A Study on Multimodal Behaviour of Plate Absorbers Mehmet Sait Özer 1 , Friedrich Beyer, Sebastian Merchel, M. Ercan Altınsoy Institute of Acoustics and Speech Communication, Chair of Acoustics and Haptics, TU Dresden Helmholtzstraße 18, 01069, Dresden

ABSTRACT Membrane absorbers, which are commonly used types of resonance absorbers, convert sound energy into thermal energy by exploiting vibrations that occur on oscillating panels. Those types of absorbers are generally tuned to be efficient in a very narrow frequency range. However, if plates are used as the front panel, it is possible to broaden the effective absorbing frequency bandwidth by exciting multiple modes. This study is devoted to investigating the multimodal behaviour of plate absorbers with closed back volumes in low-frequency range. In the numerical part of the study, the box-shaped plate absorbers are modelled using a combined BEM/FEM approach. The results are validated with measurements conducted in an anechoic chamber. In addition, the sound absorption characteristics of the plate absorbers are obtained from an experimental study conducted in a reverberation chamber. The obtained results reveal that the plate absorbers can be effective in wider frequency ranges.

1. INTRODUCTION

The importance of proper room acoustics has been increasing gradually. Above all, a suitable reverberation time, depending on how the room is used, is essential to ensure speech intelligibility or proper sound reinforcement in the room. Suggested reverberation times are specified in standards such as DIN 18041 [1]. The reverberation time can be adjusted by different types of sound absorbers, e.g. porous or resonant absorbers [2]. Although it is relatively easy to absorb sound energy in the high-frequency range using those absorbers, it can be very difficult to reduce the sound energy at low frequencies. In order to absorb the energy of long wavelengths, large amount of material is required. That increases the cost and complexity to integrate sound absorption into interior design. To overcome these drawbacks, membrane absorbers can be used. However, they are generally effective in a narrow frequency range only. The absorption is expected to be around the occurring resonant frequencies of the vibrating membrane or plate [3]. Therefore, resonant absorbers are often tuned to oscillate only at one main resonance frequency.

This study is devoted to investigate the capabilities of exploiting several modes of the panels for sound absorption to increase the effective frequency bandwidth especially in the low-mid frequency range. Therefore, the plates and the back volumes in box shaped absorbers were designed to contain resonances distributed over the required frequency range of 50 to 400 Hz. Regarding the approach of distributing vibration modes in the frequency range of interest through a specific panel and back volume design, these absorbers are named Distributed Mode Absorbers (DMA). Moreover, one of the main ideas of this project is to integrate DMAs into furniture, e.g., using them as front panels of

1 mehmet.sait_oezer@tu-dresden.de

cabinets or drawers. In addition to a larger area of application, these DMAs should be modular and cheaper than conventional panel absorbers.

In the scope of this study, prototypes with simple geometry and low-stiffness plates have been designed. After ensuring that the modes occur in the desired frequency range, physical prototypes were manufactured (see Section 2). A simple vibro-acoustic test case was analysed and validated with experiments performed in an anechoic chamber as described in Section 3. Subsequently, the absorption coefficients of the prototypes were measured. The results are presented in comparison with the vibration response of the front panels and are evaluated in Section 4. 2. PROTOTYPES

In order to predict the modal behaviour of different configurations of DMAs, several simulations were carried out beforehand. Based on these simulations, the dimensions of the prototypes and possible membrane materials were determined. Using the simulations, it was possible to reveal the displacement behaviour of the middle point of the panel. However, it was not yet possible to obtain the absorption coefficients. For the purpose of measuring the absorption performance of different DMAs, it was necessary to build actual prototypes. Since several configurations were to be measured, a design was chosen that allows for an easy exchange of front panels and back volumes.

The final DMA prototypes, with the outer membrane dimensions of 560 mm by 460 mm consist of a back volume with 5 rigid walls (19 mm MDF) and a flexible front membrane glued to an MDF frame. To easily exchange the front panels, panel frames were attached to the back structure using furniture connectors. Also, the size of the back volume is adjustable by manually inserting a 39 mm thick wooden plate at one of three positions, delivering the depth of back volumes of 20 mm, 60 mm and 120 mm. Without using the thick plate, the back volume depth remains 212 mm. Those configurations are named BC20, BC60, BC120 and BC212, respectively.

