Track nonlinear energy sinks (track NESs) have been shown to be an effective and applicable strategy to mitigate structural response in recent years. However, previous studies on track NESs has mainly focused on demonstrating the benefits of track NESs through numerical simulations and experiments, with relatively little attention paid to the analytical understanding of the unique dynamics of track NESs. This study analyzes the responses of a track NES when subjected to impulsive and harmonic excitations by the harmonic balance method. Special attention is given to the cause and effect of the peaking behavior that is a prominent characteristic of the track NES's restoring force–displacement relationship. Analytical results reveal that the special energy–frequency characteristics of track NESs can be, at times, utilized to enhance the energy robustness that is absent in the conventional cubic NESs. Based on the analytical response expression, an equivalent linearization method (ELM) for the track NESs is developed for stochastic analysis. This ELM is numerically validated on the systems with strong nonlinearities. Stochastic optimization built on the ELM is performed to obtain design parameters of the track NES that can lead to minimum response variances of the primary structure. In particular, the proposed optimization procedure can be applied to seismic optimum design in which the seismic excitations are modeled as filtered white‐noise ground motions. The analytical techniques provided in this study lay the groundwork for the practical implementation of track NESs as a robust and effective control strategy for engineering structures.

中文翻译：

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简单和随机激励作用下的轨道非线性能量汇的动力学分析

近年来，轨道非线性能量汇（轨道NESs）已被证明是减轻结构响应的有效且适用的策略。但是，以前关于轨道NES的研究主要集中在通过数值模拟和实验来证明轨道NES的好处，而对分析对轨道NES的独特动力学的关注却很少。本研究通过谐波平衡法分析了轨道NES在脉冲和谐波激励下的响应。特别要注意峰化行为的因果关系，这是轨道NES恢复力与位移关系的突出特征。分析结果表明，轨道NES的特殊能量-频率特性有时可能是 用于增强传统立方NES中所没有的能量鲁棒性。基于解析响应表达式，开发了轨道NES的等效线性化方法（ELM）进行随机分析。该ELM在具有强非线性的系统上进行了数值验证。执行基于ELM的随机优化以获得轨道NES的设计参数，该参数可以导致基本结构的最小响应差异。特别是，所提出的优化程序可以应用于地震优化设计，其中地震激励被建模为滤波后的白噪声地面运动。这项研究中提供的分析技术为轨道NES的实际实施奠定了基础，该轨道NES作为工程结构的鲁棒有效控制策略。