Investigating analysis and control approaches to unstable non-Hermitian metastructures

• Grant number: 21/14611-8
• Support Opportunities: Scholarships abroad - Research Internship - Master's degree
• Start date: June 18, 2022
• End date: December 14, 2022
• Field of knowledge: Engineering - Mechanical Engineering - Mechanics of Solids
• Principal Investigator: José Roberto de França Arruda
• Grantee: Danilo Braghini
• Supervisor: Matthew Peet
• Host Institution: Faculdade de Engenharia Mecânica (FEM). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
• Institution abroad: Arizona State University, Tempe (ASU), United States
• Associated to the scholarship: 21/05140-1 - Non-Hermitian metamaterials and non-reciprocal metastructuras, BP.MS

Abstract

In the present work, we are investigating non-Hermitian acoustic waveguides designed with periodically applied feedback efforts using electroacustic sensors and actuators. One-dimensional spectral and finite elements models for plane acoustic waves in ducts are used. It is shown that dispersion diagrams of this family of metamaterials exhibit entirely non-reciprocal imaginary frequency components, manifesting as attenuation or amplification along opposite directions for all pass bands. The effects of different designs of feedback laws and the range of each non-reciprocal coupling are investigated. Furthermore, the non-Hermitian skin effect manifesting as topological modes localized at the boundaries of finite domains was successfully predicted by the topology of the reciprocal space. The results so-far contribute to recent efforts in designing active metamaterials with novel properties associated with the physics of non-Hermitian systems, which may find fruitful technological applications related to noise control, wave localization, filtering and multiplexing. With these applications in mind, the first technological problem which arise is the structure's intrinsic instability. The currently used solution involves filtering the unstable modes, which can be made only a posteriori and depends on the particular structure under investigation. Aiming a more elegant and also wide-range solution, we want to study in deep analysis and control of the metastructures with state-of-art theoretical results and technologies. (AU)