The Study on Vibration Reduction of Nonlinear Time-Delay Dynamic Absorber under External Excitation

The nonlinear time-delay dynamic absorber has a good control effect on the main system under harmonic excitation, but the control effect on the main system under complicated excitation is not obvious. In the previous study, they do not have an effective method to obtain the time-delay control parameters under different external excitations. Because of the above problems, this paper proposed an innovative method to obtain the control parameters of time-delay dynamic absorbers. For the vibration system including the nonlinear time-delay dynamic absorber, the transient time-integration method was used to solve the nonlinear delay dynamic differential equation of the system under the specific excitation. Then, the quantitative relationship was established between the time-domain responses of the vibration system, the external excitation, and time-delay control parameters. The time-delay control parameters would be obtained when the time-domain response of the main system is minimized under specific excitation using an algorithm that continuously compares the objective function that is related to the time-domain response of the main system. This paper took the two-degree-of-freedom vibration system with a nonlinear time-delay dynamic absorber as the target system to simulate the time-domain response of the main system. The simulation results show that the time-delay control parameters calculated by the new method can obtain significant vibration reduction effects for both harmonic excitation and multiharmonic excitation. The suppression performance of the nonlinear time-delay dynamic absorber is significantly improved.