The aim of the paper is to formulate a complete set of design rules for a vibro-impact nonlinear energy sink (VI NES). Hereto, analytical and numerical methods to extract the backbone curve of vibro-impact systems are presented. The adopted approach exploits the multiple scales method and is applied to a linear oscillator coupled with a VI NES. The dynamics of the system are explored and the system’s response under harmonic forcing in the vicinity of resonance is analyzed and approximated. The presented method allows for the derivation of a closed-form approximation of a nonlinear mode. The relation between the steady state response and the input parameters is established. The resonance frequency of the examined nonlinear system for different excitation levels is estimated and the corresponding backbone curve is identified. The theoretical predictions are confirmed through a comparison with the standard resonant decay method combined with a phase-locked loop. Finally, the closed-form approximations are used to derive a complete set of design rules for a vibro-impact nonlinear energy sink.

本文的目的是为振动冲击非线性能量吸收器（VI NES）制定一套完整的设计规则。到目前为止，提出了分析和数值方法来提取振动冲击系统的主干曲线。所采用的方法利用了多尺度方法，并被应用于与VI NES耦合的线性振荡器。探索了系统的动力学特性，并分析和估计了系统在谐振附近的谐波强迫下的响应。所提出的方法允许推导非线性模式的闭合形式近似。建立稳态响应与输入参数之间的关系。估计了不同激励水平下所检查的非线性系统的共振频率，并确定了相应的主干曲线。通过与标准谐振衰减方法结合锁相环的比较，可以确认理论预测。最后，使用闭合形式的近似值来推导振动冲击非线性能量吸收器的完整设计规则集。