Abstract
In the present paper, the delayed feedback control is applied to suppress the amplitude of the vibration of a beam. The method of multiple scales is employed to obtain the analytical solutions when the primary resonance and 1:2 internal resonance occur simultaneously. The predictions from analytical solutions agree with the numerical simulations well. The analytical results show that the amplitude of the beam of the saturation control is much larger than its amplitude of the single-mode motion. The effects of the delayed feedback control on amplitude of the beam are investigated when the original system is in the saturation control. There is a tunable range of the delay could be used to suppress the amplitude of the beam for a fixed value of the gain. The amplitude of the beam can be suppressed from 0.20 to 0.10 when the gain and the delay are chosen appropriate values.
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