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2 Applied Acoustics 71 (2010) Contents lists available at ScienceDirect Applied Acoustics journal homepage: Technical Note Design of a single layer micro-perforated sound absorber by finite element analysis Onursal Onen 1, Mehmet Caliskan * Department of Mechanical Engineering, Middle East Technical University, Ankara, Turkey article info abstract Article history: Received 7 February 2009 Received in revised form 5 July 2009 Accepted 10 July 2009 Available online 22 August 2009 Keywords: Micro-perforated absorber Composite materials Acoustic impedance Finite element method Micro-perforated sound absorbers with sub-millimeter size holes can provide high absorption coefficients. This paper presents results of work on the development of an effective single layer micro-perforated sound absorber from the commercial composite material Parabeam Ò with micro diameter holes drilled on one side. Parabeam Ò is used as a structural material made from a fabric woven out of a E-glass yarn and consists of two decklayers bonded together by vertical piles in a sandwich structure with piles (thick fibers) woven into the decklayers. The paper includes, the analytical model developed for prediction of absorption coefficients, finite element solution using commercial software MSC.ACTRAN and experimental results obtained from impedance tube measurements. A simple optimization is performed based on the developed models to obtain an efficient absorber configuration. It has been anticipated that several different and interesting applications can be deduced by combining structural and sound absorption properties of this new micro-perforated absorber. Ó 2009 Elsevier Ltd. All rights reserved. 1. Introduction Micro-perforated sound absorbers are basically of metal, plastic or wooden panels (or membranes) with drilled holes of minute dimensions, placed with an air gap in front of a rigid wall backing or another perforated panel. Single layer micro-perforated absorbers are the most basic type, consisting of a micro-perforated panel, air cavity and a non-perforated backing. Effective absorption covering a bandwidth of 5 6 octaves can be obtained by proper adjustment of parameters in a single layer micro-perforated absorber. Their major advantages lie in the flexibility in design and variety of materials. Also, high sound absorption coefficients can be achieved with relatively low thicknesses compared with porous and fibrous absorbers possessing similar absorption characteristics. Micro-perforated absorbers have been investigated as clean and health-friendly absorbing materials for almost two decades as an alternative to traditional fibrous and porous absorbers. Micro-perforated absorbers are resistant to moist, oil and dust and they can be built up from any rigid material available in thin plates. They may be painted or other types of surface finishes may be applied to provide aesthetic quality. * Corresponding author. Present address: Makina Mühendisligi Bulumu, Orta Dogu Teknik Universitesi, Ankara, Turkey. Tel.: ; fax: addresses: onursalonen@tai.com.tr (O. Onen), caliskan@metu.edu.tr (M. Caliskan). 1 Present address: TUSAS-Turk Havacilik ve Uzay Sanayii A.S., Fethiye Mahallesi, Havacilik Bulvari, No: 17, Kazan-Ankara, Turkey. Tel.: x7614; fax: In this particular study, it is aimed to develop an effective single layer micro-perforated absorber from the commercial composite material Parabeam Ò with micro diameter holes drilled on one side. Parabeam Ò is a 3D glass fabric, which is woven out of E-glass yarn and consists of two decklayers bonded together by vertical piles in a sandwich structure [1]. Mechanical properties of Parabeam Ò are listed in Table 1. These piles (or namely thick fibers) are woven into the decklayers, thus forming an integral sandwich structure. The curing process by use of a thermo-set resin results in a light-weight and strong sandwich laminate structure. The cured fibers in the mid-layer is distributed and oriented inside the layer in such a way to form that looks like an eight shaped structure, which can be seen in Fig. 1 [1]. In this specific work, ParaGlass 18 is the specific product chosen for design of the micro-perforated absorber. The thickness of the fibrous layer within the gap between two decklayers is 18 mm and the thickness of the micro-perforated