Perfect and broadband acoustic absorption in deep sub-wavelength structures for the reflection and transmission problems

Abstract

The mechanisms to achieve perfect acoustic absorption by sub-wavelength structures in both reflection and transmission problems are reported. While the mechanism consists in critically coupling a single resonance independently of its nature in the reflection problem, the mechanism becomes more complicated in the transmission problem. To tackle these issues, we use asymmetric interacting resonators, whose interaction leads to the perfect absorption condition. The analyzed system consists in a panel with a periodic distribution of thin slits, the upper wall of which being loaded by Helmholtz Resonators. The propagation in the slit is highly dispersive due to the presence of the resonators, producing slow sound conditions and down-shifting the slit resonance to low frequencies. By controlling the geometry of the resonators, the visco-thermal losses are tuned to compensate the leakage of the system and fulfill the perfect absorption condition. In the case of the reflection problem, a single resonator is enough to obtain the perfect absorption. However, in the case of transmission, using an array of identical Helmholtz resonators only quasi-perfect absorption can be obtained. A possible solution is the use of double interacting resonators, one acting as reflecting wall for the previous one. This procedure can be iteratively repeated and one can design perfect and broadband acoustic absorbers based on the rainbow trapping mechanism.