The Effect of Non-Homogenous Perforation Pattern on Sound Absorption Bandwidth of Micro-Perforate Panel

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1 7th International Conference on Physics and Its Applications 4 (ICOPIA 4) The Effect of Non-Hoogenous Perforation Pattern on Sound Absorption Bandwidth of Micro-Perforate Panel Iwan Prasetiyo Engineering Physics, Institut Teknologi Bandung, Jl.Ganesa No. Bandung, 43, Indonesia Joko Sarwono Engineering Physics, Faculty of Industrial Technology, Institut Teknologi Bandung, Jl.Ganesa No. Bandung, 43, Indonesia E-ail: jsarwono@tf.itb.ac.id Indra Sihar Engineering Physics, Faculty of Industrial Technology, Institut Teknologi Bandung, Jl.Ganesa No. Bandung, 43, Indonesia E-ail: sihar.indra@gail.co Abstract Absorption bandwidth of conventional Micro-Perforated Panel backed by air cavity is liited around octave bands particularly for pore diaeter close to. Copared with porous aterial, the absorption bandwidth is relatively narrow. Hence, its applications ay becoe liited. This research shows that ultiple-peaks as result of the use of the non-hoogenous perforation pattern are useful in extending the absorption bandwidth. An analytical odel is used to predict the absorption coefficient while experiental results are provided for validation. Keywords: Micro-perforated panel, non-hoogenous perforation pattern, extending absorption bandwidth, excess sound absorber while the axiu absorption occurs at the resonant frequency f. Regarding with the effort of widening the absorption bandwidth, soe studies can be found fro literatures. Theoretically, the basic principles related with this objective were given by Dah You Ma.6 Fro his study, the absorption bandwidth becoe wider as the value acoustic reactance is saller while the value of the acoustic resistance r is larger. This approach leads to 3 or 4 octave half- absorption bandwidth. Qian J, Y. et al.7 conducted experiental study by reducing the perforation diaeter to less than in order to get larger value of acoustic resistance. It is found that half-absorption bandwidth of 3-4 octaves with the peak absorption higher than.85 are pronounced. The results is proising in ters of practical purposes but facing difficulty in anufacturing technique to fabricate such tiny holes. Hence, in practical point of view, it would take tie until an. Introduction The applications of Micro-perforated panel (MPP) as sound absorber in various areas have been widely found such as roo acoustics,, environental noise abateent3 and duct noise control4, since the forulation proposed by Dah You Maa in MPPs are usually placed in front of rigid wall with a particular air cavity in which the Helholtz resonance echanis is taken account for. Moreover, siple construction is another advantage of the MPP fro point of practical concerns. Considering these facts, MPPs can be an alternative to traditional porous aterials. However, unlike the porous aterials, the perforance of the MPP is usually liited to around one to two octaves. This narrow absorption bandwidth is as consequence of the Helholtz resonance echanis where its absorption is dependent on the perforation paraeters 5. The authors - Published by Atlantis Press 35

2 appropriate technology is ready to deal with the requireent otherwise it would be costly. Jung et al. 8 was focused to develop double and triple layer systes connected in series to obtain ultiple of 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 study conducted by Sakagai et al. 9 fro which a detail analysis with Helholtz-Kirchhoff is provided. This approach is outperfored copared with single layer but ore space required ipleenting the construction which is no always applicable in practice, e,g, roo interior surface in buildings. Moreover, in ters of optiization, it is difficult as the relation between the acoustic ipedance of each sub-syste is not clear. The use of ultiple MPPs connected in parallel was also proposed. This can introduce ultiple peaks so that wider absorption bandwidth can be expected. Soe results have been deonstrated by Sakagai. in virtue of periodic structure theory and considering excess sound absorption on boundary due to the discountinity of ipedance. Meanwhile, Su et al. use parallelcircuit rule by considering interaction/coupling between the reflected sound field exist have deonstrated parallel MPP in widening absorption bandwidth. Alternatively, air cavity can also be filled with porous aterial to extend the absorption bandwidth. Wang, C, et al. 3 proposed irregular-shaped cavity rather than exploiting the perforation paraeter in order to get wider absorption bandwidth. This approach allows ore acoustic odes in cavity coupled with air otion in MPP copared with rectangular-shaped cavity. Hence, ore resonant odes over frequency can be expected so that the absorption bandwidth becoes wider. In this anuscript, the effect of the inhoogeneous perforation pattern using two different MPP is investigated. It is considered to exploit further the effect of the ultiple absorption peaks in order to allow the absorption bandwidth to becoe wider while the pore diaeter is close to and can not be reduced further due to the liitation of anufacturing technology. This situation causes the absorption bandwidth usually only around octave. MPP Theoretical Model. Ipedance odel for perforates Following Crandall theoretical odel for short tube. 4, viscous effect of narrow tubes can be quantified by defining the specific ipedance of a single circular tube that is ratio of the sound pressure difference between the end of tube ( p ) and average particle velocity across the tube cross section ( u ). This gives p J( k j) Z jt u k j J ( k j ) where k r / is the perforate constant of perforation with r the radius of tube, the density of air, the coefficient of viscosity. J is the Bessel function of the first kind and first order and J is the sae of zeroeth order. For the case of short tubes of finite length (i.e. perforated plates) an end correction should be taken account.. Ipedance odel for icro-perforated panels () As the perforation diaeter is reduced to sub-ilieter, the forulation in section. becoes the icroperforated proble. Ma. 5 first proposed an approxiate odel to calculate sound absorption of the icroperforated panel. The odel considers the icroperforated panel consisting of parallel connected tubes in which the ipedance of a single perforated hole as defined by Eq. (). 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 based on Morse Ingard s odel. 5, this yields. 6 where z r jx () 3 t k r k d cd 3 3 t (3) x t k d.85 c t (4) 36

