Study on inhomogeneous perforation thick micro-perforated panel sound absorbers

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1 Journal of Mechanical Engineering and Sciences (JMES ISSN (Print: ; e-issn: Volue, Issue 3, pp , Deceber 26 Universiti Malaysia Pahang, Malaysia DOI: Study on inhoogeneous perforation thick icro-perforated panel sound absorbers Iwan Prasetiyo *, Joko Sarwono, Indra Sihar Acoustic Laboratory, Engineering Physics, Institut Teknologi Bandung, Ganesa Bandung 432 Indonesia, * Eail: i.prasetiyo@fti.itb.ac.id Phone: ; Fax: ABSTRACT Micro-perforated panel (MPP sound absorbers are usually ade of a thin panel and have narrow absorption bandwidth. This drawback causes the application of MPP to be liited. In this paper, the possibility of realizing wider absorption bandwidth MPP with sufficient structural strength is investigated. For this, ulti-mpp (resonator arranged in parallel to for an inhoogeneous perforation MPP is introduced to widen the absorption bandwidth. The thickness of MPP ust be.5 ties higher than perforation diaeter or ore in order to have appropriate strength. The characteristics of corresponding absorption coefficients are studied paraetrically using theoretical odels as thick panels can reduce the MPP s perforance. It is found that the absorption bandwidth of thicker panels with inhoogeneous perforation approach can be at least twice ties of classical MPP. The proble of reduced peak absorption coefficient in a thick panel can be avoided by keeping the acoustic resistance value around ±.5 Rayls. Copared with hoogeneous MPP, inter-resonator interaction exists in the inhoogeneous perforation thick MPP that causes the overall absorption to becoe higher due to the increasing of the acoustic resistance as well as the shifting of peak resonance following residual acoustic reactance. The easureent results confir all of the characteristics. Keywords: Micro-perforated panel absorber; thick panel; inhoogeneous perforation pattern. INTRODUCTION As an alternative acoustic absorber to traditional porous aterials, the applications of Micro-perforated panels (MPP can be found in various fields such as roo acoustics [-3], environental noise abateent [4], noise control [5], and etc. Dah-You [6] forulated the MPP on the basis of the Helholtz resonance echanis. The sound absorption echanis leads to narrower absorption frequency range unlike the porous aterials. Apart fro this, the ratio of perforation diaeter and the panel thickness should also be nearly one for optiu design [7]. Hence, MPP is usually ade of a thin panel which is less than thick as perforation diaeter of MPP ust be less than. The two facts cause the MPP to not always be applicable for practical purposes e.g. for the case of the interior finish of roo walls where ore physical resistance and wider sound absorption bandwidth are coonly required to deal with preferred sound fields such as the acoustic characteristics in osques [8]. 235

