A nonlinear energy sink (NES), conceived to mitigate the vibrations of a multi-degree-of-freedom host mechanical system, is considered. The high-dimensional slow invariant manifold (SIM) describing the high-amplitude slow dynamics of the system is derived and exploited to interpret its transient regimes caused by impulsive excitation. It is shown that algebraic expressions derived from the SIM formulation enable to identify the so-called interaction points, providing the conditions in which two modes of the primary system interact and share energy through the nonlinear absorber. Moreover, the mutual effect of differently activated host system modes on the NES energy dissipation mechanism is discussed. Through sections of the multidimensional SIM, modal interaction triggering resonance capture cascades (RCC) can be effectively explained. The dissipation capabilities are eventually assessed in order to evaluate the efficiency of the RCC regime.

考虑了旨在减轻多自由度主机械系统振动的非线性能量吸收器（NES）。推导了描述系统高振幅慢动力学的高维慢不变流形（SIM），并利用其解释了由脉冲激励引起的瞬态。结果表明，从SIM公式得出的代数表达式可以识别所谓的相互作用点，从而提供了初级系统的两种模式相互作用并通过非线性吸收器共享能量的条件。此外，还讨论了不同激活的主机系统模式对NES能量耗散机制的相互影响。通过多维SIM的各个部分，可以有效地解释触发共振捕获级联（RCC）的模态相互作用。