## 2 Acoustic Metasurfaces
### Resonance-Based Metasurfaces  
Resonance-based acoustic metasurfaces incorporate local resonators within unit cells to induce strong sound absorption, reflection, or scattering at targeted frequencies, particularly in the low-frequency regime. Typical configurations include Helmholtz resonators, membrane-mass systems, and micro-slit structures [48; 49; 50; 51]. Recent advances have extended this concept by integrating soft materials such as elastic membranes and tunable nanocomposites, allowing for active modulation of resonance behavior through external stimuli like magnetic fields, electric fields, or temperature changes. These designs provide high absorption efficiency relative to their physical thickness, enabling acoustic cutoff bands or frequency-selective sound insulation effects. Structural parameters that control  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Author** & \begin{tabular}{c} **Absorption Coefficient** \\ **(\(\alpha\))** \\ \end{tabular} & **Thickness (mm)** & \begin{tabular}{c} **Resonance** \\ **Frequency (Hz)** \\ \end{tabular} \\ \hline \hline \begin{tabular}{c} [PERSON] et al. [40] \\ \end{tabular} & \begin{tabular}{c} 1-layered inactive \\ \(>\)0.8 (831 Hz–1180 Hz) \\ 2-layered inactive \\ \(>\)0.8 (846 Hz–1290 Hz) \\ \end{tabular} & Membrane: 0.125 & \multirow{3}{*}{-} \\ \cline{3-3} \begin{tabular}{c} [PERSON] et al. \\ [40] \\ \end{tabular} & \begin{tabular}{c} 0.988 (235.5 Hz) \\ 0.930 (483.2 Hz) \\ 0.988 (763.6 Hz) \\ 0.930 (936.2 Hz) \\ 0.982 (998.9 Hz) \\ \end{tabular} & \begin{tabular}{c} 235.5 \\ 483.2 \\ 763.6 \\ 936.2 \\ 998.9 \\ \end{tabular} \\ \hline \begin{tabular}{c} [PERSON] et al. \\ [44] \\ \end{tabular} & \begin{tabular}{c} 0.97 (615 Hz) \\ \end{tabular} & \
\begin{tabular}{c} 2 \\ \end{tabular} &
\begin{tabular}{c} 563–615 \\ \end{tabular} \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Classification of Acoustic Metasurfaces by absorption coefficient, thickness, and resonance frequency. the resonant (or anti-resonant) frequency include membrane tension, slit geometry, or material stiffness [52]. [PERSON] et al. presented a membrane-based acoustic metasurface that uses a magnetic control mechanism to regulate low-frequency sound waves [37]. This metasurface achieves a broad tuning range of resonant frequencies, from 316 Hz without magnetic force to 904 Hz under maximum magnetic pressure. A 6-mm-diameter iron disk, acting as a central mass, is attached to a 0.1-mm-thick elastic membrane with a radius of 10 mm. The overall structure is illustrated in Figure 3. The membrane is supported by an aluminum ring with an outer diameter of 29 mm, and the entire unit is backed by a rigid cavity of 10 mm depth. In this work, polyamide was used as the membrane material, while rigid components included the iron disk, aluminum frame, and back cavity structure. Experimental results confirmed the significant frequency shift enabled by the magnetic stimulus. This metasurface enables redirection, focusing, and diffraction of low-frequency acoustic waves without physical structural changes, leveraging geometric nonlinearity and reflection-based control. The system operates under an active mechanism using static magnetic fields, allowing real-time control. Simultaneously, it exhibits tunability through post-fabrication adjustment of resonant frequency and phase delay via magnetic force modulation. The numerical analysis was conducted using COMSOL Multiphysics, based on a structure composed of a linearly elastic membrane and a central mass. A fixed boundary condition was applied to the rim of the membrane, while a uniform initial stress was applied across the entire membrane to simulate pre-stretching under geometric nonlinearity. The magnetic force was modeled as a boundary load acting on the surface of the central mass. Plane wave radiation and periodic conditions in the y-direction were employed for acoustic analysis.