2 Study on inhoogeneous perforation thick icro-perforated panel sound absorbers Copared with the classical MPP, the use of thicker panels for MPP has potential to reduce absorption perforance in ters of aplitude and frequency bandwidth due to increasing acoustic resistance ipedance and/ or reactance [9]. In principle, a wider absorption bandwidth MPP will need larger acoustic resistance and saller acoustic reactance [7, 9] but larger acoustic resistance can reduce the absorption aplitude. Hence, great care is required to introduce thicker panels to MPP. To deal with that, soe studies have been done by odifying the for of pores in order to iprove the perforance e.g. tapered holes [9, ] for icro-perforated insertion units (MIU []. Even though that can deal with the thicker panel effect on MPP but it still poses a difficulty fro the practical point of view e.g. anufacturing cost and technology. Meanwhile, soe studies have been proposed specifically regarding widening absorption bandwidth. Jung et al. [2] focused to develop double and triple layer systes to obtain ultiple absorption peaks in which a wider absorption bandwidth of ore than 4 octaves can be found accordingly. A siilar approach can also be found fro the study conducted by Sakagai et al. [3] fro which a detailed analysis with Helholt-Kirchhoff is provided. This approach outperfored the single layer but ore space was required to ipleent such constructions which is not also always applicable in practice. Moreover, the relation between the acoustic ipedance of each sub-syste is not clear. Hence, an optiization technique is not easily applied. Additionally, another effort is put by arranging ultiple conventional MPP in parallel for [4] while the backing air cavity is partitioned. Multiple peaks can be obtained fro such syste and a wider absorption can be obtained accordingly. Recently, Qian et al. [5] did an experiental investigation on the effect of reducing the perforation diaeter of MPP to less than. It was found that half-absorption bandwidth of 3 4 octaves with the peak absorption higher than.85 were pronounced. However, such approach is not always a good option as it requires special anufacturing technology e.g. using MEMS technology. More recently, a ore coplex construction of MPP incorporating panel absorber is also proposed to deal with a wider absorption bandwidth by enhancing low frequency absorption[6]. The work in this paper focuses on investigating the possibility of having wider absorption bandwidth for thick MPP. The thick MPP is considered when the panel thickness t is greater than the perforation diaeter d (t>d. The effect of t on acoustic ipedance and their interdependency are discussed in ters of absorption perforance and absorption frequency bandwidth. Subsequently, inhoogeneous perforation is introduced on thick panels in order to get wider absorption bandwidth and the corresponding characteristics are copared to that of the hoogeneous MPP. METHODS AND MATERIALS Ipedance Model for Micro-perforated Panels Dah-You [6] first proposed an approxiate odel to calculate sound absorption of the icro-perforated panel by treating the absorber consisting of parallel connected tubes distributed over surface and the panel is considered rigid. The approxiate odel was developed by siplifying the Bessel function. For noral incidence, the wave otion in all the short tubes can be regarded to be in phase and additive. Therefore, the relative acoustic ipedance with considering the end correction, this yields [7] 235

3 Prasetiyo et al. / Journal of Mechanical Engineering and Sciences ( t k 2 d t k d z zr jzi k j.85 2 cd t c 2 t ( The perforation constant k d 4 where d is the perforation diaeter, is the angular frequency, is the air density, is the coefficient of fluid viscosity, and the perforation ratio area with circular cross section 4db 2 where b is the centreto-centre distance between holes. Moreover, the ter z r is responsible for the resistance coponent of acoustic ipedance, while the ter z i is for acoustic reactance. MPP absorbers require a backing air cavity with cavity depth D. It is required to tune its absorption at resonance frequency f at which the axiu absorption can be obtained. The air cavity ipedance is expressed as given by z cav D jcot (2 c The cobined surface ipedance of the MPP and the air in the cavity z pp is thus D zpp z j cot (3 c For noral incidence, the sound absorption coefficient is thus defined as 4z r 2 2 ( zr ( zi cot D c (4 and the axiu coefficient is given by 4z r ax 2 ( zr (5 The ultiple resonance frequencies f are introduced by the following ters zi cot ( D c (6 For an acoustic copact condition, the expression of Eq. (6 is analogous to an ordinary ass-spring oscillator with the ass corresponding to z and the spring corresponding to cot ( Dc. Inhoogeneous Perforation Pattern Model The inhoogeneous perforation pattern in MPP is realized using a cobination of ultiple MPPs with different paraeters and parallel to each other with the cavity partitioned as shown in Figure in which its electrical equivalent odel can also be observed. i 2352

