Delayed resonator (DR), which enables complete vibration suppression through loop delay tuning, has been extensively investigated as a linear active dynamic vibration absorber since its invention. Besides, the nonlinear high-static-low-dynamic stiffness (HSLDS) has been widely used in vibration isolators for broadband (yet incomplete) vibration reduction. This work combines the benefits of DR and the nonlinear HSLDS characteristics, thus creating a nonlinear DR (NDR). Three unexplored topics are considered: (1). To address the nonlinear dynamics that are made complicated by the introduction of delay and the nonlinearity coupled between the NDR and the primary structure; (2). To tune the control parameters to seek possible complete vibration suppression in the nonlinear case, and accordingly, to determine the operable frequency band; (3). To evaluate how the HSLDS characteristics can enhance the performance of the linear DR (LDR) and how to design an NDR to maximize its benefits. Without loss of generality, a classic nonlinear HSLDS structure with three springs and two links is considered, and mathematical tools and computational algorithms are introduced or proposed to efficiently address theoretical analysis. Using the parameters of an experimental setup, we show that a properly tuned NDR suppresses the vibrations on the primary structure to a sufficiently low level. Besides, the HSLDS characteristics extend the operable frequency band compared with the LDR, while strong nonlinearity limits such extension. The proposed analysis procedures for delay-coupled nonlinear dynamics, alongside the control parameter tuning, determination of operable frequency bands, and structural design rules, establish a basic theoretical framework for the NDR design.

中文翻译：

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一种高静低动态刚度延迟谐振器减振器


延迟谐振器 （DR） 通过环路延迟调谐实现完全振动抑制，自发明以来，它作为线性有源动态减振器已被广泛研究。此外，非线性高静态低动态刚度 （HSLDS） 已广泛用于宽带（但不完全）减振的隔振器中。这项工作结合了 DR 的优点和非线性 HSLDS 特性，从而创建了非线性 DR （NDR）。考虑了三个未探索的主题：（1）. 解决因引入延迟以及 NDR 和主要结构之间的非线性耦合而变得复杂的非线性动力学;（2）. 调整控制参数以寻求在非线性情况下可能的完全振动抑制，并据此确定可操作的频带;（3）. 评估 HSLDS 特性如何增强线性 DR （LDR） 的性能，以及如何设计 NDR 以最大限度地发挥其优势。在不失去通用性的情况下，考虑了具有三个弹簧和两个链接的经典非线性 HSLDS 结构，并引入或提出了数学工具和计算算法来有效地解决理论分析问题。使用实验装置的参数，我们表明正确调整的 NDR 可以将主结构上的振动抑制到足够低的水平。此外，HSLDS 特性比 LDR 扩展了可操作频段，而强非线性限制了这种扩展。所提出的延迟耦合非线性动力学分析程序，以及控制参数调整、可操作频段的确定和结构设计规则，为 NDR 设计建立了基本的理论框架。