INFLUENCE OF THE PRESENCE OF LINING MATERI- ALS IN THE ACOUSTIC BEHAVIOUR OF PERFORATED PANEL SYSTEMS

INFLUENCE OF THE PRESENCE OF LINING MATERI- ALS IN THE ACOUSTIC BEHAVIOUR OF PERFORATED PANEL SYSTEMS Ricardo Patraquim Castelhano & Ferreira S.A., Av. Colégio Militar, nº 24A Benfica, Lisboa, Portugal. e-mail: patraquim@castelhano-ferreira.pt Luís Godinho, António Tadeu, Paulo Amado-Mendes CICC Centro de Investigação em Ciências da Construção, Dep. Eng. Civil da FCTUC da Universidade de Coimbra, Rua Luís Reis Santos, Pólo 2 da FCTUC, 33-788 Coimbra, Portugal. e-mail: lgodinho@dec.uc.pt; tadeu@dec.uc.pt; pamendes@dec.uc.pt Perforated panels are a common technical solution for the acoustical conditioning of closed spaces. The most usual solutions of this type make use of a perforated surface, made of plasterboard or wood, separated from a rigid structure (wall or slab) by an air cavity with a given thickness. Within this cavity, porous materials may be included to improve the absorbing effect of the system. The behaviour of these systems is, thus, complex, combining the effect of the porous absorber (embedded in the cavity) and of an acoustic resonator (originated by the combined effect of the panel s perforation and of the cavity). In many applications, the back of the panels is lined with fabric, whose characteristics can strongly influence the acoustic behaviour of the system. In this work, the authors analyze the influence of this lining in the absorbing properties of the system, performing experimental tests with different types of fabric and evaluating the acoustic absorption in the presence of different system configurations. To better understand the obtained results, the tested fabrics are also characterized in what concerns their density and air-flow resistivity, which are known to be relevant to their acoustic behaviour. The results obtained in the experimental tests are also compared with theoretical predictions, attempting to understand the accuracy of those models for the prediction of the acoustic absorption of such complex systems. 1. Introduction In order to enhance the sound absorption area of the room surfaces, ceilings and walls are usually coated using perforates (perforated panels), with an air cavity defined by the gap between their surface and the rigid wall. In these systems, the process of sound absorption is caused by the resonance of the air mass contained in the holes (bottlenecks) in a resonant cavity - as a Helmholtz resonator. According to Ingard and Bolt [1], the effect of perforated panels corresponds to an addition of mass reactance of air in each hole to the normal surface impedance under the perforated facing, whereas its acoustic resistance is negligible (for perforated panels with holes of large diameter or extra wide slots, above the viscous boundary layer). So, the back cavity under the perforated panels ICSV18, Rio de Janeiro, Brazil, 1-14 July 211 1

should be filled with porous absorbent materials in order to increase the sound absorption of the system. In many applications, the back of the perforated panels is lined with fabric (thin acoustic nonwoven), whose characteristics can strongly influence the acoustic behaviour of the system. In fact, there are few works studying the influence of this thin acoustic nonwoven on the back of perforated panels with a relatively high thickness (12mm) and a low fraction of open area (commonly between 3% and 15%). The main reason that triggered this work was the fact that perforated panels were tested in three different laboratories, and none showed a characteristic behaviour of a resonator Figure 1. Those panels (designated here as type A, and described in further detail in section 3), included a nonwoven textile glued on their back. These results indicated that, in the development and implementation of these systems, it becomes important to assess the factors that can influence their acoustic performance. Figure 1. First lab tests no resonance peak, no significant differences Since the sound absorption of the perforates is strongly dependent on the mounting conditions, an experimental parametric study is performed, in order to evaluate, using a reverberation room and according to the ISO 354:23 standard, the dependence of the sound absorption in wooden panels with circular holes on the following parameters: usage of thin acoustic nonwoven as a resistive layer; use of mineral wool on the back layer of air; small variation of the open area of the panels. A theoretical analysis is also performed, following the methodology compiled on [2], based on the works of Morse, Bolt, Ingard and Crandall [3-6]. Following this introduction, the next section presents the definition of perforation impedance and some existing formulations for computing the sound absorption of the system; Section 3 describes the experimental setups and procedures; Section 4 gives the results of sound absorption for the different tests; in Section 5, a comparison between experimental measurements and theoretical predictions is presented; finally, the concluding remarks are presented in Section 6. 