Analysis of the results of the sound absorption coefficient for low frequencies of laminate bamboo resonant membrane
Brunno Guilherme Barbosa de Sá Department of Architecture and Urbanism, Paulista University, Brasília, Brasil1.
Maria Luiza de Ulhôa Carvalho Faculty of Visual Arts, Federal University of Goiás, Brasília, Brasil2.
Jaime Gonçalves de Almeida Faculty of Architecture and Urbanism, University of Brasília, Brasília, Brasil3.
Summary This work is part of the analysis of master’s course results called "Room Acoustics and Glued Laminated Bamboo (BaLC): Panels tests for acoustic conditioning" which evaluated the using of BaLC, from the Dendrocalamus giganteus species, for the acoustic treatment of enclosures spaces. Were constructed 12 panels with 107cm x 107cm x 4mm thick in BalC, in order to set them in resonant membranes devices type to low frequencies absorption. These panels were acoustically tested with internal air cavities thick as 100mm, 75mm and 50mm and with the same cavities filled with glass wool. The calculation of the resonant frequency of each system was performed to estimate the frequency band in which the device had a maximum sound absorption. The tests of sound absorption coefficient followed the international standard ISO 354: 2007 with sample 12m² in a reverberation chamber for each thickness cavity with and without glass wool filling. The results showed the resonance frequency of 100Hz and thus the maximum sound absorption coefficient at the same frequency for all sampling configurations. In the analysis of sound absorption coefficients, were found a variation from 0,387s to empty cavity with a thickness of 50mm to 0,778s to 50mm cavity filled with glass wool, both at 100Hz. The study demonstrated a significant potential to use the BaLC for sound absorption, thus entering a non-conventional and renewable material in the room acoustics possibilities. It is suggested to improve the study, the tests using the variation in panel dimensions and their comparison with the theoretical prediction.
PACS no. 43.55.Br 1. Introduction1
The study of room acoustics related to the materials used for their conditioning is shown to be fundamental for the well being of individuals, either for the treatment of large indoor spaces, such as concert halls, theaters, among others, or for children's environments such as test rooms, classrooms, or even work environments. Thus, knowledge of the sound absorption properties of these materials becomes increasingly important for architectural design and its components - such as sound absorption devices - because their correct application will directly influence the individuals life quality [1].
These materials present different acoustic behavior and can be classified as porous or fibrous, for high frequencies absorption, Helmholtz resonators, for the absorption of medium frequencies or resonant panels, also called resonant membranes, for low frequencies absorption [2]. Therefore, it is necessary to seek balance in the application of these components to obtain a sound control suitable for a particular use. However, the acoustical conditioning materials widely available on the market, as well as the verification of their potential for sound treatment, are still mostly focused on conventional raw materials such as wood and non-
renewable resources, such as polymers, foams and mineral fibers [3]. Furthermore, Berardi and Iannace [3] point out that the study of non-conventional materials for application in acoustics and device development is relevant, so that there are several researches about the acoustic potential of natural fibers and their derivatives, such as sisal, sugarcane bagasse and coconut husks, among others, as well as the reuse of components discarded by society, such as tires and pet bottles. In this perspective, Dias [4] exposes that the application of natural renewable materials in diverse products expands the use of these resources and favors the environment, since the uncontrolled and continuous exploitation of the natural resources generates negative impacts for the human being and their environment. In the point of view of this search for renewable materials, bamboo presents itself as a raw material of vegetable origin that generates a multitude of applications in several areas, with the possibility of interfacing with wood and other industrialized materials. It is classified as a tropical, perennial and renewable plant, which annually produces stems and does not need replanting. In addition to presenting itself as an excellent carbon reducer option, because its growth is fast and has potential for recovery of green areas, configuring an exceptionally advantageous material [5].
1.1. Resonant Membranes Resonant membranes, also called resonant or vibrating panels, are specialized devices for the acoustic absorption of the low frequencies. According to Bistafa [6] these panels are made of thin sheets of wood or metal fixed on spacers on the walls or ceiling constituting a cavity with air in its interior. According to Gerges [7] the membrane is an element that does not have sufficient rigidity for a plane, requiring that it be fixed in contours. Therefore, if this fixation is made parallel to a rigid plate, the air space between the two will act as an element of rigidity. Thus, the operating principle of these panels is based on the excitation of the membrane by the incidence of sound waves in their resonance frequency and, consequently, the dissipation of the acoustic energy through the internal damping of the system. Everest and Pohlmanm [8] point out that these panels can be sized to absorb specific frequencies, since the absorption of sound waves occurs through the vibration of the system has an absorption peak
that coincides with the resonance frequency of the device, the peak of maximum absorption is the resonant frequency of the system. However, Bies and Hansen [9] note that the determination of the sound absorption coefficient of the system can also be done by an empirical method using predictive graphs published by the Hardwood Plywood Manufacturers Association in 1962 to estimate the behavior of the device. Indeed, to determine the resonance frequency of the system can be used the equation 1, according to authors.