layer is 1 mm. Parabeam Ò has a wide application area in marine and automotive industries as well as in construction sector. Parabeam Ò is anticipated to be a good candidate for a micro-perforated absorber as an integral and easy to process composite structure, which naturally solves the problem of supporting the micro-perforated layer by thick fibers between two decklayers. A simple schematic of the micro-perforated absorber developed from Parabeam Ò is given in Fig. 2. Analytical modeling is the first tool considered for fast and easy prediction of absorption characteristics. In this study, the analytical model employed basically relies on the developed models available in literature which are usually verified by experimental studies in several different applications and configurations. However, there is no applicable analytical model for such an air gap X/$ - see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:116/j.apacoust

3 80 O. Onen, M. Caliskan / Applied Acoustics 71 (2010) Nomenclature t n1 t n2 A p p 1 p 2 particle velocity at node 1 (m/s) particle velocity at node 2 (m/s) transfer Admittance (m 4 s/kg) pressure at node 1 (Pa) pressure at node 2 (Pa) R p,x p components of complex transfer p admittance j unit imaginary number (= ffiffiffiffiffiffiffi 1 ) e perforation ratio f frequency (Hz) g dynamic viscosity of air (Pa s) q 0 density of air under standard conditions (kg/m 3 ) l thickness of an arbitrary absorber layer (m) r hole radius (m) Dl correction factor (m) a hole spacing (m) Z hole specific Acoustic impedance of a hole (kg/m 2 s) x angular frequency (rad/s) h perforate constant J 0 Bessel s equation of type 1, order 0 J 1 Bessel s equation of type 1, order 1 Z perf specific Acoustic impedance of a perforated layer (kg/ m 2 s) Z total total specific acoustic impedance at the top of an absorber assembly (kg/m 2 s) Z fibrous specific acoustic impedance at the top of Parabeam Ò (kg/m 2 s) R reflection coefficient c speed of sound in air (m/s) a normal incidence absorption coefficient containing fibers like those of Parabeam Ò. So, finite element modeling is performed not only for comparison with the analytical model and more realistically modeling the whole problem, but also for estimation of absorption characteristics, namely acoustic Table 1 Mechanical properties of ParaGlass 18 (without perforations) [1]. Weight-fabric (kg/m 2 ) 1.72 Weight-laminate (kg/m 2 ) 3.61 Compressive strength (N/mm 2 ) 0.9 Shear strength (N/mm 2 ) 0.1 Shear modulus (N/mm 2 ) 1.8 Bending stiffness (Nm 2 ) 55.9 Fig. 1. Side view of Parabeam Ò with eight shaped fibers [1]. impedance of the air gap with thick fibers. Commercial acoustic finite element software MSC.ACTRAN is used for modal solution of the problem by defining proper boundary and interface conditions. Finite element model is instrumental for prediction of properties of the layer with air and fibers for use in the analytical model. Measurements are performed on a standing wave tube setup. Predictions and measurements of normal incidence absorption coefficients are carried in 1/3 octave-band center frequencies between 125 Hz and 2000 Hz, because of the limitations of the impedance tube used. An optimization is performed to obtain effective configurations for improvement of absorption performance of Parabeam Ò using the analytical model. The design and optimization is based on variations of hole diameter and hole spacing. Maa [2,3] was the first researcher who proposed developing effective perforated absorbers by reducing hole diameters to sub-millimeter size. Starting from Crandall s [4] short tube wave equation, Maa laid the theory of micro-perforated absorbers using electro-acoustical analogy. Various efforts were done to improve the theory of micro-perforated absorbers using electro-acoustical analogy [5 9]. Unfortunately, electro-acoustical analogy established by Maa is limited to absorbers composed only of air cavity and perforated layers. Various approaches were exercised for prediction of absorption properties in the existence of some other materials and structures like fibrous and porous absorbers either with planar or complex geometries, thin films and honeycomb structures [10 18]. Effective predictions were achieved with planar layers of porous absorbing materials used [14,15]. For complex problems, finite element modeling was applied with detailed physical modeling of the sample of a problem [16] or by introducing complex boundary layer conditions to simplify the model [17,18]. 