3 For this forulation, perforation constant k is defined as k d 4 (5) where d is the pore diaeter, is the angular frequency, is the air density and is the coefficient of viscosity. The perforation ratio is given by d 4 b where b is the separation of separations. It should be noted that the forulation above is valid for 9.6 % perforation otherwise the effect of interaction between hole should be taken account. Moreover, the panel thickness is ade to coparable to pore diaeter in which the bending stiffness of panel becoes eaningless. This leads to the neglecting of flexibility of panel to be accepted. MPP absorbers require a backing cavity with the depth of cavity D as shown in Fig.. The air in the cavity acts as air-cushion to the vibration of air in the tiny holes of the MPP. Therefore, the vibration energy is daped and a relatively broadband sound absorption can be obtained accordingly. The cobined surface ipedance of the MPP and the air in the cavity zpp is thus expressed as D zpp r j x cot c (6) (7) 4r ( r) ( x cot D c).3 Ipedance odel for non-hoogenous perforation pattern To enhance the absorption bandwidth, a nonhoogenous perforation pattern is considered. This MPP consists of sub-mpp with different perforation paraeters particularly the perforation ratio. As discontinuity of surface ipedance is present for the non-hoogenous perforation pattern, the wave diffraction phenoena exists accordingly. This introduces excess sound absorption on the boundary surface. Takahasi. 6 treated this proble as a scattering wave of the boundary surface on which the discontinuity of ipedance exists. Raleigh odel. 7 can be used to find the solution of the scattered field. The incident plane wave i with unit aplitude expressed in ters of the velocity potential j t and tie factor oitted throughout is e i ( x, z) e (8) j( x z) (9) where sin and cos with and incident angle. A scattered wave s is expressed with unknown coefficient as j( x z) () ( x, y) e s where L and L the period of surface. k with The boundary condition represented by the specific acoustic adittance A of each surface at z is D b i s i s z jak, on z where () t A, x l A A, l x L () Fig.. Illustration of the MPP backed by air cavity For noral incidence, the sound absorption coefficient is defined as For this case, the respective A and A correspond to acoustic adittance of each MPP generally expressed as A z with z as defined in Eq. (). Substituting Eq. (9) and () into Eq. () gives ( ) j Ψ x L Ak e Ak (3) 37

4 Applying the one-diensional Fourier expansion and rearranging the result using an infinite set of siulatenous equation with respect to, this yields MPP Air cavity Cn Dn (4) Ak e j ( n ) x L dx L (5) MPP where L Cn Fig. 3. Sketch of specien Table. MPP paraeters of speciens L Dn Ak e j n x L dx L (6) The absorption coefficient of boundary surface is regarded as the energy fraction flowing outward in noral direction to surface. Considering this concept, the angle dependent is Re[ ] Ψ Material t () d () D () MPP acrylic MPP acrylic Results and Discussion Fig. 4 presents noral absorption of non-hoogenous perforation pattern. It is clear that two absorption peaks are pronounced fro analytical results at 753 Hz and 89 Hz as indicated by solid curve. The presence of those peaks is expected as two perforation ratios are considered in the MPP. Hence, two Helholtz resonance echaniss work when incoing wave iping on the MPP surface. (7) 3. Experiental Method The easureent of absorption coefficient of MPP was conducted using ipedance tube according to ISO (see Fig. ). 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 -.6 KHz can be obtained accordingly. (noral absorption coefficient) Frequency (Hz) Fig. 4. Noral absorption coefficient of non-hoogenous perforation pattern as cobination of.79% and.7 % perforation ratio. Fig.. Experiental setup used for easuring absorption coefficient of MPP The presence of the two peaks is also present in the easureent result as arked by circle as shown in Fig. 4. However, another peak is also seen fro the easureent around 5 Hz besides the peaks at 753 Hz and 89 Hz. This peak corresponds with fundaental ode of the panel rather than caused by the Helholtz resonance. This is so as the panel Detail of speciens can be observed fro Fig. 3 while the paraeters of each MPP are listed in Table. It should be noted the pore diaeter is chosen.9 as this is the sallest pore diaeter can be fored by the anufacturing technology found by authors. 38