Due to the width of the frame, the vibrating area of the front plate of the DMAs is 500 mm by 400 mm. Three front plate configurations were investigated in this study. High Pressure Laminate (HPL) was used in two different thicknesses of 1.3 mm and 3 mm. Furthermore, some panels were made from 2 mm Plexiglas. Given the four different back volumes and three plate types, in total 12 different configurations could be investigated. The material parameters used in the simulations are presented in Table 1.

Table 1: Material properties of front plates. Material Property HPL 1.3 mm HPL 3 mm Plexiglas 2 mm Elasticity Modulus [GPa] 14.1 15.9 4.0 Poisson Ratio 0.30 0.30 0.38 Density [kg/m 3 ] 1470 1490 1253 Loss Factor [%] 2.54 3.00 7.00 3. NUMERICAL SIMULATIONS AND VALIDATION MEASUREMENTS

To evaluate the modal behaviour of DMAs, a sample test case was defined as described in [4]. The case consisted of a sound source located 2 m away from the plate surface and was generating a 94 dB harmonic signals at discrete frequencies between 20 Hz-20kHz. The amplitudes of the displacements that occur in the middle point of the plate were predicted (see Figure 1). A combination of the Boundary Element Method (BEM) and Finite Element Method (FEM) was utilized for numerical modelling purposes. In particular, commercial software Wave6 [5] was used for the simulations. The interested frequency range was defined from 20 to 1000 Hz. The sound field surrounding the DMA was modelled by generating a BEM subsystem. The sidewalls and the back wall of the DMA were assumed to be rigid. That is why only the front panel was modelled in the structural FE subsystem, using 500 shell elements. The plate is clamped from the edges for HPL 1.3 mm and Plexiglas 2 mm simulations. For the HPL 3 mm front panel simulations, pinned boundary conditions were used, since it had been seen for thicker plates that using clamped boundary conditions leaded the system to be

over-fixed. Back volumes behind the front panels were modelled with the acoustical FE approach, taking into consideration that the maximum frequency limit matches the desired frequency range. In the analysis, the density of air was set to 1.21 kg/m 3 , the speed of sound was 343 m/s and the kinematic viscosity was 1.57·10 -5 m 2 /s. Acoustical and structural FE subsystems were connected using an area junction defined on the front panel surface. Also, the BEM subsystem was tied to the structural FE subsystem using areal junctions.

Figure 1: Measurement setup in anechoic chamber (left) and model of the test case (right).

A set of experiments was conducted in the anechoic chamber of TU Dresden for validating the numerical results. As a sound source, a GENELEC 8250A studio monitor was employed and located at 2 m distance from the test specimen. As a reference microphone, a Gras 40HL was used with Gras Type 12AK Power Module in order to measure the sound pressure levels reaching the DMAs. An MMF KS95B.100 mini accelerometer was placed on the mid-points of the front panels for capturing the surface vibrations. The data acquisition processes were performed in Klippel dB-Lab. The displacement values were calculated from the acceleration measurement by a double integration in the frequency domain. The displacement values are presented in proportion to the sound pressure levels reaching the panels. This can be considered as weighting the displacement values according to incoming sound pressure. The predicted values for the HPL 3 mm front panel are presented in Figure 2. Here solid lines represent the experimental results and dotted lines represent the numerical results.

There is a visible positive correlation between the results for the first three modes. However, numerical predictions could not match the fourth mode in experimental results. The numerically predicted damping characteristic is slightly underestimated since the experimentally obtained frequency peaks are more rounded.

‘Structural FE = Acoustical FE Subsystem Subsystem (HPL, Plexiglas) (air) Measurement Point Monopole BEM Sound Source Subsystem (Air)

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Figure 2: Experimental (solid lines) and simulated (dashed lines) displacement results for DMA

with HPL 3 mm front panel with a) BC20, b) BC60, c) BC120 and d) BC212.

The measured and predicted peak frequencies of the 12 combinations are compared in Table 2, where f m and f p represent measured and predicted values, respectively.

Table 2: Measured and predicted natural frequencies and corresponding error percentages.

