On the use of metamaterials with negative effective parameters for dual sound energy control

This study investigates the comprehensive control of sound energy through a acoustic metamaterial. The unit cell is composed of a main waveguide periodically loaded with labyrinthine tubes that may feature a different number of coiled channels. A theoretical approach employs the four-pole transfer matrix, taking into account viscothermal effects, to explore the behavior of the metamaterial. Furthermore, experimental tests were conducted in an impedance tube for normal incidence waves. The results of the reflection problem showed that an effective sound energy control (alpha >= 85% at 520 Hz and >= 99% at 1287 Hz) only exists outside the bandgap regions and that accumulation of absorption peaks is possible by increasing the periodicity of the structure. On the other hand, in the transmission problem, high sound transmission loss (70 dB at 750 Hz and 30 dB at 465 Hz) was obtained. This result is primarily due to the bandgap property, as the behavior of the transmission coefficient is strongly attributed to the wide stopband property in the structure. Therefore, the proposed metamaterial can manipulate sound waves in a wide frequency domain and enables broadband and low-frequency sound insulation. A method for retrieving parameters was used from the experimental reflection and transmission coefficients to obtain the effective parameters of the structure. The effective bulk modulus and the effective mass density exhibited negative values at specific frequencies, providing a better understanding of the physical mechanisms of the metamaterial. Finally, this work contributes to advances in the area of control and manipulation of sound energy through periodic structures as well as understanding the dual properties revealed by the structure.