H∞ optimization of dynamic vibration absorbers (DVAs) to minimize the maximum response amplitude of primary structures is a classical topic. The commonly used fixed-point method only provides approximate solutions requiring the primary structure is undamped. Instead, we perform exact optimization and investigate the less-reported parametric effects on optimization operability. To handle the known restrictions posed by grounded dampers, a typical DVA model mounted on a damped primary structure, with components connected to both the primary and the base, is considered. We explore three elaborated cases depending on the grounded dampers distributing in the primary structure and the DVA. Our findings reveal that the frequency responses of the primary structure with dual resonant peaks of equal height may not be the global optimum, and we establish a nontrivial necessary condition for operable exact optimization. Furthermore, we elucidate the effects of structural arrangements on the optimized results and provide design rules to maximize vibration suppression performance. The optimization follows the proposal of a so-called resultant-based algorithm that guarantees global optimum with high efficiency and a generalizable core by exclusively constructing univariate polynomial equations. This study contributes a systematic analysis framework alongside efficient calculation tools for exact optimization and DVA performance evaluation.

中文翻译：

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动态减振器的精确 H∞ 优化：基于单变量多项式的算法和可操作性分析


动态减振器 （DVA） 的 H∞ 优化以最小化初级结构的最大响应幅度是一个经典话题。常用的定点方法仅提供需要主结构无阻尼的近似解。相反，我们执行精确优化并研究较少报道的参数化对优化可操作性的影响。为了处理接地阻尼器带来的已知限制，考虑了安装在阻尼初级结构上的典型 DVA 模型，其中组件同时连接到初级和底座。我们根据分布在主结构和 DVA 中的接地阻尼器探讨了三种详细的情况。我们的研究结果表明，具有相同高度的双谐振峰的一级结构的频率响应可能不是全局最优的，我们为可操作的精确优化建立了一个非平凡的必要条件。此外，我们阐明了结构布置对优化结果的影响，并提供了设计规则以最大限度地提高振动抑制性能。优化遵循一种所谓的基于结果的算法的提议，该算法通过专门构建单变量多项式方程来保证高效和可推广的核心的全局最优。本研究提供了一个系统的分析框架以及用于精确优化和 DVA 性能评估的高效计算工具。