𝑓" =12𝜋
'ρ𝑐*
𝑚𝐿 + 0,6𝐿√𝑎𝑏 (1)
Inwich,𝑓"isthesystemresonancefrequency,inHz,𝑚isthepanelsurfacedensity,inkg/m²,𝐿isthe thicknessof theair layer inmeters,𝜌 is thespecificmassoftheairinkg/m3,𝑐isthespeedofsoundinm/s;𝑎isthepanelwidthinmetersand𝑏isthepanellengthinmeters.By observing the estimate provided by thepresented equation it can be verified that thethicknessoftheairlayerandthetypeofmaterialusedforthepanelareparametersthatinfluencethedeterminationoftheresonancefrequencyofthesystem.Therefore,reducingthesurfacemassof the material will cause an increase in theresonant frequency, just as the decrease in thethicknessof the air layerof thedevicewillalsoleadtoanincreaseinthatfrequency.Further, the air layer of this type of system may also be filled with some porous or fibrous absorbent material, spaced from the panel so that it can also vibrate freely, which will cause a decrease in the system's peak absorption of sound and increase absorption at frequencies close to the resonance. Thus, the introduction of these materials into the air layer will decrease the efficiency of the absorption peak sized for the system, but will increase the range of frequencies that the device can absorb [7].
1.2. Bamboo: natural and constructive characteristics
Bamboo is a material of natural origin and has been prominent as an ally of wood derivatives and other industrialized materials, through the interface that its processing can offer in various uses, as well as the rapid growth of its shoot, which takes from three to six months to reach up to thirty meters [5]. Some researches published in the II National Bamboo Seminar [10] shows that bamboo physical
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properties with respect to strength, rigidity and specific mass, surpass those of concrete and wood and are similar to those of steel, although there is a lot of ongoing research on this material. Besides the possibility of using the stem of this plant in its cylindrical format, some species, such as Guadua sp. and Dendrocalamus sp., enable their application in the form of laminate material. To do this, the bamboo stump is cut to create slats that are glued side by side, so that panels, blocks and pillars can be produced, among others. Another important aspect of bamboo is its biomass. Liese [11] points out that the biomass characteristic of bamboo depends mainly on the species, the climate, the quality of the soil in which it is found. Thus, the production of bamboo varies between 50 and 100 tons per hectare, so that 60% to 70% is relative to the stem, 10% to 25% to the branches and 15% to 20% to the foliage. Thus, Vos [12] observes that the high yield of biomass per planted hectare makes bamboo a renewable and sustainable material, and the yield of a bamboo plantation produces about 3 to 4 times more biomass than an average forest. Another advantage of the plant is its rapid growth, in which bamboo reaches its maximum growth in a period of 6 months, which provides, according to Lugt [12] a great capacity of carbon fixation that varies between 2 and 2.5 times larger than a medium-sized forest.
2. Development and characterization of bamboo resonant membrane
For the purpose of an experimental model that provided the test of different resonance frequencies for the system, a membrane consisting of a panel of laminate bamboo was conceived in only one thickness due to the supply of raw material and variable air box with thickness to be dismantled and reassembled. The parts were designed with 4 layers of differentiated air, a bottom membrane that would confine the air inside the device and a movable pressure frame on the bamboo membrane to hold the structure and make the components function as a cohesive whole. Thus, there is a system consisting of pressure frame, bamboo membrane, collapsible intermediate rings and bottom membrane. The thickness of the bamboo membrane was dimensioned based on the ideal width and length produced by the slat slitting machine and the minimum thickness produced by the slat leveling machine. In this way, a slat with a thickness of about 0.2cm, a width of 2.5cm and a length of 120cm is obtained. Also, in order to avoid the