2. Modelling sound absorption of perforated panels The methods of modelling the sound absorption of perforated panels are based on the conversion of acoustic impedance of a single hole in an average value corresponding to the open area of the panel. The perforated panel is considered as a set of short tubes of identical length to the thickness of the panel, and the non-perforated material very dense and rigid, and therefore perfectly reflective. It is further assumed that the wavelength of the sound that propagates is sufficiently large compared with the cross-sectional dimension of the tube (i.e., hole). This method includes the terms due to viscosity of air, radiation (from a hole in a baffle), interactions between holes and the effects of reactance of the cavity. 2

These acoustic systems are studied using the concept of the transfer matrix method, which determines the acoustic impedance along the normal direction of an interface of a material using the continuity of particle velocity (on both sides of the interface) and knowing the acoustic properties of the medium (characteristic impedance, c a, and the wavenumber or propagation constant, k a ). When the nonwoven acoustic textile is placed right behind the perforated panels, then the resistance behaves as though it actually occurs in the openings. According to Ingard and Bolt [1] and to Vér and Beranek [7], acoustic resistance of the absorber is increased to σ t ε (where σ is the flow resistivity of the nonwoven acoustic textile, t is its thickness and ε is the fraction of open area or porosity of the perforated panel). From the knowledge of the acoustic impedance is possible to determine the sound absorption coefficient and then estimate its value for diffuse field. The arrangement of the absorber is shown in Figure 2. We consider the system as locally reacting, assuming that the sound in the absorber can propagate only perpendicularly to the plane of the interface. t d 1 D=2r air space c, k, Mineral wool σ a, k a, ca s 3 2 1 Perforated Panel Thin acoustic nonwoven y x Rigid Wall Figure 2. Arrangement of absorber for prediction At Point the normal surface impedance is infinite ( wall. The normal surface impedance at point 1, ( ) s1 ca a 1 s = ), since it is considered a rigid = i cot k d (1) where c a is the characteristic impedance of the mineral wool, and k a is the wavenumber (or propagation constant). So, to use this model is necessary to have the mineral wool characterized in respect of these physical quantities by means of measurement, as reported by Cox and D Antonio [8], or using an empirical predictions from regression analyses of measured data. As written above, the normal surface impedance at point 2 is: t t = s + σ σ i cot( ) 2 s 1 c k a ad1 ε = + ε (2) and the surface impedance of the system (point 3) along the normal direction is: = + (3) s3 s panel s 2 where the normal surface impedance of a perforated panel corresponds the idea of the impedance of one hole (tube) is converted into a single averaged value corresponding to the fraction of perforated open area and is given by: stube s = (4) panel ε 3

And, according with Crandall [6], the impedance of one hole (tube) is ( s ) ( k r) J ( k r) 1 2 2 J1 k r 2 2r s s λ i ωρ s l 1 2 2 ωρη ρ c π i ωρ δ = + + + tube where ρ is the air density, ω is the angular frequency, l is the thickness of the perforated panel, r is the radius of the circular hole, η is the coefficient of air viscosity, λ is the wavelength, J n is the n th order of Bessel function and ks = iωρ η is the Stokes wave number. The second term on the right hand side is the end correction, which also accounts for the interaction between the orifices via the expression (see [7] and [8]) 16r δ = 1 1.47 ε +.47 3π 3 ε The sound absorption coefficient for a sound incidence angle θ with respect to the normal of the surface is given by ( ) 2 α θ = 1 R( θ ) (7) where R( θ ) is the reflection coefficient that can be expressed in terms of the normal surface impedance s 3 of the system: R( θ ) = s3 s3 cosθ cosθ+ where = ρc is the acoustic impedance of the air. To estimate the sound absorption coefficient for random incidence, i.e. diffuse field, the authors follow the proposal Vér and Beranek in [7], which state that there is a very close correlation between the calculation of α ( θ) from Eq. (7), for incidence of θ = 45 and more complex approaches proposed by other authors for diffuse incidence. 