2. Theory and analytical modeling 2.1. Acoustic impedance of micro-perforated layer Fig. 2. A simple schematic of the micro-perforated absorber developed from Parabeam Ò. The acoustic impedance at the top of a micro hole whose length is short compared with the wavelength of the sound wave is firstly proposed by Maa [2] and recently modified by Cox and D Antonio [8] with additional terms for radiation resistance for an orifice and end correction for the radiation reactance of the hole. Acoustic impedance of a typical micro-perforated layer can be obtained by dividing the corrected impedance of hole by the perforation ratio e, where x is the angular frequency, l is the length of the hole (also equal to thickness of the perforated layer), J 0 and J 1 are the Bessel s

4 O. Onen, M. Caliskan / Applied Acoustics 71 (2010) Acosutic Impedance [N/s] Parabeam - Real Parabeam - Imaginary Air Cavity - Real Air Cavity - Imaginary Freq. [Hz] Fig. 3. Real and imaginary parts of acoustic impedance at the top of fibers obtained from finite element modeling and acoustic impedance of an air cavity with same height of 18 mm. equations of first type and of order zero and one, respectively, and perforate constant h. Z perf ¼ jxq " 0 l 1 p 2 e h ffiffiffiffiffi J p 1ðh ffiffiffiffiffi # pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi j Þ p j J 0 ðh ffiffiffiffiffi 2xq þ 0 g þ j1:7xq 0 r ð1þ j Þ 2e e rffiffiffiffiffiffiffiffiffi h ¼ r ð2þ e ¼ pr2 a 2 xq 0 g Resulting total acoustic impedance at the top of the micro-perforated layer is simply the sum of acoustic impedance at the top of fibrous layer Z fibrous and acoustic impedance of micro-perforated layer Z perf as: Z total ¼ Z fibrous þ Z perf where Z fibrous is obtained by finite element modeling which is given in Fig. 3 and described in detail in Section 3.2. The reflection coefficient R and the resulting normal incidence absorption coefficient a can then be calculated as: R ¼ Z total q 0 c Z total þ q 0 c a ¼ 1 jrj 2 3. Finite element modeling Prediction of the normal incidence absorption coefficients considering the effect of fibers inside Parabeam Ò can only be obtained by the finite element solution, because there is no analytical or empirical model in literature exists for impedance of such a layer which contains thick fibers and very high void ratio. Common empirical models for fibrous materials are valid for very thin fibers and low void ratios [8]. In the finite element modeling procedure, a simplified three-dimensional solid model of a small portion of the absorber and air at the top of the micro-perforated layer is developed and meshed in MSC.PATRAN with the acoustic elements of the MSC.ACTRAN material library. Air cavity inside the Parabeam decklayers and air placed at the top of the perforated layer is meshed with fluid elements and thick fibers are modeled with elastic solid elements [19]. Modal solution employing the finite element model is performed by one of the built-in solvers of MSC.ACTRAN, Sparse[19]. Two finite element models are built separately, one for prediction of the acoustic impedance at the top of the fibers (for use in ð3þ ð4þ ð5þ ð6þ the analytical model) and the other for determination of resulting normal incidence absorption coefficients of different absorber configurations. A MSC.ACTRAN boundary layer condition is applied to model, by implementing an interface definition simulating the impedance of the micro-perforated layer onto the model, rather than directly modeling the micro holes and air around the holes. This method of modeling by defining such an interface utilizing Mechel s formula for micro-perforations is proposed by MSC.AC- TRAN [19]. It avoids fine meshing, which is time consuming both in modeling and solution processes. Also, the defined interface for use with different micro-perforation configurations evades the necessity of rebuilding of model for each configuration. Different samples and an optimized case are analyzed by only changing the required lines of interface definition in the analysis input file Overview of finite element models A model with a simplified geometry is built up by mainly keeping the ratio of total fiber volume to the volume of the whole cavity around 15%. Care