# Low-Frequency Sound Absorption in Air Pipelines and Water-Filled Pipelines Based on Metamaterials
## 1 Introduction
Given the spatial constraints of pipeline systems, which often involve various configurations, including liquid-filled and air-filled pipelines, designing silencers with consistent and thinner thickness using the same fundamental design paradigm presents both significant practical value and substantial challenges. In our study, we proposed a method based on HR for constructing low-frequency asymmetric absorption metamaterials by coupling absorption-reflection acoustic modes in air pipelines and further studied the absorption characteristics of other types of metamaterials in water-filled pipelines. The absorption mode should display high dissipation levels (with resistance near 1 and reactance near 0) to absorb sound energy. Conversely, the reflection mode should display lower damping and behave as a soft boundary to reflect incident sound energy. Helmholtz resonators (HRs) are well-known structures that are typically utilized to reduce pipeline noise. In our research, we utilize two distinct HRs to create an asymmetric absorption metamaterial, where the smaller and larger neck radii of the HRs support the highly dissipated absorption mode and minimally dissipated reflection mode, respectively. As a result, sound entering the port nearest to the absorption mode undergoes substantial absorption, while sound entering the port adjacent to the reflection mode is largely reflected, thus exemplifying asymmetrical reflections/absorptions. Furthermore, in order to realize low-frequency sound absorption in the water-filled pipeline with a similar design paradigm to the above HR, a rubber layer was introduced at the bottom of the cavity to ensure impedance matching. The rubber layer, having significant damping, causes the HR resistance with the rubber layer to deviate from zero. As the HR loses its soft boundary characteristics, it no longer exhibits a reflective mode but instead functions as a low-frequency sound absorber. The Nelder-Mead optimization algorithm was employed to optimize the composite metamaterial unit with the rubber layer, with the optimized unit achieving an absorption peak of 0.85 at 446 Hz. Finally, by connecting four basic composite metamaterial units in parallel, the coupled composite metamaterial we developed demonstrates broadband sound absorption capability, with an absorption coefficient greater than 0.8 across the 380-508 Hz range. We have developed a low-frequency pipeline silencer design paradigm based on Helmholtz cavities. Through further design of the basic paradigm, the two types of metamaterials have similar thickness, which means that metamaterial units with similar configurations can overcome the significant impedance mismatch between water and air, achieving low-frequency sound absorption in both air and water pipelines at comparable scales. The use of the same basic paradigm eliminates the need to design different structural solutions for pipelines with different filling materials to maintain similar thickness. This reduces the complexity of designing noise reduction solutions for systems with pipelines of different media in narrow spaces and enhances the reliability of the noise reduction scheme. On the other hand, the asymmetric sound-absorbing metamaterials applied to air pipelines are still unable to achieve sound absorption over a wide target frequency band. The composite metamaterials applied to water-filled pipelines do not have a sufficiently wide sound absorption bandwidth, failing to fully cover the target frequency band mentioned in the references [3].