用于多模态振动控制的多重调谐质量阻尼器的$H_\infty$ optimization
$H_\infty$ optimization of multiple tuned mass dampers for multimodal vibration control
摘要：
本文提出了一种新的多调谐质量阻尼器多模态减振计算方法。传统上，最大振幅的最小化是使用直接$H_\infty$优化来执行的。然而，正如本文所示，鉴于手头问题的非光滑特性，这种方法容易陷入局部极小值。这就是为什么本文通过范数同伦优化提出了这种方法的原始替代方案。这种方法，结合一种有效的技术来计算结构响应，被证明优于直接$H_\infty$优化的速度和性能。基本上，该算法的结果导致全等峰设计的概念，其中所有受控峰的幅度相等。这种独特的设计相对于现有的知识体系是新的。
英文摘要：
In this paper, a new computational method for the purpose of multimodal vibration mitigation using multiple tuned mass dampers is proposed. Classically, the minimization of the maximum amplitude is carried out using direct $H_\infty$ optimization. However, as shall be shown in the paper, this approach is prone to being trapped in local minima, in view of the nonsmooth character of the problem at hand. This is why this paper presents an original alternative to this approach through norm-homotopy optimization. This approach, combined with an efficient technique to compute the structural response, is shown to outperform direct $H_\infty$ optimization in terms of speed and performance. Essentially, the outcome of the algorithm leads to the concept of all-equal-peak design for which all the controlled peaks are equal in amplitude. This unique design is new with respect to the existing body of knowledge.
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