efficiency of the vibration control.

Nonlinear Vibration Mitigation of a Beam Excited by Moving Load with Time-Delayed Velocity and Acceleration Feedback