5 vibration can not be totally oitted fro specien while such vibration is neglected fro analytical odel by assuing the panel is rigid instead on elastic one. Bravo et al. 9, addressed such phenoena in MPP. The large discrepancy in absorption is clearly seen at frequency of 85 Hz to 5 Hz where the easured absorption coefficient around.74 which is higher than that of the analytical result which is only found.44 as the lowest one. The results are getting closer in agreeent when the period of surface L reduces as indicated in Fig. 5. This approach is opted to allow representing the actual condition of easureent where the periodic surface of specien is quite sall in c disc. This result indicates that the effect of the excess sound absorption is ore significant as L get saller than the sound wavelength. (noral absorption coefficient) Frequency (Hz) Fig.5 The effect of reducing the surface periodic on the absorption coefficient. Copared with conventional MPP fro which single perforation ratio eployed, the use of non-hoogenous perforation pattern has a wider absorption bandwidth as shown in Fig. 6. It is found that the.79 % perforation ratio provides the half-absorption bandwidth of 373 Hz while that of.7 % perforation ratio is 5 Hz. Meanwhile, the non-hoogenous pattern as cobination of.79 % and.7 % perforation ratio can provide the half-absorption bandwidth of 7 Hz which is higher than octave. (noral absorption coefficient) Frequency (Hz) Fig. 6. Absorption bandwidth coparison between hoogenous perforation and non-hoogenous perforation 5. Conclusion Copared with conventional MPP fro which single perforation ratio eployed, the use of non-hoogenous perforation pattern is useful in extending the absorption bandwidth. Care need to be taken as the effect of excess sound absorption is ore significant when the ratio of periodic surface to sound wavelength get saller. Moreover, as panel vibration cannot be totally oitted particularly for non-rigid panel so that the absorption peak obtained are related to either Panel controlled or Helholtz controlled resonances. Acknowledgeents This research is funded by Institut Teknologi Bandung through Innovation research and research group progra. References. Fuchs HV, Zha X. Acrylic-glass sound absorbers in plenu of the Deutscher Bundestag. ApplAcoust 997;5: 7. Fuchs HV, Zha X. Micro-perforated structures as sound absorbers a review and outlook. ActaAcoust 6;9: Asdrubali F, Pispola G. Properties of transparent sound absorbing panels for innoise barrier. J AcoustSoc A 7;:4. 4. Wu MQ. Micro-perforated panels for duct silencing. Noise Control Eng 997;45: Maa DY. Theory and design of icroperforated panel sound-absorbingconstructions. SciSinica 975;7: Maa DY. Potential of icro-perforated panel absorber. J AcoustSoc A 998;4:

6 7. Qian, Y, et al. Investigation on icro-perforated panel absorber with ultra-icro perforations, Applied Acoustics, 3, 74, Jung, S S, Ki, YT and Lee, D H, Sound Absorption of Micro-Perforated Panel, Journal of the Korean Physical Society, 7, 5, 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,, 7, Sakagai, K, et al. Pilot studi on wideband sound absorber obtained by cobination of two different icrperforated panel (MPP) absorbers, Acoust. Sci. & Tech. 3, (9). Su, K.S, et al, Use of parallel Microperforated Panel Subabsorber for Noise Control in Ducts, ICSV3, Vienna, (6).. N. Atalla and F. Sgard, Modeling of perforated plates and screens using rigid frae porous odels, J. Sound Vib.33, 95 8 (7) 3. Wang, C, Cheng, L, Yu, G, Sound absorption of a icroperforated panel backed by an irregular-shaped cavity, J AcoustSoc A ;7:38 4. Crandall IB. Theory of vibrating systes and sound. New York: D. Van Nostrand& Co. Inc.; 97. pp P. M. Morse and U. Ingard, Theoretical Acoustics, McGraw-Hill, New York, 968, pp D. Takahashi, Excess sound absorption due to periodically arranged absorptive aterials, J. Acoust. Soc. A., 66, p. 5 (989). 7. Lord Rayleigh, "On the dynaical theory of gratings," Proc. R. Soc. London A 79, (97) 8. ISO 534-, Acoustics Deterination of sound absorption coefficient and ipedance in ipedance tubes Part : Transfer-function ethod 9. Teresa Bravo, Cédric Maury and CédricPinhède,Vibroacoustic properties of thin icro-perforated panel absorbers J. Acoust. Soc. A. 3, 789 () 4