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.

本文提出了一种基于多重调谐质量阻尼器的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。但是，正如本文所显示的那样，鉴于当前问题的不平滑特性，这种方法很容易陷入局部最小值。这就是为什么本文通过规范同伦优化提出了这种方法的原始替代方法的原因。这种方法与一种有效的技术来计算结构响应相结合，表现出优于直接的方法。$H_{\infty }$在速度和性能方面进行优化。本质上，算法的结果导致了全等峰设计的概念，所有受控峰的幅度都相等。相对于现有知识体系，这种独特的设计是新的。