The multi-stable vibrational systems have attracted widespread attention due to their rich nonlinear dynamic phenomena. This study constructs a tristable nonlinear energy sink with time-varying potential barriers (VP-TNES) for the first time, aimed at enhancing vibration suppression efficiency of traditional TNES. The VP-TNES builds time-varying potential barriers with symmetrical magnetic oscillators. Then, the VP-TNES is coupled with a linear oscillation (LO). A new nonlinear model of 4-degree-of-freedom (4DOF) coupled system of TNES control is developed, distinct from the previous 2DOF design. The effect of the movable magnets’ spring stiffness on the dynamics and vibration suppression efficiency of the VP-TNES is investigated. The results demonstrate that the barrier depths are dynamically adjusted. Therefore, the VP-TNES crosses the potential barriers more easily, leading to chaotic inter-well oscillations. Consequently, this nonlinear strong modulated phenomenon can improve the vibration reduction performance of VP-TNES, especially for low-amplitude excitation vibrations. Moreover, the design principles for the symmetrical magnetic oscillators are provided. This study proposed a TNES with time-varying potential barriers and clarified its vibration reduction mechanism. The dynamics adjustment phenomenon can not only enhance the vibration reduction efficiency of traditional TNES, but also be applied to other fields of vibration energy regulation.

中文翻译：

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具有时变势垒的三稳态非线性能量阱


多稳态振动系统因其丰富的非线性动力学现象而受到广泛关注。本研究首次构建了具有时变势垒的三稳态非线性能量汇 （VP-TNES），旨在提高传统 TNES 的振动抑制效率。VP-TNES 使用对称磁振荡器构建时变电位势垒。然后，VP-TNES 与线性振荡 （LO） 耦合。开发了一种新的 TNES 控制 4 自由度 （4DOF） 耦合系统非线性模型，与以前的 2DOF 设计不同。研究了可动磁体弹簧刚度对 VP-TNES 动力学和振动抑制效率的影响。结果表明，障碍深度是动态调整的。因此，VP-TNES 更容易越过潜在障碍，导致混乱的井间振荡。因此，这种非线性强调制现象可以提高 VP-TNES 的减振性能，尤其是对于低振幅激励振动。此外，还给出了对称磁振荡器的设计原理。该文提出了一种具有时变势垒的 TNES，并阐明了其减振机制。动力学调整现象不仅可以提高传统TNES的减振效率，还可以应用于振动能量调节的其他领域。