Abstract This paper investigates the nonlinear mass and damping effects of nonlinear electromagnetic shunt damping (N-EMSD) for vibration isolation performance enhancement of a permanent magnets (PMs) based nonlinear vibration isolator (NVI). An electromagnetic structure composing of two coils and two PMs is designed to realize equivalent nonlinear damping and mass. The nonlinear mechanic-electromagnetic coupling coefficient is analyzed and modeled. The voltage frequency of the circuit is twice the displacement frequency that is totally different with that of the linear electromagnetic shunt damping (L-EMSD). The amplitude frequency response function of the NVI with N-EMSD is theoretically derived via the harmonic balance method (HBM) and the stability is judged with Jacobian matrix. Then the equivalent nonlinear damping and nonlinear mass of the N-EMSD is derived. The numerical predictions agree with the experimental results, which demonstrate that the use of inductance in shunt circuit can change the equivalent nonlinear mass and the “jump” frequency of the NVI. Large value of inductance deteriorates the vibration isolation performance and the optimal inductance is slightly smaller than zero. Furthermore, N-EMSD can realize nonlinear damping to achieve wide band vibration isolation of the NVI. The optimal negative resistance is discussed.

中文翻译：

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用于增强非线性隔振的电磁并联阻尼的非线性阻尼和质量效应

摘要 本文研究了非线性电磁并联阻尼 (N-EMSD) 的非线性质量和阻尼效应，以提高基于永磁体 (PM) 的非线性隔振器 (NVI) 的隔振性能。设计了由两个线圈和两个永磁体组成的电磁结构，以实现等效的非线性阻尼和质量。对非线性机械-电磁耦合系数进行了分析和建模。该电路的电压频率是位移频率的两倍，与线性电磁并联阻尼（L-EMSD）的电压频率完全不同。N-EMSD的NVI幅频响应函数通过谐波平衡法(HBM)从理论上推导出来，稳定性用雅可比矩阵判断。然后推导出N-EMSD的等效非线性阻尼和非线性质量。数值预测与实验结果一致，表明在并联电路中使用电感可以改变等效非线性质量和 NVI 的“跳跃”频率。电感值大会使隔振性能变差，最佳电感值略小于零。此外，N-EMSD 可以实现非线性阻尼，实现 NVI 的宽带隔振。讨论了最佳负电阻。电感值大会使隔振性能变差，最佳电感值略小于零。此外，N-EMSD 可以实现非线性阻尼，实现 NVI 的宽带隔振。讨论了最佳负电阻。电感值大会使隔振性能变差，最佳电感值略小于零。此外，N-EMSD 可以实现非线性阻尼，实现 NVI 的宽带隔振。讨论了最佳负电阻。