deformation by moisture and dilation of the pieces, a membrane of two layers of slats, oriented perpendicularly, was dimensioned, 105cm long by 105cm wide and 0.4cm thick. For the control of the experiments and also for the classification of each composition in which the air layer is changed, by means of the assembly and disassembly of the removable rings, a specific denomination was created with the following abbreviations: a. BE100: Test of prototypes of the resonant membrane device in laminate bamboo with the internal air cavity 100 mm thick, sealed and empty. The system resonance peak is estimated at 112 Hz; b. BE075: Assay of the prototype of the resonant membrane device in laminate bamboo with the internal air cavity of 75mm thickness, sealed and empty. The system resonance peak is estimated at 129Hz; c. BE050: Assay of the prototype of the resonant membrane device in laminate bamboo with the internal air cavity of 50mm thickness, sealed and empty. The resonance peak of the system is estimated at 158Hz. In this way, 3 different measurements were obtained in which the air chamber inside the device is sealed and empty, thus a sharp absorption peak was expected at the calculated resonance frequency. However, with the possibility of insertion of porous or fibrous material inside the air box, the following conformations with their abbreviations were also projected: d. BEL100: Assay of the prototype of the resonant membrane device in laminate bamboo with the internal air cavity of 100mm thickness, sealed and filled with glass wool with a thickness of 50mm. The system resonance peak is estimated also at 112 Hz; e. BEL075: Assay of the prototype of the resonant membrane device in laminate bamboo with the internal air cavity of 75mm thickness, sealed and filled with glass wool with a thickness of 50mm. The system resonance peak is estimated also at 129Hz; f. BEL050: Assay of the prototype of the resonant membrane device in laminate bamboo with the internal air cavity of 50mm thickness, sealed and filled with glass wool with a thickness of 50mm. The peak resonance of the system is estimated also at 112Hz. The final products were 12 prototypes of resonant membrane type acoustic absorbers as specified in the design. This quantity was produced due to the
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recommendations of the absorber area for the reverberation chamber test, according to ISO 354: 2007 - Measurement of sound absorption in a reverberation room - to obtain the acoustic behavior of this material. Figure 1 shows a unit of the material prepared for analysis.
Figure 1. Laminate bamboo resonante membrane.
3. Methodological procedures for testing After the execution of the prototypes, the experiment was carried out to the acoustic laboratory. In this stage, the EAC/UFSM, the Acoustic Engineering Laboratory from the University of Santa Maria supports the assays. All the devices were made, being 12 pieces with the final dimensions of 107x107x011cm each and 1m² of free area for the bamboo membrane vibration. The methodological procedures are based on the international standard ISO 354: 2007: Measurement of sound absorption in a reverberation room that determines all the necessary characteristics for the test, such as the dimensions of the chamber, the bands of frequency, environmental conditions and necessary devices, among others. The reverberation chamber has walls at non-parallel angles whose dimensions range from 7.55 to 7.90m in length, 5.80 to 5.95m in width. The height of this enclosure is also variable, with the smallest dimension being 4.60m and the largest being 4.75m with th measurements total a volume of 207m³. suspended by chains fixed in the ceiling. Regarding the equipment and software used, following are presented their manufacturers and models: a. Data acquisition system: Sound Level Meter Brüel & Kjaer - Model 2270 bp2025;
b. Data acquisition and processing software: Frequency Analysis Brüel & Kjaer bp2430 and bp2152; c. Brüel & Kjaer Power Amplifier Type 2716; d. 1 Brüel & Kjaer Sonni Source OmniPower Source Type bp1689; e. 1 Brüel & Kjaer ½ Type 4189 bp2210 microphone with preamplifier; f. Brüel & Kjaer Type bp1311; g. Kiltler digital thermo-hygrometer mod. 986HI.
4. Tests and result in reverberant chamber The prototypes were analyzed in six different assemblies, with the empty cavity in the thicknesses of 100, 75, 50mm of air layer and with the cavity filled with 50mm glass wool, in the assemblies of 100, 75 and 50mm. In all the tests the panels followed the same arrangement, as a set forming 12 panels, and 12 m2 of absorption area, inside the room, according to Figure 3. Although, the prediction was made based on the study for wood plywood, so that the final result may be different from that presented. It is worth mentioning that the laminate bamboo with the proposition of use for resonant membrane sound absorption devices is still little explored and it is expected that this study will encourage the use of bamboo derivatives, especially glued laminate, for room acoustic conditioning.
Figure 2. Laminate bamboo resonante membrane positioned in the reverberation chamber.
