## 1 Introduction  
Investigating noise annoyance problems in places where users are the main sound source and spaces are strictly confined, like open-plan offices [1], restaurants [2; 3; 4], and call centers and markets [5], has become a frequent research topic in recent years. In these cases, adding sound absorbing treatments proved to be an easy and efficient method for limiting the problem of high sound pressure level and controlling the speech intelligibility [6]. Among the various sound absorbing materials that are available for the purpose, with different finishing and different acoustic behavior, aesthetic factors combined with ease of maintenance often play a major role in the selection process [7]. Perforated and micro-perforated panels, when compared to more conventional porous absorbers, may offer significant advantages in terms of hygiene, fire-proofing, and durability. Moreover, their acoustic properties could be precisely targeted, achieving a strong absorption at specified frequency band, while being optimized and predicted by computational methods [8; 9; 10]. In addition, by using proper materials, such absorbers might easily become eco-friendly, which is an ever increasing requirement among sound absorbers [11; 12]. In practical applications, perforated and micro-perforated panels are normally placed in front of a rigid surface with an air cavity between them, forming a series of parallel Helmholtz resonant cells. The sound is absorbed by the viscous loss and specific acoustic impedance of the air in holes and cavity. Accordingly, their sound absorption coefficients are dominated by the diameter and depth of the hole, the perforation rate, and the cavity thickness [10]. After decades of development, the fundamental laws underlying the design of perforated and micro-perforated panel absorbers have been clarified [8; 9; 10; 13; 14] and several proposed prediction models have been validated against measurements [15; 16; 17; 18; 19]. For the predictions of homogeneously perforated absorbers, the theoretical models that were proposed by [PERSON] [16], [PERSON], and [PERSON] [17], are better used to model absorbers with circular perforations, while for other cross-sectional perforations, the models of [PERSON] [18] or [PERSON] and Sgard [19] can be used instead. [PERSON] and other researchers have also developed a method to model multi-layer perforated absorbers, while using a transfer matrix solution, taking each layer in turn [8; 9; 20]. Finite Element Method (FEM) [21; 22], Equivalent Circuit Method (ECM) [23], Parallel Transfer Matrix Method (PTMM) [24; 25], and Admittance Sum Method (ASM) [26] are other computing methods used to model heterogeneous perforated absorbers. [PERSON] et al. [27] explored the adequacy of these four different methodologies in the case of heterogeneous absorbers with isolated or shared cavities, and found that only ECM and FEM yield correct results for both conditions. Depending on the resonance system, single-leaf perforated panel absorbers always have a limited frequency band, showing only one sharp-narrow absorption peak. Many researchers proposed the use of more complex perforated absorbers, including multi-layer systems [28], three-dimensional (3D) micro-perforated panels [29], combinations of micro-perforated panels with membranes [30; 31], arranging the parallel micro-perforated panel absorbers with different cavity depths [32], or combining perforated panels with micro-perforated partitions [33], to achieve a wider absorption band. [PERSON] and colleagues studied the theory behind the acoustical property of multi-leaf membranes [34], double-leaf micro-perforated panel [35], their combinations [26; 31], and the combination with porous materials [36]. [PERSON] et al. [37] investigated the sound absorption coefficient of multiple perforated panel systems that were composed of coin fiber and one air gap.