# Low-Frequency Sound Absorption in Air Pipelines and Water-Filled Pipelines Based on Metamaterials
## 3 Results
### Low-Frequency and Broadband Composite Absorbing Metamaterial in Water-Filled Piplines
The relevant geometric parameters of HR-7 are listed in Table 1. Detailed geometric parameters are listed in Table 1. Furthermore, to analyze the sound absorption mechanism of the Helmholtz resonator with the rubber layer in water-filled pipelines, we plotted the energy dissipation density distribution and displacement distribution diagrams for HR-7. The upper panel of Figure 10b presents the energy dissipation density profile of HR-7. The profile illustrates that, unlike traditional Helmholtz resonance in air, the region of higher energy density is concentrated in the rubber layer rather than the neck. This shift indicates that introducing the rubber layer not only modifies the impedance but also enhances the energy dissipation for incoming sound waves. In Figure 10a, we also plotted the percentage of energy loss occurring in the rubber layer and the neck. It is noted that viscous heat loss at the neck accounts for 28% of the total energy loss, with the majority of the energy being dissipated in the rubber layer. The lower half of Figure 10b depicts the displacement distribution of the rubber layer. During quasi-Helmholtz resonance, the larger displacements observed in the rubber layer suggest that strong sound-structure coupling occurs at the boundary between the water and the rubber layer. Because of the sound-structure coupling, the incoming longitudinal waves are predominantly converted into shear waves. These shear waves are more easily dissipated within the viscoelastic material due to internal friction and elastic relaxation processes. As a result, the composite metamaterial unit, composed of the HR cavity and the rubber layer, demonstrates exceptional low-frequency sound absorption capabilities for water-filled pipelines. Figure 9: **(a)** The cutaway view of the HR pairs with rubber layer (gray rectangular area in the red dashed box). **(b)** Absorptance, reflectance, and transmittance curves of the composite metamaterial formed by HR-1 and HR-2 pairs for water-filled pipeline with (red, blue, and green lines) and without (black line) rubber layer. **(c)** Absorptance and reflectance curves of HR-1 (red and blue lines) and HR-2 (black and green dashed lines). Both HRs are bonded with rubber layers. **(d)** The distributions of absolute sound pressure \(|\)P\(|\) and particle velocity \(v\) of HR-1 with the rubber layer. Broadband low-frequency absorption capability is significant in noise reduction for pipeline systems because the noise in the industrial pipeline system usually manifests as a line spectrum in broadband. We construct a composite metamaterial by parallel combination of four basic composite metamaterial units to achieve broadband acoustic absorption in water-filled pipelines. A 3 mm rubber layer is attached to the bottom of each basic unit, with the corresponding geometric parameters of HR-8, HR-9, HR-10, and HR-11 listed in Table 1. Figure 11a-d illustrate that the four basic units demonstrate quasi-Helmholtz resonance under incident wave excitation at 388 Hz, 425 Hz, 456 Hz, and 496 Hz, respectively. The absorption spectra of the individual units are depicted in Figure 11e. Despite the relatively low peak values of the analytical absorption coefficients of the basic units, the composite metamaterial unit exhibits a markedly enhanced overall absorption profile. The disparity in the absorption characteristics between the basic and composite units indicates that coherent coupling among the basic units results in extended bandwidth. The coupled composite metamaterial demonstrates an absorption coefficient exceeding 0.8 across the broadband frequency range of 380-508 Hz.