We propose an acoustic metasurface for perfect absorption at dual frequencies within a compact space. Meta-molecules of the metasurface contain four subwavelength meta-atoms whose cavities are coiled by three foldings. The meta-atoms comprising a meta-molecule have slightly different neck sizes to obtain hybrid resonances at desired frequencies. In order to consider an effect of coiled spaces in the meta-atoms, we use equivalent straight cavities with an effective length in an analytical model. By using the analytical model, metasurfaces are optimally designed for perfect absorption at desired frequencies. The experimental results show that a λ/23-metasurface exhibits over 99% energy absorption at 294 Hz and 406 Hz. Furthermore, we define another optimization problem to minimize the thickness of the metasurface for perfect absorption at two desired frequencies. The experimental results show that a λ/32-metasurface exhibits over 91% energy absorption at 281 Hz and 99% sound energy absorption at 403 Hz.

We investigate theoretically an acoustic metasurface with a high absorption coefficient at two frequencies and design it from subwavelength structures. We propose the use of a two-dimensional periodic array of four Helmholtz resonators in two types to obtain a metasurface with nearly perfect sound absorption at given target frequencies via interactions between waves emanating from different resonators. By considering how fluid viscosity affects acoustic energy dissipation in the narrow necks of the Helmholtz resonators, we obtain effective complex-valued material properties that depend on frequency and on the geometrical parameters of the resonators. We furthermore derive the effective acoustic impedance of the metasurface from the effective material properties and calculate the absorption spectra from the theoretical model, which we compare with the spectra obtained from a finite-element simulation. As a practical application of the theoretical model, we derive empirical formulas for the geometrical parameters of a metasurface which would yield perfect absorption at a given frequency. While previous works on metasurfaces based on Helmholtz resonators aimed to absorb sound at single frequencies, we use optimization to design a metasurface composed of four different Helmholtz resonators to absorb sound at two distinct frequencies.

During the last decade, most of acoustic cloak research has been done within a theoretical framework in which the medium is at rest. However, such an acoustic cloak cannot preserve its unique properties or functions to make an object acoustically invisible in the presence of flow. In this study, we propose a theoretical framework to accurately investigate the effect of compressibility and non-uniformity in flow on the scattering pattern of acoustic cloak. In the formulation, the wave operator is coupled with the non-uniform velocity vector, and the equivalent source terms due to mean flow are divided into the compressibility effect and the non-uniformity effect with their own physical meanings. Numerical simulation shows the difference in far-field directivity between previous and present formulations. The polarity of the equivalent sources in the present formulation shows hexapole and skewed quadrupole patterns for non-uniformity and compressibility effects, respectively, and their magnitudes increase with power laws of Mach number as the Mach number increases. As an application, we make use of the present formulation for predicting the acoustic scattering from newly designed convective cloaks. The simulation results show better performance compared to the existing convective cloak.

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