has been exercised to keep the profile and crosssection of modeled fibers as close as to the actual fibers. A simple overview of the model is illustrated in Fig. 4. The finite element model is composed of 50,592 three-dimensional (3D) elements of air and fibers. In the model, three types of elements are employed including 8-node 3D fluid and 3D elastic solid elements (HEX8), 6-node 3D fluid elements (WEDGE6) and 4- node two-dimensional (2D) surface elements (QUAD4). There are 46,288 3D fluid elements with properties of air including 200 WEDGE6 and 46,088 HEX8 elements and there are D elastic solid elements with properties of fiber including 96 WEDGE6 and 3912 HEX8 elements. Also, there exist D QUAD elements of interfaces and modal excitation [19]. The absorber model built corresponds to a sample size of 6mm 9.6 mm and thickness of 18 mm. Average edge length of the elements is taken around 0.5 mm. This sample size is chosen by consecutive runs of finite element solution of samples of different sizes using augmentation of the same pattern. Results are observed by increasing the sample size step by step. It has been certified that after this size, there is no significant change in results. Modal Basis Property in Analytic Module of the MSC.ACTRAN is used as a modal excitation to the model [19]. All the free faces in the model are reflective (non-absorptive), apart from the faces through which the interface is defined for simulating micro-perforation effect. In the Model Basis, a modal acoustic excitation in

5 82 O. Onen, M. Caliskan / Applied Acoustics 71 (2010) Fig. 4. A general view of finite element model with whole model (a), a closer view to absorber (b) and fibers modeled inside the cavity (c). terms of duct modes is introduced to the system. Only the longitudinal mode of the cavity is excited, very similar to the propagation inside an impedance tube. The resulting duct modes in the cavity are identified in terms of transversal and longitudinal wave numbers, and average modal intensities of the incident and reflected waves are computed. MSC.ACTRAN solves for the resulting duct modes of the modal excitation input to model. The resulting sound field in the duct is a combination of the incident and reflected sound field, which are also defined as linear combinations of duct modes. The result file outputs the average intensity of the reflected wave. The absorption coefficient can directly be computed by multiplying the average intensity by the cross-sectional area, when the amplitude of the input excitation is specified as 1. Reflection coefficient R and the absorption coefficient a for the absorber can then be calculated. This finite element model is also used to obtain acoustic impedance at the top of fibers of Parabeam Ò just below the micro-perforated layer. There exist several empirical models for prediction of surface acoustic impedance of fibrous materials. Such models are not applicable to mid-layer of Parabeam Ò with thick fibers and a total void ratio around 85% for the whole layer. A second model very similar to the model described above is built for determination of the surface acoustic impedance at the top of the fibrous layer Parabeam Ò. Fibers, air cavity between the fibers and air at the top of the fibers are modeled as if the top plate of Parabeam Ò is removed, in the absence of the gap and the interface for the micro-perforated layer. Several field points are defined in the input file of the finite element model for determination of the acoustic impedance. The points are placed at nodes corresponding to the bottom of micro-perforated layer of Parabeam Ò. Complex acoustic pressure and complex particle velocity components in x, y and z directions at these field points are stored separately, in the output file of the finite element solution. Complex particle velocity can be obtained by multiplying the complex displacement values obtained from the output file by jx. Acoustic impedance, at the top of the fibrous layer of Parabeam Ò can be evaluated through dividing averaged complex pressure by the averaged particle velocity at the designated field points. The finite element model for acoustic impedance prediction is composed of 50,976 3D elements including 296 WEDGE6 and 50,680 HEX8 elements and fibers and also 384 2D QUAD elements [19] with modal excitation corresponding to a sample absorber