# Low-Frequency Sound Absorption in Air Pipelines and Water-Filled Pipelines Based on Metamaterials
## 1 Introduction  
Piping systems that convey fluids are extensively utilized across numerous industries, including central air-conditioning pipelines, intake and exhaust systems for large-scale fans, gas turbines, nuclear power machinery, and cooling pipelines carrying liquids [1, 2]. The movement of fluids within these systems induces rheological vibrations in the pipes, propagating acoustic waves along the interior, leading to rheological noise. Low- frequency waves can pass through with minimal attenuation. Therefore, low-frequency sound waves often have higher noise pressure levels both in air pipelines and water-filled pipelines. [PERSON] et al. [3] studied the flow-induced noise at the evaporator of a refrigerating system, and the noise level exceeding 50 dB appeared in the frequency band of 315 Hz-500 Hz. [PERSON] et al. [4] found that the noise pressure level of elbow wall pipes of cruise central air conditioning exceeds 65 dB from 200 Hz to 500 Hz. For a section of the pipeline, silencers are usually arranged within a limited space to dissipate the low-frequency noise at the inlet. However, efficiently designing low-frequency flexibility according to the different medium environments in pipelines remains challenging. The concept of acoustic metamaterials has evolved progressively over the past few decades. Acoustic metamaterials have many unmatched advantages over natural materials due to their negative equivalent density, bulk modulus in acoustic focusing and imaging [5; 6; 7], invisible cloaking [8; 9; 10; 11], acoustic energy collection [12; 13; 14], and cross-medium sound transmission [15; 16; 17; 18; 19]. Due to the large density of states at low frequencies, the high-efficiency and subwavelength acoustic absorber is one typical application [20]. The emergence of acoustic metamaterials has sparked an array of absorber designs, such as Helmholtz resonator (HR) absorbers [21; 22; 23; 24], impedance gradient structures [25; 26; 27; 28], acoustic membrane absorbers [29; 30; 31], and spiral space absorbers [32; 33; 34]. Many of these absorbers above exhibit deep-subwavelength complete absorptions (PAs). The absorbers utilized in the different systems above are based on an ideal single-outlet model wherein the outlet port is rigid. However, recent studies indicate that a more productive absorption method can be accomplished through a standard double-outlet design [35; 36; 37], like a conduit system. [PERSON] et al. [38] proposed that asymmetric absorption can be achieved by decorating a two-port system with hybrid membrane resonators. Although the hybrid membrane resonator achieves efficient sound absorption at 291 Hz, its thickness reaches 95 mm. More importantly, for a system composed of mass blocks and membranes, the resonant frequency is controlled by the elastic modulus and the pre-tension of the membrane boundary. When the pipe is filled with water with a higher modulus, the membrane material may exceed the pre-tension value to achieve effective sound-structure coupling. [PERSON] et al. [39] designed a resonance-labyrinthine silencing structure, which exhibits transmission loss values that are greater than 10 dB within the 230 Hz to 816 Hz range, with a structure thickness of 125 mm. Efficient dissipation is achieved by folding the resonant channel length in three-dimensional space. However, to achieve resonance silencing for water-filled pipelines by the same strategy, extremely long channel lengths are required, which leads to a significant increase in the actual thickness of the structure. [PERSON] et al. [40] reported the application of Helmholtz resonators in water-filled pipelines, where the structural thickness reaches 300 mm to achieve efficient sound isolation in the 356.5 Hz to 645.5 Hz range. To achieve the same frequency range for air-filled pipelines, the required thickness is approximately 71 mm [41]. When applying the muffler design paradigm for single-medium-filled pipelines to other pipeline types, several challenges arise, particularly concerning non-uniformity in thickness.