HPL 3 HPL 1.3 Plexiglas 2 f m [Hz] f p [Hz] Err. (%) f m [Hz] f p [Hz] Err. (%) f m [Hz] f p [Hz] Err. (%) BC 20 144.28 151.78 -5.2 82.03 93.26 -13.7 79.83 87.58 -9.7 208.01 214.45 -3.1 129.71 135.97 -4.8 126.71 127.69 -0.8 288.57 298.274 -3.4 208.74 211.11 -1.1 202.88 192.12 5.3 349.36 272.46 275.74 -1.2 253.42 247.02 2.5 BC 60 109.13 104.1 4.6 84.96 90.38 -6.4 73.97 82.25 -11.2 218.26 204.58 6.3 133.3 127.69 4.2 120.12 118.05 1.7 278.32 293.62 -5.5 158.2 172.11 -8.8 156.01 156.63 -0.4 347.17 219.73 221.3 -0.7 216.8 201.39 7.1 BC 120 93.02 82.25 11.6 72.51 79.7 -9.9 63.72 72.53 -13.8 221.92 204.58 7.8 113.53 116.21 -2.4 102.54 104.1 -1.5 278.32 293.62 -5.5 152.34 161.63 -6.1 147.22 147.09 0.1 344.97 218.26 221.3 -1.4 209.47 201.39 3.9 BC 212 84.96 69.19 18.6 61.52 68.11 -10.7 55.66 61.02 -9.6 213.87 204.58 4.3 109.86 110.86 -0.9 99.61 102.48 -2.9 278.32 293.63 -5.5 145.75 156.63 -7.5 146.48 147.09 -0.4 364.48 220.46 221.3 -0.4 216.8 204.58 5.6

The presented values reveal that there is a generally good agreement between results. However, for the first mode, the errors are considerably higher compared to the second and third mode. It should be also noted that there is not a constant frequency shift for all modes of a single combination. Those can be caused by local effects, inner frictions, fixing conditions and other minor variations in the structures that were not taken into consideration in modelling. Overall, the utilized numerical approach can be used for predicting the vibro-acoustic behaviour of plate absorbers. 4. SOUND ABSORPTION MEASUREMENTS

The absorption measurements of DMAs were performed according to ISO 354 [6] in the reverberant room of TU Dresden. Absorption coefficients were calculated from reverberation times measured with and without specimens. Due to the reverberant room size, the required sample number is defined as 48 DMAs (area of 12 m 2 ) in each condition. Because of the high number of necessary DMAs, the prototypes were built in the adjustable way, mentioned above.

According to the standards (ISO 354), reverberation times are calculated in third octave frequency bands. Since the DMAs, however, show very sharp resonance peaks it was decided to express the results within this study at an increased frequency resolution of 1/24 octave bands as in [7].

In the measurement room, four microphones (Microtech Gefell M-370) were placed in arbitrary positions. Considering 3 different loudspeaker positions, a total of 12 source-microphone combinations were measured and averaged according to ISO 354. As a sound source GENELEC 8250A loudspeakers were employed. It should be noted that the directivity of this kind of speaker does not remarkably affect the absorption coefficients measured in a reverberant room [8].

In addition to the absorption measurements, three mini accelerometers (MMF KS95B.100) were placed in the middle points of three DMAs to measure the surface vibrations. The obtained acceleration signals were averaged over the three measurements due to the different loudspeaker positions. The displacement was calculated by double integration in the frequency domain. The displacement values were divided by the sound pressure levels obtained from a microphone located very close to the surface. In the following only the displacement signal from the DMA with the close microphone will be evaluated. The measurement setup is presented in Figure 3.

Figure 3: Measurement setup in reverberant room with 48 DMAs; on left HPL 3 mm and on right

Plexiglas 2 mm.

The absorption coefficients and averaged displacements of DMAs with 3 mm HPL front panels are presented in Figure 4 for different back volume depths. It can be observed that there is a strong evidence of sound absorption in multiple frequencies. Furthermore, similar trends in measured displacement and sound absorption can be recognized. Besides, the measured displacements in Figure 4 have similar characteristics as the previously predicted numerical results and experimental results from the anechoic chamber. This promotes that it is possible to estimate the absorption characteristics with numerical simulations to some extent. The absorption coefficient curves indicate one main

absorption peak corresponding to the first vibration mode. This highest absorption peak shifts to lower frequencies with increasing back volume depth. Moreover, there are also visible sound absorption peaks, especially around 200-300 Hz. For the BC20 case, the absorptions above 200 Hz are higher than for the other configurations. This can be caused by the compression of the tight back volume that remains effective for the higher modes.

