Nonlinear energy sink (NES) refers to a typical passive vibration device connected to linear or weakly nonlinear structures for vibration absorption and mitigation. This study investigates the dynamics of 1-dof and 2-dof NES with nonlinear damping and combined stiffness connected to a linear oscillator. For the system of 1-dof NES, a truncation damping and failure frequency are revealed through bifurcation analysis using the complex variable averaging method. The frequency detuning interval for the existence of the strongly modulated response (SMR) is also reported. For the system of 2-dof NES, it is reported in a similar bifurcation analysis that the mass distribution between NES affects the maximum value of saddle-node bifurcation. To obtain the periodic solution of the 2-dof NES system with the consideration of frequency detuning, the incremental harmonic balance method (IHB) and Floquet theory are employed. The corresponding response regime is obtained by Poincare mapping, it shows that the responses of the linear oscillator and 2-dof NES are not always consistent, and 2-dof NES can generate extra SMR than 1-dof NES. Finally, the vibration suppression effect of the proposed NES with nonlinear damping, and combined stiffness is analyzed and verified by the energy spectrum, and it also shows that the 2-dof NES system demonstrates better performance.

非线性能量汇（NES）是指一种典型的被动振动装置，连接到线性或弱非线性结构上，以吸收和减轻振动。本研究调查了具有非线性阻尼和连接到线性振荡器的组合刚度的 1 自由度和 2 自由度 NES 的动力学。对于一自由度NES系统，采用复变量平均法通过分岔分析揭示了截断阻尼和失效频率。还报告了存在强调制响应 (SMR) 的频率失谐间隔。对于2-dof NES系统，在类似的分叉分析中报道，NES之间的质量分布影响鞍节点分叉的最大值。为了获得考虑频率失谐的2-dof NES系统的周期解，采用增量谐波平衡法 (IHB) 和 Floquet 理论。通过庞加莱映射得到相应的响应机制，表明线性振荡器和 2-dof NES 的响应并不总是一致的，2-dof NES 可以产生比 1-dof NES 额外的 SMR。最后，通过能谱分析和验证了所提出的具有非线性阻尼和组合刚度的NES的振动抑制效果，这也表明2-dof NES系统表现出更好的性能。