# Prediction of the Absorption Characteristics of Non-Uniform Acoustic Absorbers with Grazing Flow
## 1 Introduction  
Noise, as one of the main environmental pollutants, is increasingly affecting our daily lives. Attenuating noise pollution through effective control measures has attracted great interest due to stringent noise control regulations. Conventional micro-perforated plate (MPP) absorbers have been widely used to attenuate narrowband noise. Different materials can be selected to cope with the harsh operating conditions, such as high temperature environments. Using the impedance equations proposed by [PERSON] [1], the acoustic absorption characteristics of MPPs can be predicted, and the desired absorption performance can be achieved by choosing the appropriate structural parameters for the MPP absorbers [2; 3; 4; 5]. An absorber with a complex structure by artificial design is called a metamaterial absorber [6]. Based on the metamaterial design, [PERSON] et al. [7] developed a highly efficient, perfect, large angular and ultrawideband solar energy absorber. [PERSON] et al. [8] designed three-layered metamaterial acoustic absorbers based on reused PVC membranes and metal washers. Taking advantage of its sound-absorbing properties, many acoustic absorbers have been developed, such as spatial folding [9; 10], Helmholtz resonance [11; 12], thin film [13; 14] absorbers, etc. Acoustic absorbers have important applications in the field of acoustic absorption of ducts. The absorber placed in a duct is called an acoustic liner. It is usually composedof a uniform perforated facesheet over a honeycomb cavity and called a single degree of freedom (SDOF) acoustic liner [15], which typically absorbs acoustic energy in a narrow frequency band dictated by the resonance and antiresonance frequencies of the cavities. A double degree of freedom (2 DOF) acoustic liner [16] can offer a higher absorption bandwidth and is capable of covering the necessary source spectrum. To obtain an adjustable acoustic absorption performance, [PERSON] [17] designed a 2 DOF honeycomb acoustic liner and demonstrated the feasibility of adjustable acoustic absorption by changing the height of the back cavity. [PERSON] [18] investigated the acoustic performance of a 2 DOF Helmholtz resonator and elaborated on the effect of changing the internal dimensions of the resonating cavity on the underlying acoustic attenuation. Historically, traditional SDOF and 2 DOF acoustic liners have been designed for reduction of noise at a fixed frequency. However, there is a high demand for broadband noise reduction in engineering practice. To this end, the energy of dominant source modes can be made to redistribute into higher order modes which are more easily suppressed by the absorber. This modal conditioning technology is generally achieved by non-uniform acoustic absorption structures. In recent years, the non-uniform acoustic absorption structure, characterized by the spatial variations of the impedance, has received extensive attention. Previous studies demonstrated that the optimized absorption structures with spatially varying impedance offer increased attenuation compared to uniform absorption structures. Several investigators have investigated the possibility of improved absorption structure performance by means of modal redistribution by incorporating a circumferentially or axially segmented absorption structure into the duct. [PERSON] [19] evaluated the acoustic performances of circumferentially segmented duct absorption structures for a range of frequencies and source structures, and concluded that the circumferentially segmented absorption structure gives better broadband performance than the uniform absorption structure and is not particularly sensitive to changes in modal structure of the source. [PERSON] et al. [20] explored a broadband absorption structure by varying the facesheet porosity and the hole diameter for each individual cavity along the axial direction of the duct, while keeping the facesheet thickness and core depth constant.