Research on energy transfer and vibration suppression of nonlinear energy sink with nonlinear damping

The nonlinear energy sink is a nonlinear shock absorber that provides targeted energy transfer and plays a crucial role in structural vibration suppression. In this paper, the energy transfer and dynamic characteristics of nonlinear damping nonlinear energy sink systems are analyzed. Firstly, the theoretical model of the nonlinear damping NES system is described, and secondly, the equations of the system in the free state are derived by using the complex variable average method and the multi-scale method to obtain the energy transfer efficiency equation of the system. Through the study of the slow invariant manifold and energy transfer efficiency of the system, the influence of each system parameter on the energy transfer efficiency is analyzed. Then the equations of the system under harmonic excitation are processed in the same method to obtain the boundary equations of the system, through which the saddle-node bifurcation diagram of the system is plotted to study the influence of each system parameter on the saddle-node bifurcation characteristics of the system. Finally, the slow-varying equation of the system under harmonic excitation is derived, and the influence of each system parameter on the frequency detuning parameter interval of the strongly modulated response is obtained using the phase trajectory and a one-dimensional mapping diagram of the system, and the time-mileage diagram and Poincare section are used to prove the damping effect of the strongly modulated response.