size of 6 mm 9.6 mm and thickness of 18 mm. Average edge length of the elements is still around 0.5 mm. The acoustic impedance at the top of fibers and the acoustic impedance of an air cavity with same height of 18 mm is calculated and illustrated in the Fig. 3, with real and imaginary parts presented separately in 1/3 octave-band center frequencies. It is observed that the fibrous cavity between decklayers with 85% void ratio acts very much like an air-filled cavity possessing almost purely imaginary acoustic impedance (no acoustic resistance). The high void ratio and resulting distance between fibers avoids dissipation by boundary layer friction. Fibers act as a minor modification of the cavity with very little difference between imaginary parts of acoustic impedance between air-filled cavity and cavity with such fibers Simulation of micro-perforations by Mechel s Formula Computations involving finite element models of micro-perforated plates can be very time consuming even in the perspective of small sample sizes with evenly spaced holes. Modeling each hole requires enhancement of the number of elements and with numerous holes, and also effort and time needed for modeling and solution considerably. Hence, apart from modeling each hole, the effect of micro-perforations is simulated by a transfer method utilizing Mechel s formula [20]. The interface defined includes two coupling surfaces with one placed at the upper surface of the air elements inside Parabeam Ò and second surface being placed at lower surface of air elements at the top of micro-perforated layer physically. Be-

6 O. Onen, M. Caliskan / Applied Acoustics 71 (2010) Table 2 Sample configurations. Sample # a (mm) r (mm) A p ¼ 1=ðR p þ j X p Þ R p ¼ 1 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 16pfgq e 0 1 þ l 2r X p ¼ 2 e pfq 0ðl þ 2DlÞ ð10þ ( Dl ¼ 0:85r 1 2:34 r a 0:668r 1 1:90 r a 0 < r < 0:25 a 0:25 < r < 0:5 a ð8þ ð9þ ð11þ tween these two coupling surfaces, the relations resulting from micro-perforation are defined by introducing the transfer admittance calculated from Mechel s formula. Mechel s formula utilizes the acoustic relationship between two concurrent nodes one placed at one surface of the micro-perforated plate and one at the opposite surface of the micro-perforated plate through which the interface defined, by the following set of equations [20]: t n1 t n2 ¼ Ap A p A p A p p1 p 2 where t n1 and t n2 are normal particle velocities at nodes 1 and 2 whereas p 1 and p 2 are complex pressure values at these nodes through which the interface is defined. A p represents the transfer admittance, as a function of Rp and Xp which are also functions of: the complex constant j, frequency f, dynamic viscosity g, density of air at standard conditions q 0, hole spacing a, hole radius r, perforation ratio e (which is also a function of a and r),length of hole (or thickness of perforated plate) l and correction factor Dl. ð7þ 4. Results Four samples of different micro-perforation configurations are prepared for verification of the models. Distance between holes in the square grid a and radius of holes r are varied apart from fixed parameters, that are, thicknesses of the fibrous layer t f (=18 mm) and of the micro-perforated layer t p (=1 mm). These sample configurations are given in Table 2. Absorption coefficient measurements are also performed for verification of models using a standing wave impedance tube setup with samples of 69 mm in diameter. Normal incidence absorption coefficients of the samples are measured according to related standard, ISO :1998 [21]. The impedance tube measurements are performed on a Hilton B400 Acoustic Insulation Test Apparatus. The set up involves a clear rigid plastic impedance tube with the upper frequency limit for the impedance tube used is estimated as 2500 Hz, thus upper frequency limit is chosen as 2000 Hz. The predictions and measurements in 1/3 octave-band center frequencies up to 2000 Hz are illustrated in Figs Fig. 5. Results of predicted and measured normal incidence absorption coefficients for Sample 1: analytical model (diamond), finite element model (square), impedance tube measurements (triangle). Fig. 6. Results of predicted and measured normal incidence absorption coefficients for Sample 2: analytical model (diamond), finite element model (square), impedance tube measurements (triangle).

