This thesis explores the innovative potential of active acoustic metamaterials in the manipulation of sound waves through dynamic control and topological principles. Traditional acoustic metamaterials, while capable of achieving remarkable feats such as negative refraction and cloaking, are limited by their passive nature. This work addresses this limitation by introducing active components, enabling real-time tunability and reconfigurability of acoustic properties.

The primary contributions of this research include the use of active electroacoustic resonators, which serve as the fundamental building blocks of a modular active metamaterial called active metacrystal. These resonators are equipped with a real-time feedback control scheme, allowing dynamic adjustment of local and non-local properties of the crystal.

This capability facilitates the realization of a tunable Su-Schrieffer-Heeger acoustic metacrystal, a one-dimensional topological insulator, demonstrating dynamic control over topological phases through virtual displacement of resonators within the unit cell. The thesis extends the exploration of topological acoustic metamaterials into the nonlinear regime, investigating the emergence of amplitude-dependent topological interface states. These states exhibit robustness against perturbations, providing insight into the interplay between nonlinearity and topology. Additionally, the study delves into non-reciprocal topology, focusing on the non-Hermitian skin effect, and demonstrates the localization of amplitude-driven acoustic modes at the boundaries of the metamaterial through active control. Finally, the research establishes interdisciplinary connections by drawing analogies between active acoustic metamaterials and the cochlea, suggesting that these metamaterials could serve as a model for understanding the complexities of the human auditory system.

The findings of this thesis not only advance our understanding of topology through active acoustic metamaterials, but also open up new avenues for exploring physical phenomena through analogy.