Research On Energy Sink With Geometrically Nonlinear Damping Forvibration Suppression

Nonlinear energy sink(N ES) is a specificly kind of nonlinear device which generally consists of a linear damping, a nonlinear stiffness and a mass, and can be connected to a primary structure to reduce the unwanted vibra tion. This paper aimed at vibration suppression for the sensitive parts of a spacecraft, formulated a kind of NES that have nonlinear damping and nonlinear stiffness at the same time. And investigated its dynamics and application for vibration suppression by comparing to the NES of linear damping based on the method and theory of nonlinear dynamics.First, we study a system which use a single-degree-of- freedom N ES for free vibration suppression of a single-degree-of- freedom linear primary system. We investigated the periodic obits, and obtained the nonlinear normal modes and frequency energy plot by non- smooth- translation method. Two necessary and sufficient conditions for targeted energy transfer and frequency of targeted transfer were calculated by complex- averaging technology and discrete breather theory. Finally wavelet transforms were implied for contrast analyzing the model jumping phenomenon and the rule of targeted energy transfer for the two systems.Considering the forced vibration under harmonic loading. We investigated the saddle- node and Hopf bifurcation for the linear and nonlinear damping system in the condit ion that the excitation frequency is in the neighborhood of the characteristic frequency of primary structure, in addition, the response regime and condition for non-periodic response for both systems in the resonant frequency were determined.In consideration of the complex response regime of system in the neighborhood of the resonant frequency. Poincare map were applied in modal reduction and response analysis for system with different parameter. We use energy as the index, compared the energy spectrum of periodic and non- periodic response for vibration suppression and find that non- periodic response can be more efficient for vibration suppression in both linear and nonlinear damping systems, what’s more,we find that N ES which designed with nonlinear damping can be more efficient for vibration suppression than the linear one.In order to study the mult i-degree-of- freedom N ES with nonlinear damping for vibration suppression. We formulated a system modal that consists of a system single-degree-of- freedom primary structure coupled to a two-degree-of- freedom NES and with primary structure und er harmonic excitation. First, analatical analys is were done to investigated the saddle- node and Hopf bifurcation phenomenon, mainly considered the effect of mass distribution between the N ESs. And, in the sense of the excitation frequency can be changed, the periodic solut ions and their Stability were obtain by Incremental Harmonic Balance Method and Floquet theory, respective ly. Poincare map and energy spectrum were used for analyzing the rule of system response in the neighborhood of resonant frequency. The conclusion is that multi-degree-of- freedom N ES can reduce the maximum response in the neighborhood of resonant frequency and is more efficient than the single one for vibration suppression.