Research On The Dynamics And Performance Of Vibration Suppresion Of Nonliner Energy Sink

Since spacecraft faces complicated vibration environment which poses greatthreat to the structure and sensitive equipment on it during practical missions,vibration suppression is always a focus in the field of spacecraft design. Thisresearch is focus on a kind of nonlinear vibration absorber which terms as nonlinearenergy sink. It’s a method for vibration suppression using the principle of targetedenergy transfer, and it processes good application foreground for local vibrationreduction of spacecrafts. Research of the dynamics and efficiency of vibrationsuppression of NES is the key point of theoretical research, which is also importantfor application in actual projects.NES has two features while used for free vibration suppression: First, NESbecomes most efficient when the vibration energy of the system reaches a certainvalue; Second, for realizing targeted energy tranfer, the mass ratio between the NESand the main structure must beyond a certain value. The above two features arequalitative conclusions, and will be analyzed quantitatively in this research. Theanalytic conditions for vibration energy completely transfers between the mainstrucure and the NES is derived for the conservative system, and the minimum massratio between the NES and the main structure for realizing optimal targeted energytransfer is also abtained. Then, the relation between cubic stiffness and intial energyis generalized to non-conservative systems which contain small damping. Based onthe above conclusions, the method for designing the cubic stiffness according to theinitial input energy to the main structure is developed on the cases of small damping,and the method is verified numerically.The ability of suppressing two different vibration peaks is an important aspectto evaluate the efficiency of the NES. So, vibration mitigation of atwo-degree-of-freedom linear system under harmonic excitation by means of NES isstudied with two methods: the decoupled formula of equilibrium points of the slowdynamics are derived, and the periodic response of the system is obtained usingcomplex-averaging method when the excitation frequency is fixed. The stability ofthe equilibium points are studied based on Lyapunov’s theorem; The periodicresponse of the system is studied using incremental harmonic balance method whenthe excitation frequency is tuning, and the stability of the periodic response isstudied based on Floquet’s theorem. Sadle-node bifurcation and Hopf bifurcation arerevealed from different aspects with the two methods, and the effectiveness ofvibration suppression for the two different energy peaks is also revealed. Analyticalconclusions are verified using numerial simulations. The effeciency of vibration suppression varies drastically with the changing ofinitial energy of the main structure when the NES is used for free vibration control.It is proposed that the problem could be reliefed with the application of a kind oftwo-degree-of-freedom NES. The advantage of the-two-degree-of-freedom NES isverified numerically. The phenomenon of resonance capture when targeted energytranfer occurs is studied using Hilbert-Huang transform. Then, dynamics of thesystem is analyzed using shooting method and complexification-averaging method,and the analytical results support the frontal conclusions.A fruther study of the two-degree-of-freedom NES is carried out for forcedvibration suppression under harmonic excitation since the superiority of thetwo-degree-of-freedom NES is found in chapter4. The slow dynamics of the systemis derived and the equilibrium points of the slow dynamics is studied analyticallywhen the excitation frequency is equal to the natural frequency of the main structure.The stability of the equilibrium points is also studied. The periodic response of thesystem is studied using incremental harmonic balance method when the excitationfrequency is tuning, and the stablility of the periodic response is given. Localbifurcations of the system are revealed and verified using numerical method, and itis also revealed which response regime is more favorable for vibration suppression.Finally, the efficiency of vibration suppression under harmonic force of thetwo-degree-of-freedom NES is compared with the single-degree-of-freedom NES.