3. Experimental setup and characteristics of the absorbing system To assess the sound absorption coefficient of the perforated panels under diffuse sound incidence, standardized laboratory tests were performed in a reverberation chamber, following the procedures specified in the ISO 354:23 standard. In this section, a brief description of the test conditions is given, together with some details concerning the tested sound absorbing systems. To perform the sound absorbing tests, a large size reverberant chamber, with a total volume of 23.98m 3 and a floor area of 5.85m x 5.85m, existing in the laboratory infrastructure of ITeCons, at the University of Coimbra, was used. This reverberant chamber has previously been prepared in order to fulfil the requirements of the ISO 354 standard, namely in what concerns the creation of a diffuse field and the limitation of the reverberation times of the empty chamber. A detailed description of the testing conditions within the chamber can be found in [9], and for the purpose of this work it is enough to just highlight that 15 sound polycarbonate diffusers, with convex and concave shapes, totalizing 3 m 2, were used to ensure the correct behaviour of the chamber. Each test sample had an area of approximately 1.8m 2, and consisted of perforated wooden panels over mounted over the floor in a E-5 configuration, incorporating a small resonant cavity between the panel and the floor. The perforated wooden panels were 12 mm thick, with circular holes with a diameter of D=8 mm, equally spaced 32 mm along the two orthogonal directions (see Figure 3). To allow the use of an adequate test area, panels with 6 mm x 6 mm were used, (5) (6) (8) 4

forming a grid with 6 by 5 individual panels. These panels were supported by a light wooden structure, mounted over the floor, consisting of an external frame with 4 wooden beams, complemented by internal beams equally spaced 6 mm, disposed along the smaller dimension. Two different types of panels were used, designated as A and B, corresponding to different global perforation areas. In terms of global perforated area, although the hole diameter and spacing remain constant between all solutions, panel B presents an additional row of holes along each side of the panel, which originates a slight increase in the perforated area. Thus, in the case of panel A, this area is approximately 3.57% of the panel area, while in panel type B the perforation corresponds to 4,52% (see Figure 3). 6 32 28 32 32 32 6 28 D=8 a) Figure 3. Perforation scheme of the different panels (dimensions in mm): a) type A; b) type B. D=8 b) The support wooden structure is approximately 4 mm thick, which ensures the presence of a small air-gap with that thickness bellow the panels. Three different solutions were tested, corresponding to: an air-gap, without any absorbing material; a cavity filled with a mineral wool with a density of 4 kg/m 3 ; a cavity filled with a mineral wool with a density of 7 kg/m 3. On the back of the perforated panels, a nonwoven acoustic textile mat was used, which is a very usual constructive solution in these type of panels, mostly to avoid the emission of small particles from the mineral wools. For the purpose of this work, three types of textile mats were used, which will here be designated as M1, M2 and M3. M1 and M2 correspond to nonwoven textile mats that are of current use on the back of thin micro perforated metal sheets, in order to improve their sound absorption; M3 is a standard nonwoven textile mat that is commonly used on the back of wooden or plasterboard perforated panels. Although no precise data could be obtained for these mats, it was possible to perform a brief laboratory characterisation, evaluating their air-flow resistivity, an essential parameter to incorporate the effect of these mats in the theoretical models of section 2. These values were of 79 MKS rayl, 71 MKS rayl and 27 MKS rayl for the M1, M2 and M3 nonwoven, respectively. 4. Experimental results An experimental parametric study was performed to evaluate the influence of the different variables identified before in the behaviour of the system. Figure 4a illustrates the sound absorption obtained for the tested system with panels of type A, and with the cavity filled with mineral wool (with density of 7 kg/m 3 ). Results for the three nonwovens are presented, together with reference measurements performed without any nonwoven, with and without the mineral wool. For an empty cavity, and without the nonwoven, the resonant behaviour of the system can, as expected, be observed between 4 Hz and 5 Hz, although with a relatively small absorption coefficient (α=.4). When mineral wool is used, this resonance lowers to the frequency band of 315 Hz, due to impedance of this material, and the peak becomes notoriously higher (around α=1.). The introduction of the M3 nonwoven textile produces only a slight variation in this response, with the behaviour of the system maintaining the same features. In fact, a slight broadening effect occurs, with a small decrease in the peak value together with a very slight increase in the absorption observed at low and high frequencies. This effect is clearly related to the additional resistivity introduced by M3. How- 5