The BE075 test, with the empty cavity, showed a very expressive result, since its maximum sound absorption coefficient at the resonance frequency of the system, observed at 100Hz, was close to that of
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tests with the filled cavity, according to Figure 3. For all sealed cavity tests, BE100, BE075, BE050, BEL100, BEL075 and BEL050, the resonant frequency of the device was maintained at 100Hz. The highest values for the sound absorption coefficient at the resonant frequency were found in the BEL050 test, followed by the BEL075 and then the BE075. The panels with empty cavity and thickness of the air layer with 100, 75 and 50mm will be analyzed together, since they constitute similar systems with only the variation of the internal air layer and, therefore, they form closed systems in which there is no direct communication of the air of the internal cavity of the devices with the external medium. In these tests, the prototypes were sealed by the removable rings where pressure was applied to the edges of the membrane through the rim and bolts with nuts and washers so that the system became a rigid part, so the figure 3 demonstrates the results for the cited trials. The results for empty cavity showed that the sound absorption system obtained significant values between the frequencies of 80Hz to 400Hz. According to the pre-dimensioning, for the BE100 assembly of the device, a sharp peak of absorption in the range of 123Hz, with a sound absorption coefficient between 0.4 and 0.6 was predicted. Observing the results obtained in the reverberant chamber, a sharp absorption peak in the range of 100Hz was observed, so that the calculated resonance frequency differed from that tested in the laboratory. The maximum value of sound absorption coefficient obtained was 0.56 at the resonance peak, corroborating the prediction of
design. Thus, the absorption of the panel, with the 100mm cavity, increases until the resonance peak and decreases until the frequency of 160Hz, then presents a lower peak in the range of 200Hz, with a value of 0.26 and then decreases again gradually. The estimate for BE075 predicted the system's resonance peak at 142Hz and a sound absorption coefficient close to 0.4. However, the result obtained in the laboratory was different and higher than the calculation estimate. The resonance frequency of the system remained at 100Hz and, as in the BE100 sample, it also showed a marked peak, but the maximum value of sound absorption coefficient was obtained in 0.74, showing a great difference in relation to estimated forecast. The behavior of the curve remained similar to the previous assay, with the absorption coefficient rising to the resonance peak and then decaying up to 160Hz, where it rises again to a peak of 0.26 at 250Hz and then gradually falls. The calculation of the resonance frequency for BE050 estimated the absorption peak in the range of 174Hz and the maximum value for the sound absorption coefficient close to 0.4. With the observation of the values found in the test, it was verified that the resonance frequency remained at 100Hz, as in the other tests, diverging from what was predicted. However, the maximum sound absorption coefficient was 0.38, corroborating the estimate of the theoretical prediction. The curve presented also did not behave as expected because it does not show a sharp peak, so that a sound absorption coefficient similar to that of 100Hz is maintained at 250Hz and then gradually decays.
Figure 3. Comparison of sound absorption coefficients of resonant membrane prototypes.
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The initial estimate predicted the same resonance frequencies for the hollow cavity system, for BEL100 at 123Hz, BEL075 at 142Hz and BEL050 at 174Hz. However, the maximum values for the sound absorption coefficients measured were close to 0.8 for BEL100, between 0.6 and 0.8 for BEL075 and, finally, close to 0.6 for BEL050. In figure 4 the graph of sound absorption coefficient calculated by the laboratory tests can be observed. It can be seen that the insertion of the wool into the cavity of the device contributes to the raising of the coefficients of sound absorption of the system. The absorption curve behaved as expected, with the amplification of the frequency range absorbed and the presentation of a less accentuated peak. However, the resonance frequency for the three tests remained at 100Hz, differently from what was predicted in the calculation. The BEL100 conformation test obtained the maximum sound absorption coefficient of 0.67, but the prediction was close to 0.8, while BEL075 and BEL050 obtained a similar maximum coefficient of 0.771 and 0.778 respectively. The BEL075 test corroborated the coefficient prediction, between 0.6 and 0.8, however, the BEL050 test exceeded the absorption expectations, as the forecast was close to 0.6 and obtained a value of 0.778. Further, the sound absorption of the device increases greatly at the lower frequencies until it reaches the resonant peak and then slowly decays to the frequency of 500Hz. 5. Conclusions
According to the results obtained in the reverberant chamber tests, it was found that the resonant membrane-type panel prototypes presented different results in their sound absorption coefficient for those with fibrous material in their cavity and those with empty interior. Therefore, the difference was significant, since the wool provided an increase in the sound absorption coefficients tested. The experiments showed that the empty cavity of 75mm, in the BE075 test, obtained a maximum sound absorption coefficient close to the highest coefficient found in all the tests, thus demonstrated the capacity of the bamboo membrane allied to the air layer in this system, presented superior performance for the empty cavity, surpassing the calculated estimates. With the 50 mm thick glass wool filling in the inner cavity, the BEL050 test, with 50 mm of air layer, presented a satisfactory
performance, since it had a high maximum sound absorption coefficient and, compared with the BE050 test, of empty cavity, there was a great variation of absorption in the frequencies of 63 to 250Hz.
Acknowledgement The results shown at this research were developed in University of Brasília and tests were made at Federal University of Santa Maria in Brazil. The study is part of a multidisciplinary group that covers research on the use of renewable materials in architecture.
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