Analysis of vibration suppression of master structure in nonlinear systems using nonlinear delayed absorber

In this paper, a nonlinear delayed absorber is proposed by a delayed feedback loop and is utilized to absorbor suppress the vibration of a two-degree-of-freedom nonlinear system when the primary resonance and the 1:1 internal resonance occur simultaneously. To explain analytically mechanism of performance of the absorber, an integral equation method is provided to obtain the second order approximation and the amplitude equations. As a result, the feedback gain and time delay which make the amplitude of the main system equal to zero can be derived analytically. Optimal working conditions of the system are extracted from the time delay-response curves, the force-response curves and the frequency-response curves. In the illustrative example, the appropriate choice of feedback gains and time delays can reduce the amplitude of the main system by more than 98% in comparison with the amplitude with no time delay. All analytical predictions are in excellent agreement with the numerical simulations.