ever, when this resistivity is higher (nonwovens M1 and M2), the obtained curves show a very different behaviour, even if the remaining parts of the system are kept constant. For those cases, the resonant behaviour almost disappears, and the corresponding curves exhibit much smaller absorption along the mid-frequency range (particularly between 2 Hz and 1 Hz). This is an important observation, which shows that the use of such types of nonwovens can dramatically change the behaviour of the system, decreasing its expected performance. Between M1 and M2, some differences can still be noted, with the latter exhibiting an even lower absorption coefficient throughout the analysed frequency range. In Figure 4b, results for the same mineral wool are presented for the nonwovens M2 and M3, comparing their effects for the two types of panels analysed in this work. It is clear, in that figure, that for both types of nonwovens the increase in the open area provides a perceptible improvement of the absorption. Although this variation is much more evident for M2, even for M3 it can reach α=.15 above the resonance frequency, which can be considered a significant gain. a) b) Figure 4. Results for the 7 kg/m 3 mineral wool: a) effect of different nonwovens for a given mineral wool s density, using panel type A; b) influence of the nonwoven for panel types A and B. In Figure 5a, results measured for panel type B using different mineral wool densities and different nonwovens are presented. In this plot, it can be seen that, when using nonwoven M3, the increase of wool density produces a very small change in the absorption curve in the mid-frequency range. Indeed, there is even a small absorption decrease at the resonance peak, which the authors believe is due to the higher contrast between the two materials when higher density wool is used. a) b) Figure 5. Influence of the nonwoven for different mineral wool densities: a) results for panel type A; b) results for panel type B. This may indicate that a small coupling effect occurs between the thin layer of the nonwoven, which lowers the peak efficiency of the system. A small increase of absorption in the high frequency range is also observed in some of the plots, which was not expected and that the authors 6

believe is only related to the experimental conditions. Figure 5b presents additional results obtained for panels of type A. A reference curve, obtained without mineral wool nor nonwoven, is added to allow comparison. When just the M3 nonwoven is introduced, there is a striking gain in the absorption coefficients throughout the frequency range; this is performance gain can reach α=.25 at the peak of resonance. The introduction of mineral wool, within the cavity provides a further step up in performance, with maximum values of α=1. being reached at the resonance frequency. As in Figure 5a, no practical differences are observed between the two mineral wools, with the lower density solution even exhibiting slightly higher peak absorption. 5. Comparison with theoretical predictions The theoretical model presented in section 2 was used in order to understand the efficiency of those models in predicting the behaviour of the tested systems. Although several tests were performed for different cases, we here just illustrate a comparison between the theoretical model results and the experimental results obtained for a reduced number of cases. In a first set of results, consider the system composed of type A panels, for which case the perforated area represents 3.57% of the panel, incorporating the nonwoven mat M3 on its back and with an air gap filled with 4 kg/m 3 mineral wool; an air-flow resistivity of 14152 rayl/m is assumed for this wool, while the nonwoven M3 is characterized by an air-flow resistivity of 27 rayl. Figure 6a presents a comparison between the theoretical prediction and experimental measurement for this case. In the plot it becomes apparent that the results match very well, with the peak resonance occurring at the same frequency. In the lower frequency region, the two curves have very similar trends, and only a small mismatch is visible when the peak absorption is reached at 315 Hz. At higher frequencies, a larger difference is clear, with an increase in the absorption determined experimentally that is not predicted by the