4 Study on inhoogeneous perforation thick icro-perforated panel sound absorbers D MPP- MPP-2 Z Z 2 Z 3 MPP-3 c Z q 2P Z D MPP-q Figure. Inhoogeneous perforation pattern MPP arrangeent (side view and its electrical equivalent odel To predict the absorption coefficient of such syste, the surface ipedance in Eq. (3 is odified to include the effect of different perforation paraeters on the sound absorption. Using electro-acoustic equivalent, the overall surface ipedance of MPP can be regarded as parallel coposition of single MPP. Hence, the ipedance over entire surface Z can be derived statistically as follows pp Z q a pp q i Zpp, q Z pp (7 where q is the nuber of MPP on the sae panel surface, and aq Aq A is ratio area T of the sub-mpp to the total area. Therefore, the cobined surface ipedance of the MPP and the air in the cavity z pp can be expressed as D Zpp Zpp j cot (8 c In which the air cavity depth D is considered to be the sae for all the sub-mpp. Subsequently, the absorption coefficient can be obtained using Eq. (4. It should be noted that the cavity needs to be partitioned rather than connected for all MPP to enable the sub-mpp to work individually. Actually, the surface ipedance expressed by Eq. (7 does not include the effect of discontinuity of acoustic ipedance that is present due to two different adjacent MPP. Such discontinuity can introduce excess absorption. Hence, the forulation is extended to incorporate the wave scattering on panel surface using the following expression [7]. Ψ (9 2 Re[ ] where cos with, 2, and the incident angle (noral incidence angle 2 2,, and Ψ is unknown wave scattering coefficient. 2353

5 Prasetiyo et al. / Journal of Mechanical Engineering and Sciences ( PARAMETRIC SURVEY Effect of Panel Thickness Figure 2 presents the effect of panel thickness on the absorption coefficient for the sae cavity depth with properties listed in Table unless otherwise stated. The MPP is categorized as the hoogenous perforation MPP. It can be seen that the peak frequency shifts to lower frequency with increased thickness This situation can be explained in accordance with Eq. (6. The thicker panels have greater total ass of air inside the perforation copared with that of the.5 thick panel while the stiffness of resonator syste is unchanged due to the sae air cavity depth. Hence, the resonant frequency related to that frequency peak becoes lower. Table. Properties of icro-perforated panel. Material t ( d ( D ( Acrylic Noral Absorption Coefficient ( t=.5 t= 3 t= 5 t= Figure 2. Absorption coefficient coparison for different panel thickness t with air cavity depth D = 5 Table 2. Absorption and acoustic ipedance characteristics of hoogeneous MPP for different panel thickness. t ( f (Hz ax half-absorption bandwidth (Hz* zr zi *frequency bandwidth evaluated at.5 Considering the thickness t in Eq. (, this paraeter affects the resistance and reactance part of acoustic ipedance. The axiu absorption requires the resistance coponent zr to be close to as indicated by Eq. (5. Meanwhile, the absorption 2354

6 Study on inhoogeneous perforation thick icro-perforated panel sound absorbers bandwidth is ore wide for saller acoustic reactance zi. Fro Table 2, it is clear that the MPP with zr close to has the higher absorption coefficient. Likewise, it can also be seen that the acoustic reactance zi of MPP increased as the panel thickness increased so that the associated bandwidth becoes narrower. The results suggest that it is iportant to find the balance between the value of acoustic resistance and reactance in the design process in order to aintain the MPP s perforance as both coponents are influenced by the panel s thickness. It is found fro paraetric survey that the value of acoustic resistance zi close to ±.5 causes the MPP panel to have reasonable coefficient absorption ( =.9, while the saller or higher acoustic resistance than that value will bring to lower absorption coefficient. Meanwhile, acoustic reactance zi that is greater than 4 will lead to narrower bandwidth hence it is only effective for specific noise control e.g. tonal noise proble. Controlling the perforation rate can be useful for the thick panel as long as the target frequency range is not the ain concent. It can be seen fro Figure 3 that the thick panel will be outperfored by the thinner one as this is dependent on the ratio of (b/d as shown in Figure 3. It is found that in order to have reasonable absorption coefficient for thick panel, the perforation ratio area need to be kept high. Hence, Eq. (5 reduces to ax 4 5.b t t d 2 (.9.8.5% %.5 % 2 %.7 ax t ( Figure 3. Effect of thickness on the axiu absorption coefficient and perforation area ratio. Effect of Inhoogeneous Perforation Pattern Inhoogeneous perforation pattern is considered as the results of the cobination of two sub-mpps. The perforation paraeters are kept the sae (see Table except the distance between holes b is varied so that the perforation ratio area of each MPP varies. It can be seen fro Figure 4 that the overall half-absorption frequency bandwidth becoes wider for larger bratio = (b/b2 which is alost twice that of individual MPP as indicated for the case of bratio of 2. Care ust be taken as the wider bandwidth is able to sacrifice the absorption aplitude. Hence, this approach has potential to widen the absorption bandwidth. 2355