7 84 O. Onen, M. Caliskan / Applied Acoustics 71 (2010) Results displayed in Figs. 5 8 show that, predicted values show fairly good agreement with measured ones of normal incidence absorption coefficients. A slight shift of frequencies where absorption peaks occur is observed about by one 1/3 octave in Figs. 5 and 6. On the other hand, both finite element and analytical method predictions peak out at a lower frequency by two 1/3 octaves. Best agreement between predictions and measurement is obtained in Fig. 8 with no shift in frequencies at which peak absorption takes place. General characteristics of absorption curves are similar, especially for the Samples 1 and 2. Also, for Samples 3 and 4, absorption characteristics are at resemblance. As a design methodology, it is quite evident that, the analytical model developed is the quickest tool for the design of micro-perforated absorbers. Analytical model can firstly be used by several runs for quick and primary design, and then the resulting absorption coefficient values can be further investigated in detail using fi- Fig. 7. Results of predicted and measured normal incidence absorption coefficients for Sample 3: analytical model (diamond), finite element model (square), impedance tube measurements (triangle). Fig. 8. Results of predicted and measured normal incidence absorption coefficients for Sample 4: analytical model (diamond), finite element model (square), impedance tube measurements (triangle). Fig. 9. Results of predicted and measured normal incidence absorption coefficients for the optimized absorber: analytical model (diamond), finite element model (square), impedance tube measurements (triangle).

8 O. Onen, M. Caliskan / Applied Acoustics 71 (2010) nite element model and impedance tube measurements. However, the analytical model is shown to underestimate absorption coefficients for four samples considered in the study. Optimization is performed by use of a spreadsheet is developed in MS EXCEL for obtaining a feasible and effective configuration of micro-perforated absorber from Parabeam Ò. The routine is used to optimize the absorption coefficient values by varying the parameters hole spacing and hole diameter, which are limited by manufacturing tools and techniques. The optimized values for hole spacing and hole diameter are obtained by several trials. In the case of Parabeam Ò, punching and hot drilling results in degradation of structure and poorly finished holes and surface. Drilling the holes by laser is not possible. Among common manufacturing techniques, conventional drilling is employed as the most feasible way. Diameter of the holes must be, at least, 0.5 mm due to physical constraints by this technique with common tools. This simple optimization technique has yielded an optimum configuration with hole spacing of 13 mm and hole radius of 0.4 mm. Predictions and measurements for this configuration are illustrated in Fig. 9. It should be also noted that the optimum case is observed through several trials to be the only possible optimum solution with the fixed gap thickness of 18 mm and constant top micro-perforated plate thickness of 1 mm. The hole spacing and hole diameter appear to have limited effect on the absorption characteristics of absorber with this specified air gap of 18 mm. 5. Conclusions Results obtained from analytical model, finite element model and impedance tube measurements show fairly good agreement. With such an agreement between the results shown especially between finite element model and measurements, it can be concluded that finite element model developed is able to represent the physics of the micro-perforated absorber made from Parabeam Ò almost properly. Analytical model, utilizing the impedance at the top of the fibers is also anticipated as a safe and quick design tool for the absorber. However, the absorption coefficients resulting from all three methods show that the micro-perforated absorber built from Parabeam Ò is effective in a relatively narrow frequency band covering at most 3 octaves with the current configuration, which is mainly limited to such a range by the thickness of the air layer with fibers below the micro-perforated plate. The effect of fibers in the middle layer of Parabeam Ò is studied by the calculated impedance values at the top of the fibers, through the finite element model developed. It is made clear that presence of fibers do not considerably affect the resulting acoustic