Interactions among an inerter, spring, and energy dissipation element (EDE) in an inerter system can result in a higher energy dissipation efficiency compared to a single identical EDE, which is referred to as the damping enhancement effect. Previous studies have mainly concentrated on the vibration mitigation effect of the inerter system without an explicit consideration or utilization of the damping enhancement mechanism. In this study, the theoretical essence of the damping enhancement effect is discovered, and a universal design principle is proposed for an inerter system. A fundamental equation is found and demonstrated on the basis of closed‐form stochastic responses, which establishes a bridge between the damping deformation enhancement factor (DDEF) and the response mitigation ratio, thus clarifying the relationship of the damping enhancement effect and the response mitigation effect. Inspired by the equation, a novel damping‐enhancement‐based strategy is proposed to determine the key parameters of an inerter system. Following the performance‐demand‐based design philosophy, the parameters of the inerter system can be determined in the design condition of a target‐damping‐enhancement effect. Through the implementation of the damping enhancement equation, the damping parameter of an inerter system can be directly obtained by the prespecified DDEF and the displacement response mitigation ratio. The influence of parameters on the response mitigation effect and the damping enhancement effect is then investigated to determine ways of obtaining the other two parameters in an inerter system. Finally, design examples are conducted to verify the proposed strategy and the theoretical relationship revealed by the damping enhancement equation. The results show that the proposed design strategy explicitly utilizes the damping enhancement effect for vibration control, where the target of the DDEF is effective in enhancing the efficiency of the EDE for energy dissipation. In the design condition of the target DDEF, the implementation of the proposed damping enhancement equation provides an inerter system with a practical equation to determine the key parameters of an inerter system in a direct manner.

中文翻译：

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惯性系统的阻尼增强原理

与单个相同的EDE相比，惰性系统中惰性，弹簧和能量耗散元件（EDE）之间的相互作用可导致更高的能量耗散效率，这被称为阻尼增强效果。先前的研究主要集中在惰轮系统的减振效果，而没有明确考虑或利用阻尼增强机制。在这项研究中，发现了阻尼增强作用的理论实质，并提出了用于惯性系统的通用设计原理。在闭合形式的随机响应的基础上找到并证明了一个基本方程，该方程在阻尼变形增强因子（DDEF）和响应缓解率之间建立了桥梁，从而阐明了阻尼增强效果和响应缓解效果之间的关系。受方程启发，提出了一种新的基于阻尼增强的策略来确定惯性系统的关键参数。遵循基于性能需求的设计理念，可以在目标阻尼增强效果的设计条件下确定惰化系统的参数。通过执行阻尼增强方程，可以通过预先指定的DDEF和位移响应缓解率直接获得惯性系统的阻尼参数。然后研究参数对响应缓解效果和阻尼增强效果的影响，以确定在惯性系统中获取其他两个参数的方式。最后，通过设计实例验证了所提出的策略和阻尼增强方程所揭示的理论关系。结果表明，所提出的设计策略明确地利用了阻尼增强效果来进行振动控制，其中DDEF的目标有效地提高了EDE的能量消耗效率。在目标DDEF的设计条件下，所提出的阻尼增强方程的实施为惯性系统提供了实用的方程式，可以直接确定惯性系统的关键参数。DDEF的目标可有效提高EDE的能量消耗效率。在目标DDEF的设计条件下，所提出的阻尼增强方程的实施为惯性系统提供了实用的方程式，可以直接确定惯性系统的关键参数。DDEF的目标可有效提高EDE的能量消耗效率。在目标DDEF的设计条件下，所提出的阻尼增强方程的实施为惯性系统提供了实用的方程式，可以直接确定惯性系统的关键参数。