7 Prasetiyo et al. / Journal of Mechanical Engineering and Sciences ( Noral Absorption Coefficient ( b 8 b2 7 Noral Absorption Coefficient ( b 8 b Noral Absorption Coefficient ( b 8 b2 5 Noral Absorption Coefficient ( b 8 b Figure 4. Effect of inhoogeneous perforation pattern with two sub-mpps on the noral absorption coefficient. The red solid line indicates the overall noral absorption coefficient due to both sub-mpps. Table 3. Half frequency bandwidth absorption coparison for different thickness Panel Thickness ( Half-absorption bandwidth (Hz Noral Absoprtion Coefficient ( t =.5 t = 3 t = Figure 5. MPP absorption coefficient coparison for different thickness as a result of cobination MPP (=.79% and MPP2 (=2.8% with cavity depth 5. The rest of the paraeters are kept the sae 2356

8 Study on inhoogeneous perforation thick icro-perforated panel sound absorbers It is instructive to have a look at the absorption characteristic of inhoogeneous perforation pattern on thicker panels. The results can be observed fro Figure 5. It is clear that the absorption bandwidth gets wider copared with the hoogeneous ones for the sae panel thickness. As indicated intable 3, the half-absorption bandwidth are 444 Hz, 378 Hz, and 37 Hz for panel thickness.5, 3, and 5 respectively. The bandwidth are twice wider than the hoogenous perforation MPP (see Table 2. Moreover, the axiu absorptions are in the range of.79 up to.99. Hence, the MPP is still useful for absorber aterial. Despite this, the effect of thickness on absorption characteristic is still present i.e. the absorption coefficient decreased and the bandwidth is reduced for thicker panels e.g. for the case of the.5 thick MPP and the 5 thick MPP. RESULTS AND DISCUSSION Experiental Setup For experiental work, the basic specification of icro-perforated speciens are ade 9 of.5 thick acrylic with following properties: Young s odulus, E 3.2 N/ 2, 3 Poisson s ratio, vp.35, and density.6 kg/3. Meanwhile, the pore diaeter of specien is.9 and the air cavity depth is 5 unless otherwise stated, i.e. specien for investigation of the effect of inhoogeneous perforation. The design paraeters of the MPP are listed in Table 4. It should be noted that the inhoogeneous perforation pattern is realized by cobining two MPPs designated as MPP- and MPP-2 with arrangeent as shown in Figure. Table 4. Geoetrical properties of speciens. Specification Specien t( D ( (% Varying thickness Inhoogeneous perforation pattern PC/Laptop Power Aplifier White Noise MC Ch. FFT Speaker Mic. Micro-Perforated Panel (MPP Movable piston Figure 6. Scheatic diagra of ipedance tube test ethod. 2357

