# $H_\infty$ optimization of multiple tuned mass dampers for multimodal vibration control

## TL;DR

This paper introduces a novel norm-homotopy optimization method for multimodal vibration control using multiple tuned mass dampers, outperforming traditional $H_
Infty$ optimization in speed and effectiveness.

## Contribution

It presents an original norm-homotopy optimization approach for multimodal vibration mitigation, leading to the new all-equal-peak design concept.

## Key findings

- Outperforms direct $H_
Infty$ optimization in speed and performance.
- Introduces the all-equal-peak design concept.
- Efficient response computation technique.

## Abstract

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.