Abstract Tuned-Mass-Dampers (TMD) have been widely used to suppress undesirable structural vibrations within a user-defined frequency band. Nevertheless, the performance of TMDs designs is quite sensitive to slight deviations in model parameters such as the ratio between the TMDs natural frequency and the frequency of the main structure. This paper proposes (i) a systematic approach to design a set of spatially distributed TMDs aiming at minimizing the system response when upper bounds for damping ratios should be taken into account and (ii) a straightforward way to analyze the level of robustness of the optimum design under different levels of model uncertainties. Some numerical results are presented considering the design of a set of spatially distributed TMDs to be placed over a rectangular plate with non-ideal boundary conditions. The optimum solution is determined by means of an optimization algorithm and the robustness of the optimum solution is computed by means of Monte Carlo Simulation analyses. The analyses consider that uncertainties may come from TMD model parameters, from plate model parameters and from both of them simultaneously. These analyses allow one to build a design chart from which one may obtain the robustness of the optimum solution as a function of model uncertainties. Finally, robustness assessment in time domain is performed considering a random excitation along with model parameter uncertainties.

中文翻译：

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空间分布调谐质量阻尼器的优化设计和鲁棒性

摘要 调谐质量阻尼器 (TMD) 已被广泛用于抑制用户定义频带内的不良结构振动。然而，TMDs 设计的性能对模型参数的轻微偏差非常敏感，例如 TMDs 自然频率与主要结构频率之间的比率。本文提出 (i) 一种设计一组空间分布 TMD 的系统方法，旨在在应考虑阻尼比上限时最小化系统响应，以及 (ii) 一种分析最优稳健性水平的直接方法不同水平模型不确定性下的设计。考虑将一组空间分布的 TMD 设计放置在具有非理想边界条件的矩形板上，给出了一些数值结果。最优解通过优化算法确定，最优解的稳健性通过蒙特卡罗模拟分析计算。分析认为不确定性可能来自 TMD 模型参数、板模型参数以及两者同时产生。这些分析允许人们建立一个设计图表，从中可以获得作为模型不确定性函数的最佳解决方案的稳健性。最后，考虑随机激励和模型参数的不确定性，在时域中进行稳健性评估。从板模型参数和两者同时进行。这些分析允许人们建立一个设计图表，从中可以获得作为模型不确定性函数的最佳解决方案的稳健性。最后，考虑随机激励和模型参数的不确定性，进行时域鲁棒性评估。从板模型参数和两者同时进行。这些分析允许人们建立一个设计图表，从中可以获得作为模型不确定性函数的最佳解决方案的稳健性。最后，考虑随机激励和模型参数的不确定性，进行时域鲁棒性评估。