1 Multiple ‐ layer microperforated panels as sound 2 absorbers in buildings : a review

Sound absorbing materials are used in building to dissipate sound energy into heat by 11 viscous and thermal processes. Sound absorbers increase the transmission loss of walls, decrease 12 the  reverberation  time  of  rooms  and  attenuate  the  noise  generated  by  internal  sound  sources. 13 Porous  absorbers  (fibrous,  cellular  or  granular)  are  the most  used materials  in  noise  control 14 applications, since their high performance‐to‐cost ratio in the frequency band of interest. However, 15 when cleaning and health reasons are of concern, microperforated panel (MPP) absorbers can be 16 preferred.  MPPs,  consisting  of  many  minute  (sub‐millimetric)  holes  in  a  panel,  are  tunable 17 absorbers in a prescribed frequency band, which main shortcomings are high manufacturing cost 18 and limited absorption frequency band. Production cost of MPP can nowadays be drastically cut 19 down by means of modern techniques. Absorption frequency band can be considerably enlarged 20 by designing multiple‐layer MPPs (ML‐MPPs). The aim of this article is to review the high potential 21 of ML‐MPPs as a modern, clean and healthy alternative of porous materials for sound absorption. 22


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Porous and fibrous materials are excellent sound absorbers at a reasonable cost. They are used 26 in most situations where sound must be dissipated, either for increasing the sound insulation of 27 multilayer walls of buildings or, as liners, for decreasing the reflective characteristics of inner walls.        impedance Z0 finds this MPP system, the impedance contrast (Z1-Z0) causes a wave reflection, and as 78 a consequence, produces sound absorption. At normal incidence, the reflection, R, and absorption,

98
The Maa and EF models for the MPP, ZMPP, and more specifically, for the impedances of the 99 perforations, Zhole, and edges, Zedge, will be reviewed in the following.
105 where u is the particle velocity in the tube, r1, is the radial coordinate in the tube,  is the air viscosity,

106
and p is the presuure difference at both sides of the tube. Solving for u, and averaging on the tube 107 surface, the following equantion is otained 109 which affords for the hole impedance ∆ / ,

132
These are the resistive and reactive terms used in most MPP models and will be also assumed in 133 this article. Notice that 134 2 2 2√2 2√2 . (10)

135
The reactive term can be also interpreted as an excess of vibrating mass, 2 0.85 , Figure 3,

136
where a multiplying factor of 2 is used to take into account both sides of the hole.

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The edge impedance of Eq. (9) assumes that the perforations are separated enough from each 138 other (low perforation ratio ) so that there is not edge interaction effects. However, these 139 interactions can become significant when the holes are close each others. Melling [24] proposed to    article. Figure 5 shows the Fok function (correction factor of the mass reactance) as a function of 155 porosity. As it can be seen, the correction factor is small for low porosity values but begins to be 156 significant for porosities higher than 2%. Since this factor corrects the length excess of the oscillating 157 mass in the holes, the effect of overperforaton is to cut out this length excess.

161
The normal incidence absorption coefficient, which can be calculated by introducing this Eq.    186 Maa [2] proposed designing SL-MPPs with d=t. As it is seen in Figure 10, which dispalys the 187 absorption coefficient of a SL-MPP as a function of (d,t) for f=1500 Hz, =1% and D= 2 cm, this is a 188 reasonable guess.
189 Figure 11 shows the absorption curves of a SL-MPP as a function of frequency, for t=0.5 mm, D=

433
The random incidence d depends on the reaction properties of the boundary. Ingard [36] 434 proposed the notation 0, 1 and 2 for naming the absorption coefficients at normal incidence, 435 random incidence for locally reacting surfaces, and random incidence for bulk reacting surfaces, 436 respectively. Figure

447
It is usual to design MPPs at normal incidence, since the mathematical problem is much 448 simpler. However, the designed MPP will likely have to perform at diffuse field. The bandwidth of 449 the designed normal incidence SL-MPP will be similar to that of the random incidence provided that 450 the interface is working as a local reaction surface. This can be easily achieved if the air cavity is 451 properly partitioned, for example with a honeycomb structure.

474
The input impedance to the DL-MPP system is 475 ,  impedances to the three interfaces are Z1, Z2 and Z3. Also, the characteristic impedance of the air is Z0.

495
Sound waves reach the TL-MPP system from the left at normal incidence.

516
Cobo et al. [38] confirmed that it is possible to manufacture cheap, optimised by Simulated

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Annealing, TL-MPPs by drilling epoxy laminates primarily used for advanced circuitry applications.