resistance of the layer. This configuration of fibers within decklayers produces almost purely imaginary impedance values. Impedance characteristics obtained from the finite element model are very close to that of a common enclosed air layer as illustrated in Fig. 3. Fibers are discovered to modify the imaginary part of the impedance characteristics. The major function of fibers seems to be structural rather than acoustical for such high void ratio measured for this particular configuration of the Parabeam. An average constant absorption coefficient value around 0.15 is obtained for each sample including the optimized sample from the measurements at the frequencies up to 250 Hz. There is not much possibility to obtain such low frequency absorption. It can be anticipated that this result is due to Parabeam Ò itself. In the optimization procedure, it is clearly seen that an absorber covering a wider band is not too much possible by the nature of Parabeam Ò. As observed from existing literature, an effective wideband micro-perforated absorber requires smaller thickness of micro-perforation layer and smaller hole diameters. These two parameters should also be chosen close to each other. It is quite evident that the absorption performance that can be achieved by this configuration of Parabeam Ò is mainly constrained by the distance between the two decklayers. High void ratio around 85% avoids the chamber between decklayers contribute for acoustic resistance. This problem can possibly be solved by lowering the void ratio, thus increasing the fiber ratio. Acknowledgements Aydın Kuntay of BIAS Inc. of Turkey, Jonathan Jacqmot of FFT Technologies Pty. Ltd. and Jaap Jan Kleef of Parabeam Ò 3D Glass Fabrics B.V. are gratefully acknowledged for their support and assistance. References [1] Parabeam Product Family Brochure, Parabeam Ò 3D Blass Fabrics B.V. [2] Maa DY. Microperforated-panel wideband absorbers. Noise Control Eng J 1987;29(3): [3] Maa DY. Potential of microperforated panel absorber. J Acoust Soc Am 1998;104(5): [4] Zwikker C, Kosten CW. Sound absorbing materials. New York: Elsevier Publishing Company, Inc.; [5] Kang J, Fuchs HV. Predicting the absorption of open weave textiles and microperforated membranes backed by an airspace. J Sound Vib 1999;220: [6] Kang J, Fuchs HV. Effect of water-films on the absorption of membrane absorbers. Appl Acoust 1999;56: [7] Sakagami K, Morimoto M, Koike W. A numerical study of double-leaf microperforated panel absorbers. Appl Acoust 2006;67: [8] Cox TJ, D Antonio P. Acoustic absorbers and diffusers: theory, design and application. Oxon: Spon Press; [9] Sugie S, Yoshimura J, Ogawa H. Absorption characteristics of fibrous material covered with perforated facing and film. Acoust Sci Technol 2006;27(2): [10] Lee FC, Chen WH. Acoustic transmission analysis of multi-layer absorbers. J Sound Vib 2001;248(4): [11] Godbold O, Kang J, Soar R, Buswell R. From MPA to strategically designed absorbers using solid freeform fabrication techniques. In: 19th International congress on acoustics Madrid; September [12] Yairi M, Sakagami K, Morimoto M. Double leaf microperforated panel space absorbers an experimental study for further improvement. In: 19th International congress on acoustics Madrid; September [13] Toyoda M, Takahashi D. Sound insulation characteristics of a micro perforated panel with a subdivided air layer. In: 19th International congress on acoustics Madrid; September [14] Zou J, Shen Y, Yang J, Qui X. A note on the prediction method of reverberation absorption coefficient of double layer micro-perforated membrane. Appl Acoust 2006;67: [15] Chongyun Z, Quibai H. A method for calculating the absorption coefficient of a multi-layer absorbent using the electro-acoustic analogy. Appl Acoust 2005;66: [16] Chen H, Lee FC, Chiang DM. On the acoustic absorption of porous materials with different surface shapes and perforated plates. J Sound Vib 2000;237(2): [17] Lee FC, Chen WH. On the acoustic absorption of multi-layer absorbers with different inner structures. J Sound Vib 2003;259(4): [18] Panteghini A, Genna F, Piana E. Analysis of a perforated panel for the correction of low frequency resonances in medium size rooms. Appl Acoust 2007;68: [19] MSC.ACTRAN manual. FFT Technologies; [20] MSC.ACTRAN Lecture Notes: Mechel s Formula. [21] ISO :1998. Acoustics determination of sound absorption coefficient and impedance in impedance tubes part 1: method using standing wave ratio.