theoretical model. A second plot corresponding to the case in which the air-gap is empty and no nonwoven is used on the back of the panels is presented in Figure 6b. In this case, a much lower absorption coefficient is measured and estimated theoretically, and, again, a reasonable agreement between curves can be observed up to the resonance frequency. As expected, due to the presence of the mineral wool, this resonance is now slightly shifted to the right, and occurs at the 4 Hz band. Again, an unexpected raise in the measured absorption can be observed above 2 Hz in the experimental data, which finds no correspondence in the theoretical predictions. a) b) c) Figure 6. Comparison between theoretical and experimental results (panel A) for three configurations: a) nonwoven M3 and mineral wool; b) panels without nonwoven nor wool; c) nonwoven M1 and mineral wool. A final plot, displayed in Figure 6c, illustrates the behaviour of the system when the nonwoven M1 is used; it is important to note that the flow resistivity is now much higher, with a measured value of 75 rayl. The theoretical curve now exhibits a much smoother shape, with a pronounced decrease in the peak absorption being registered; the resonant behaviour can still be identified, although in a less pronounced manner. The effect of the higher resistivity of the nonwoven M1 is thus very visible in the theoretical curve, reducing the peak absorption and broadening the curve so that better performances are observed at higher frequencies. Comparing to the experimental re- 7

sult, the behaviour is not as similar as in the previous cases. In the experimental curve, the resonance effect of the panel can hardly be identified, and only a small peak is visible at the frequency of 2 Hz. It can thus be inferred that for higher values of the air-flow resistivity larger discrepancies between the theoretically expected behaviour and the experimental results were observed. 6. Final remarks This work analysed the behaviour of perforated wooden panels used to provide sound absorption in closed spaces. Particularly, the work addressed the effect of using different nonwoven textiles on the back of the panels together with mineral wools of different densities and different perforated open areas of the panels. The air-flow resistivity of the nonwoven was found to be a determinant variable, influencing the sound absorption of the system. In fact, when used together with a cavity filled with mineral wool, a nonwoven with high resistivity clearly hinders the development of the resonant behaviour of the system, dramatically lowering the absorption provided by the panels at mid-frequencies. If the nonwoven has a small air-flow resistivity, this behaviour is not observed, and the resonance peak in the absorption curve is still very pronounced. A comparison with theoretical results revealed a good agreement when the nonwoven textile exhibits a small resistivity; for higher values of this parameter, larger discrepancies between the theoretically expected behaviour and the experimental results were observed. Acknowledgments The authors would like to thank Castelhano & Ferreira, S.A. and ITeCons - Instituto de Investigação e Desenvolvimento Tecnológico em Ciências da Construção for the support provided during the preparation of this work. REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. K.U. Ingard and R.H. Bolt, Absorption characteristics of acoustic material with perforated facings, Journal of the Acoustical Society of America 23, 533-54 (1951). R. Patraquim, Perforated wooden panels: design and experimental evaluation of solutions, Master s Thesis submitted to Instituto Superior Técnico, Portugal, in partial fulfilment of the requirements for the Degree of Master of Science in Mechanical Engineering (28). P.M. Morse, R.H. Bolt and R.L. Brown, Acoustic Impedance and sound absorption, Journal of the Acoustical Society of America 12-2, 217-227 (194). R.H. Bolt, On the design of perforated facings for acoustic materials, Journal of the Acoustical Society of America 19, 917-921 (1947). K.U. Ingard, On the theory and design of acoustic resonators, Journal of the Acoustical Society of America 25, 137-162 (1953). I.B. Crandall, Theory of vibrating systems and sound, Van Nostrand, New York (1926). I.L. Vér and L.L. Beranek, oise and Vibration Control Engineering, John Wiley & Sons, 2 nd ed., New York (25). T.J. Cox and P. D Antonio, Acoustic absorbers and diffusers: theory, design and application, Spoon Press, 1 st ed. (24). I. Castro, A. Tadeu, J. António, A. Moreira, P. Amado Mendes and L. Godinho, Câmaras móveis ITeCons para a realização de ensaios acústicos: parte II preparação e caracterização das câmaras horizontais, Proceedings of Acústica 28, Coimbra, Portugal, October 2-22 (28). 8