Complex Dynamics And Vibration Reduction Evaluation Of Nonlinear Energy Sinks

As a typical passive absorber,the nonlinear energy sink has advantages of small additional mass and broad absorption bandwidth.Therefore,it has extensive application prospects in fields,such as aerospace structures.In this paper,the nonlinear energy sink is investigated,and the coupling complex dynamics are studied.A generalized vibration suppression evaluation method is proposed.A novel lever-type nonlinear energy sink is innovatively designed and implemented in the complex dynamics research.The dissertation is organized as follows:Chapter 1 clarifies the topic and significance of the thesis and surveys the research status of two aspects,i.e.,vibration suppression methods and nonlinear energy sink.The harmonic balance method with arc-length continuation is summarized.The two kinds of stability discriminating methods based on the steady-state periodic solution are discussed.Finally,the main research work and innovation of this paper are presented.In chapter 2,Poincaré mapping is utilized to examine the effect of nonlinear energy sink designed parameters on the global bifurcation of the structure.The nonlinear dynamic time series analysis method is used to determine the motion state of the system,such as time history diagram,spectrum analysis,phase diagram and the Poincaré section.Finally,the harmonic balance method covered with the arc-length continuation is applied to predict the amplitude-frequency response of the system.The linearization theory is used for the stability judgment.The unstable branches and the bifurcation points are further analyzed.In chapter 3,a generalized transmissibility is proposed to evaluate nonlinear vibration absorbers.Periodic steady-state responses of the coupled system are analytically predicted by the method of harmonic balance with arc-length continuation.The stabilities of the responses are determined based on the linearization theory.The Phase portraits,Poincaré map,and frequency spectrum reveal that quasi-periodic motions occur when periodic responses are unstable.Finally,two evaluation approaches based on the energetics and the transmissibility are compared.In chapter 4,a novel type nonlinear energy sink is proposed by introducing a lever to reduce the necessary mass.The lever-type nonlinear energy sink is attached to a simplified model of whole satellite subjected a harmonic excitation.The method of harmonic balance with arc-length continuation is applied to predict the variation of the transmissibility with the excitation frequency.The Floquet theory combined with Hsu algorithm is employed to the stability analysis.In particular,the disappearance of closed detached resonance response may dramatically decrease the transmissibility.With a suitable fulcrum location,the lever-type nonlinear energy sink outperforms a conventional nonlinear energy sink with the same parameters.In chapter 5,based on the fourth-order Runge-Kutta method and the Poincaré mapping,the global bifurcation diagrams are presented to reveal the effects of the parameters of the nonlinear energy sink on the complex dynamics.The nonlinear dynamic time series analysis method is used to determine the motion state of the system,such as time history diagram,spectrum analysis,phase diagram and the Poincaré section.Finally,in order to present a dynamic and complex complete view generated by the energy sink,the method of harmonic balance with arc-length continuation is applied to predict the amplitude-frequency response of the system.The Floquet theory is used to establish the stability analysis.The emphasis was placed on the analysis of the amplitude-frequency response of the structure from the steady-state to the unsteady state,and the bifurcation characteristics of the isolated resonance response from the appearance to the disappearance.Chapter 6 gives the summary of the full thesis presents the conclusion of this study and related research work which is to be carried out further.