Influence of the VI-NES on the resonance response regime and amplitude–frequency characteristics for the duffing system

The vibro-impact nonlinear energy sink (VI-NES), as a typical lightweight attachment coupled to the prime structure, is capable of inducing fast target energy transfer (TET) under broadband excitation. In recent studies, most of the current research on VI-NES is based on the linear prime system, while the dynamic response regime of nonlinear VI-NES system is still unclear. Besides, the Duffing oscillator has significant nonlinear characteristics, which the efficient vibration reduction methods under different excitation amplitudes are still to be further studied. Therefore, a dynamic model is constructed for the nonlinear Duffing system with a VI-NES in this paper, to study the influence of the VI-NES on dynamic response and amplitude–frequency characteristics. Based on the multi-scale asymptotic analytical method, the amplitude–frequency characteristics of the system under different excitation amplitudes are solved. It is found that the amplitude–frequency response curve with the dynamic absorber is composed of two branches, in which the system response is mainly controlled by the branch with a lower amplitude. In addition, when the system is under the 1:1 resonance capture state, VI-NES can significantly suppress the nonlinearity of the Duffing oscillator, which is represented by the reduction of bending of the amplitude–frequency response curve, the decrease of the vibration amplitude and the diminution of the multi-solution interval. Furthermore, based on sweep-frequency and constant-frequency analysis, the numerical simulations under different NES clearances and excitation amplitudes are carried out, which indicate that the theoretical analysis results are consistent with the numerical results, and the transient chaotic phenomenon will appear in the transition region of the local stable state and unstable state. Additionally, the response of VI-NES parameters under different external excitation amplitudes are discussed which show that the system still has better vibration suppression effect on the boundary between states of the strongly modulated response (SMR) and steady periodic response of symmetric impacts per cycle under the low excitation amplitude, while the enhanced energy dissipation effect occurs in the SMR state under the large excitation amplitude.