Métamatériaux multi-résonnants et trous noirs acoustiques : vers une absorption parfaite large bande en régime linéaire et non linéaire

Abstract

Acoustic absorbers are essential for improving sound quality in various environments. Conventional materials like porous and fibrous materials provide broad-frequency absorption but require substantial thickness to be effective at low frequencies, while also posing flammability and health risks. On the other hand, traditional resonators can efficiently absorb sound in the mid and low frequencies depending on the available volume, but they typically offer only a narrow absorption peak. Acoustic metamaterials, with their multiple resonances, offer a promising alternative for effective sound absorption in mid and low frequencies with minimal thickness. The multi-pancake absorber is an acoustic metamaterial consisting of thin annular cavities arranged periodically and connected by a constant main pore, displaying multiple absorption peaks, some at low frequencies. However, these absorption peaks are relatively narrow, which can effectively attenuate tonal sounds but may be less suitable for broadband sounds. Additionally, multi-resonant materials are likely to be used in extreme environments with high sound levels. However, the acoustic behavior of these metamaterials becomes nonlinear under high sound levels, and the amplitude of absorption peaks is highly sensitive to excitation levels. This thesis aims to design, based on the multi-pancake absorber, metamaterials with effective acoustic absorption over a broad frequency range, both in linear regime and under high acoustic excitation. The research project is divided into three parts, each presented as a scientific paper: • In the first article, metamaterials with geometric variations of the main pore profile are studied, including acoustic black hole profiles, which feature a gradual decrease in the main perforation. An analytical model based on transfer matrix formulation is proposed to predict the acoustic properties, validated by numerical simulations and experimental measurements. An analysis of the influence of the main pore radius at the front and back of the structure allows for the design of an acoustic black hole profile, resulting in a high absorption coefficient over a wide frequency band. However, this high absorption band is only achieved at relatively high frequencies (beyond 1500 Hz with a total thickness structure of 3 cm composed of 15 thin cells). • The second article aims to achieve an absorption band at lower frequencies by combining a constant main pore profile with an acoustic black hole termination. This approach exploits the low-frequency absorption of the constant profile metamaterial while using the coupling with the local resonances of the termination cavities to form a lower-frequency absorption band with fewer peaks. An equivalent mass-spring analytical model for low frequencies is developed and validated by numerical simulations and experimental measurements. An optimization code is used to obtain two profiles that provide wide and high absorption bands between 500 and 1500 Hz, still with a total structure thickness of 3 cm. • In the third article, the acoustic behavior of the metamaterial under high sound levels is studied using the complex frequency plane in a linear regime. This tool allows for the direct anticipation of absorption evolution as the sound level increases. Constant profiles are selected to present resonances with different loss levels, and measurements are conducted to validate the expected evolution of absorption under high sound levels. Finally, an acoustic black hole profile is determined for improved broadband absorption at high levels, which is experimentally confirmed. In addition to the various identified profiles, this thesis provides insights into the acoustic behavior of the multi-pancake metamaterial, as well as its design, highlighting its broad potential for adaptation to different absorption objectives in terms of frequency band and sound level.

Date	11 Mar 2025
Original language	French
Awarding Institution	École de technologie supérieure
Supervisor	Thomas Dupont (Supervisor) & Olivier Doutres (Co-supervisor)