Figure 4: Measured displacement (blue) and sound absorption coefficients (green) of DMAs with

HPL 3 mm front panel with a) BC20, b) BC60, c) BC120 and d) BC212.

The results of the DMAs with HPL 1.3 and Plexiglas 2 mm are exemplarily presented for a back cavity depth of 120 mm in Figure 5. The agreement between displacement peaks and sound absorption coefficients can be qualitatively seen. Considerably higher absorption values for the several modes are obtained for these configurations.

If the plots of selected configurations are individually investigated, it is seen that higher displacements generally result in higher sound absorption. On the other hand, for the similar level of displacements for DMAs with different front panels, considering e.g. Figure 4c and Figure 5, different levels of absorptions were obtained. Not only the material properties but also their relations with each other may be the reason for this complexity of sound absorption behaviour. Therefore, several further studies should be conducted for clarifying the dominant properties of the front panels.

Figure 5: Measured displacement (blue) and sound absorption coefficients (green) of DMAs with

a) HPL 1.3 mm and b) Plexiglass 2 mm front panel with BC120.

5. CONCLUSIONS

The present study was designed to determine the performance of plate absorbers that exploit multiple vibration modes. First, numerical models have been built for investigating the vibro-acoustic behaviour of the proposed plate absorbers named DMAs. Then, the numerical simulations were validated with the experimental results obtained from measurements in an anechoic chamber. It was summarized that the selected modelling approach is an appropriate tool for modelling the vibro- acoustic behaviours.

Afterwards, sound absorption measurements were performed in a reverberant room. The results of this investigation showed that DMAs can provide effective sound absorption at more than a single resonance frequency. The absorption behaviour highly depends on both the material of the front panel and the enclosed air volume. It was also seen that some DMA configurations could reach quite high absorption values at some frequencies.

In further studies, a detailed parametric study should be performed for determining the most dominant panel properties or their combinations on sound absorption performance. Also, an optimization study is required for increasing the number of modes in the selected frequency range and to widen the absorption peaks. Besides, the overall absorption should be increased. 6. ACKNOWLEDGEMENTS

This project is supported by the Federal Ministry for Economic Affairs and Climate Action (BMWK) on the basis of a decision by the German Bundestag. We also want to thank Hommel Manufaktur GmbH Reichenbach for their productive and pleasant cooperation. 7. REFERENCES

1. DIN 18041, Hörsamkeit in Räumen - Anforderungen, Empfehlungen und Hinweise für die

Planung , 2004-05. 2. Cox, T. & D'Antonio, P. Acoustic Absorbers and Diffusers: Theory, Design and Application ,

Spon Press, 2005. 3. Ford, R.D. & McCormick, M.A. Panel Sound Absorbers. Journal of Sound and Vibration , 10(3) ,

411-423 (1969). https://doi.org/10.1016/0022-460X(69)90219-3 . 4. Özer, M. S., Beyer, F., Zenker, B., Merchel, S. & Altinsoy, M. E., Modelling Vibro-Acoustic

Behaviour of Membrane Absorbers, Proceedings of 48. DAGA , pp. 899-902, Stuttgart, Germany, 21-24 March 2022. 5. Wave 6, Dassault Systèmes Simulia Corp, Provid RI, USA, 2022. 6. ISO 354, Acoustics - Measurement of sound absorption in a reverberation room , 2003-05.

7. Beyer, F., Özer, M. S., Zenker, B., Merchel, S. & Altinsoy, M. E., Study on the Effect of Back

Cavity and Front Panel Materials on the Sound Absorption of Distributed Mode Absorbers, Proceedings of 48. DAGA , pp. 1026-1029, Stuttgart, Germany, 21-24 March 2022. 8. Beyer, F. Vergleich omnidirektionaler Messlautsprecher , Student research project (Unpublished),

TU Dresden, 2016.