9 Prasetiyo et al. / Journal of Mechanical Engineering and Sciences ( The easureent of absorption coefficient of MPP was conducted using ipedance tube as per ISO [8]. The scheatic diagra of the test can be seen in Figure 6. In principle, the white noise was generated in sound source and the travelling plane waves through a c radius tube were picked up using two icrophones. Fro this, the transfer ipedance can be deterined and the sound absorption coefficient for frequency ranging fro 64 Hz to.6 khz can be obtained accordingly. Effect of Panel Thickness The coparison results as shown in Figure 7 indicate that the predicted results and easured ones have siilar tendency (speciens, 2, and 3. Moreover, the peak frequencies of the easured ones are close to the theoretical odel (Maa odel which correspond with Helholtz resonance. The discrepancy of the Maa odel results and the easureent ones are around 4% up to 4 % at half absorption frequency range. Soe peaks are also present that are related with the panel resonances [9, 2]. Those peaks are not considered in the Maa odel so they are issing fro the predicted results. The issue of absorption bandwidth found in the paraetric survey where the thicker panel has narrower bandwidth is also confired by the easureent results. Considering the coparison results, it is possible to have thick MPP with reasonable perforance which is useful for practical purposes..9 Noral absorption coefficient, Figure 7. Absorption coefficient coparison of Maa odel and easureent for different panel thickness (Maa odel: t.5 ; t 3 ; -- t 5 ; easureent results - t.5 ; -- t 3 ; -- t 5 Effect of Inhoogeneous Perforation Pattern Figure 8 (a presents noral absorption coefficient coparison of prediction results and easureent results for inhoogeneous perforation MPP (specien 4. It is clear that two absorption peaks are pronounced fro the easureent results at 766 Hz and

10 Study on inhoogeneous perforation thick icro-perforated panel sound absorbers Hz as indicated by the blue circle. Copared with the hoogeneous perforation pattern MPP- and MPP-2, see the green dashed lines, the inhoogeneous pattern is apparently fored by two individual MPP as expected. The analytical results, particularly calculated using Eq. (8, is in good agreeent with the easureent results except the presence of gap in frequency of around 84 Hz up to 59 Hz. This gap exists as the effective perforation area is reduced by ½ of the original value considering the nonresonating MPP behaves as a rigid wall. Hence, the acoustic resistance is increased by two ties. The effect of finite specien size is also present as the analytical odel particularly Eq. ( is developed using periodic condition for infinite syste so that its result is less accurate copared with that of Eq. (8. A siilar situation is found for the case of 3 thick MPP and 5 thick MPP respectively [see Figure 8 (b and (c]. Moreover, the analytical odels eployed in this paper are still useful to predict the absorption coefficient of inhoogeneous perforation thick MPP. Meanwhile, the presence of the peak seen at 52 Hz corresponds to fundaental ode of the panel rather than was caused by the Helholtz resonance. Noral Absorption Coefficient ( Measureent MPP (=.79 % MPP 2(=2.8 % Electrical Equivalent Eq. 8 Calculation Eq. Noral Absorption Coefficient ( Prediction odel easureent (a (b Noral Absorption Coefficient ( Prediction odel easureent Figure 8. Noral absorption coefficient of inhoogeneous perforation coparison of easureent results and analytical ones: (a.5 thick MPP; (b 3 thick MPP; and (c 5 thick MPP It is also interesting to see that the corresponding peaks do not perfectly atch copared with individual MPP or even for inhoogeneous perforation analytical odel (c 2359

11 Prasetiyo et al. / Journal of Mechanical Engineering and Sciences ( results. Actually, the two Helholtz resonator systes in the inhoogeneous perforation MPP work individually rather than siultaneously. However, considering the two MPP are laid on the sae surface, the acoustic reactance of the non-resonating MPP will be negative or positive. It can be seen fro Figure 9 fro which the acoustic reactance of ipedance of two MPPs is copared. The peak frequency of MPP- shifts to higher frequency as residual of I(Zpp= zi cot ( D c. This condition iposed an added-stiffness effect. Coversely, the peak frequency of MPP-2 shifts to lower frequency as residual of I(Zpp= zi cot ( D c so that an added-ass effect is present. Hence, there is what is so called as inter-resonator interaction contributing to the overall absorption coefficient. 5 I( z pp The first resonance peak The second resonance peak =.79 % =2.8 % Figure 9. Acoustic reactance characteristic of MPP-(.789% and MPP-2 ( 2.8 % CONCLUSIONS The characteristic of inhoogeneous perforation pattern on thick MPP has been studied. A thick MPP experiences higher acoustic resistance as well as acoustic reactance copared with the classical one where the ratio of perforation diaeter and panel thickness is nearly one to obtain an optial design. For axiu absorption coefficient, it is iportant to keep the acoustic resistance value around ±.5 Rayls. Meanwhile, the absorption bandwidth can be widened through the inhoogeneous perforation approach as the reduction of absorption bandwidth cannot be avoided for thicker panels. This can lead to at least twice ties hoogeneous MPP. It is also found that inter-resonator interaction contributed to the overall absorption coefficient in the inhoogeneous perforation MPP. Copared with hoogeneous MPP, this causes the overall absorption to becoe higher due to the increasing of the acoustic resistance as well as the shifting of peak resonance due to residual acoustic reactance. The theoretical odel based on statistical odel and wave scattering can produce reasonable results for prediction purposes. After testing the MPP specification with thickness up to 5, it is still possible to have ore applicable MPP where ore resistance to physical contact and wider absorption bandwidth are usually required. Moreover, the use of conventional circular perforation in the inhoogeneous perforation thick MPP can help to anufacture the MPP in a ore sipler way. 236

