## 3 Bulk-Type Acoustic Metamaterials
### Resonance-Based Metamaterials
These area-conserving magnetic field-regulated metamaterials can be used in adaptive acoustic bandgap control or variable vibration isolation. Figure 12: Magneto-mechanical metamaterials for tunable surface coverage. (**A**) The unit cell structure and its magnetization-induced deformation. (**B**) Folding behavior of a single-layer design under a magnetic field, transitioning from the initial mode [1] to the folded mode [2]. During this transformation, the local area density increases while the global area remains unchanged (blue/red dashed boxes). (**C**) Deformation of a single-layer structure on a curved surface showing partial area coverage. (**D**) The bilayer metamaterial deforms to follow a curved substrate while maintaining full surface coverage throughout actuation. Arrows indicate the direction of deformation. Scale bars: 20 mm. Reproduced with permission from [93], Advanced Materials, 2023. [PERSON] et al. proposed an acoustic metamaterial that improved low-frequency sound absorption performance by using a parallel-connected Helmholtz resonator with a built-in opening to improve low-frequency sound absorption performance through structural shape control [94]. The tangential cut surfaces of various openings of rectangles, dumbbells, and olives, as well as the effects on the cross-sectional resonant frequency, such as circles and equilateral triangles, were analyzed by 2D/3D acoustic finite element analysis. Figure 13 displays the different tangent sectional shapes investigated and their impact on sound absorption performance. In particular, the combination of the olive tangential cut surface and the circular cross-section induced the lowest resonant frequency at 327 Hz, showing excellent low-frequency sound absorption performance. As a result of manufacturing and measuring an optimized multi-parallel structure specimen based on this, an average sound absorption coefficient of 0.7821 was achieved in the 500-820 Hz section, even with a thin thickness of 30 mm. This study provides practical design guidelines for the design of small, low-frequency sound absorption devices through precise control of structural shapes. This study provides practical design guidelines for the design of small, low-frequency sound absorption devices through precise control of structural shapes. [PERSON] et al. proposed a magnetic membrane-based adjustable acoustic metamaterial cell manufactured using SLA 3D printing for the purpose of controlling real-time resonant frequency by magnetic fields [99]. This structure is based on a Helmholtz resonator and consists of a magnetic membrane using a superparamagnetic resin. The design of this tunable unit, including its 3D-printed Helmholtz structure and magnetic membrane, is illustrated in Figure 14. As a result of the experiment, this metamaterial recorded a resonance frequency of 88.73 Hz when the magnetic field was 0 mT, and when a magnetic field of 392.5 mT was applied, the resonance frequency was adjusted to 86.63 Hz. This indicates that the frequency change range is 2.1 Hz (88.73 Hz to 86.63 Hz), and this frequency adjustment occurs when the membrane tension changes according to the change in the magnetic field. In addition, the prediction result through the mathematical model confirmed that the resonance frequency was 88.18 Hz in the absence of a magnetic field,  
Figure 13: Various tangent sectional shapes. (**a**) Round, (**b**) regular triangle, (**c**) square, (**d**) regular pentagon, (**e**) regular hexagon. (**f**) The effect of their analysis on sound absorption performance. Adapted under a Creative Commons Attribution 4.0 license [94], materials, 2023.  
showing a small difference of 0.55 Hz from the experimental result. This work shows that resonant properties can be tuned in the low-frequency region, and it can be applied to the development of next-generation adaptive devices for low-frequency modulation.