12 Study on inhoogeneous perforation thick icro-perforated panel sound absorbers ACKNOWLEDGEMENTS The research was funded by the ITB s Research Innovation Grant under project nuber 44.23/AL-/DIPA/PN/SPK/23 REFRENCES [] Fuchs HV, Zha X. Acrylic-glass sound absorbers in the plenu of the deutscher bundestag. Applied Acoustics. 997;5:2-7. [2] Sarwono J, Prasetiyo I, S Andreas, Willia A. The Design of MPP and its Application to Enhance the Acoustics of a Real Auditoriu. Inter-Noise 43rd International Congress on Noise Control Engineering. Melbourne24. [3] Fuchs HV, Zha X. Micro-Perforated Structures as Sound Absorbers R A Review and Outlook. Acta Acustica united with Acustica. 26;92: [4] Asdrubali F, Pispola G. Properties of transparent sound-absorbing panels for use in noise barriers. The Journal of the Acoustical Society of Aerica. 27;2:24-2. [5] Yu X, Cheng L, You X. Hybrid silencers with icro-perforated panels and internal partitions. The Journal of the Acoustical Society of Aerica. 25;37: [6] Dah-You M. Theory and design of icroperforated panel sound-absorbing constructions. Scientia Sinica. 975;8:55-7. [7] Maa D-Y. Potential of icroperforated panel absorber. The Journal of the Acoustical Society of Aerica. 998;4: [8] Kassi DH, Putra A, Nor MJM, Muhaad N. Effect of pyraidal doe geoetry on the acoustical characteristics in a osque. Journal of Mechanical Engineering and Sciences. 24;7: [9] Sakagai K, Morioto M, Yairi M, Mineura A. A pilot study on iproving the absorptivity of a thick icroperforated panel absorber. Applied Acoustics. 28;69: [] Randeberg RT. Perforated panel absorbers with viscous energy dissipation enhanced by orifice design: Norwegian University of Science and Technology, Trondhei; 2. [] Pfretzschner J, Cobo P, Sion F, Cuesta M, Fernández A. Microperforated insertion units: An alternative strategy to design icroperforated panels. Applied Acoustics. 26;67: [2] Jung SS, Ki YT, Lee DH, Ki HC, Cho SI, Lee JK. Sound absorption of icro-perforated panel. Journal-Korean Physical Society. 27;5:44. [3] Sakagai K, Matsutani K, Morioto M. Sound absorption of a double-leaf icro-perforated panel with an air-back cavity and a rigid-back wall: Detailed analysis with a Helholtz Kirchhoff integral forulation. Applied Acoustics. 2;7:4-7. [4] Sakagai K, Nagayaa Y, Morioto M, Yairi M. Pilot study on wideband sound absorber obtained by cobination of two different icroperforated panel (MPP absorbers. Acoustical Science and Technology. 29;3:54-6. [5] Qian Y, Kong D, Liu S, Sun S, Zhao Z. Investigation on icro-perforated panel absorber with ultra-icro perforations. Applied Acoustics. 23;74:

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