Table of Links Abstract and 1 Introduction 2 Unit cell design and analysis 3 Unit cell experimental and numerical characterization 4 Rainbow AM labyrinthine panel 4.1 Panel design and fabrication 4.2 FE model of the AM panel 4.3 AM panel characterization 4.4 AM panel sound absorption results 5 Numerical evaluation of different labyrinthine sound absorption panel solutions 5.1 Macrocell with backing cavity 5.2 Results Conclusions, Acknowledgements, and References Appendix I 4.3 AM panel characterization The measurement of the sound absorption of the complete panel is performed in a small-scale reverberation room at the Politecnico di Torino. A full validation of the performance of the room is presented in [21], highlighting the 400-5000 Hz general validity frequency range. The mean reverberation time of the empty room between 100 Hz and 5000 Hz is of 0.95 s with a Schroeder frequency fs of 1152 Hz [45]. In order to ensure a high diffusivity of the sound field, the room is equipped with 8 diffusers on the ceiling, covering 13.5% of the total room area. The panel characterization procedure consists in using the integrated impulse response method [41] for simultaneous measurements on six different microphone positions in two conditions, i.e. with and without the sample on the floor of the room. The measurement chain includes a set-up of six 1/4" BSWA Tech MPA451 microphones and ICP104 (BSWA Technology Co., Ltd., Beijing, China), two ITA High-Frequency Dodecahedron Loudspeakers with their specific ITA power amplifiers (ITARWTH, Aachen, Germany) and a Roland OctaCapture UA-1010 sound card (Roland Corporation, Japan) in order to perform 12 measurements (the minimum number required by ISO 354 [41]). We use a Matlab code combined with the functions of the ITA-Toolbox (an open-source toolbox from RWTH-Aachen, Germany) for sound generation, recording and signal processing. We perform a spatial averaging considering all the 12 sources and microphone combinations, checking the temperature (≥ 15 °C) and humidity (between 30-90 %) conditions. In accordance with ISO 354, before measurements the equivalent specimen absorption area is calculated (in square meters), using the formula 4.4 AM panel sound absorption results As shown in Fig. 7, the panel has a flat upper surface and an uneven lower surface. The upper surface is equipped with apertures from which the sound waves access the UCs, while the lower surface is fully sealed. Fig. 10a displays the experimental test configuration of the panel: the flat surface is facing the sound source. This configuration corresponds to the configuration in which the panel has an attenuating effect on sound waves. In Fig. 10b, the comparison of analytically, numerically and experimentally predicted absorption spectra is shown. Frequencies of interest are reported as thirdoctave bands in the range of interest (250-5000 Hz). The orange line shows the effective sound absorption of the upper surface, which is close to the ideal value of 1 in the desired frequency range between 800 and 1300 Hz. Additionally, an analytical absorption curve (in blue) is obtained for a fine band spectrum computing the overall impedance of the panel considering the UCs working in parallel, as detailed in [37]. Although the pressure field of the analytical and numerical model impinges normally on the surface, while in experimental testing conditions of the reverberation room there is a diffused field, the two absorption spectra show good agreement, in the main absorption peak range, indicating the effectiveness of the panel also in non-normal conditions. Numerical results, calculated with the model described in the previous Section (again for normal incidence), are also included in the plot in Fig. 10b, showing excellent agreement with analytical and experimental results. Some discrepancy emerges at higher frequencies (above 3 kHz) between experimental and predicted results, probably due to the greater influence of a non-normal incidence angle. This paper is available on arxiv under CC BY-NC-ND 4.0 DEED license. Authors:
(1) F. Nistri, Department of Applied Science and Technology, Politecnico di Torino, Torino, Italy and Politecnico di Milano, Milano, Italy;
(2) V. H. Kamrul, Politecnico di Milano, Milano, Italy;
(3) L. Bettini, Politecnico di Milano, Milano, Italy;
(4) E. Musso, Politecnico di Milano, Milano, Italy;
(5) D. Piciucco, Politecnico di Milano, Milano, Italy;
(6) M. Zemello, Politecnico di Milano, Milano, Italy;
(7) A.S. Gliozzi, Department of Applied Science and Technology, Politecnico di Torino, Torino, Italy;
(8) A.O. Krushynska, Faculty of Science and Engineering, University of Groningen, Groningen, The Netherlands;
(9) N. M. Pugno, Laboratory for Bioinspired, Bionic, Nano, Meta Materials & Mechanic, University of Trento, Trento, Italy and School of Engineering and Materials Science, Queen Mary University of London, United Kingdom;
(10) L. Sangiuliano, Phononic Vibes s.r.l., Milano, Italy;
(11) L. Shtrepi, Department of Energy "Galileo Ferraris", Politecnico di Torino, Torino, Italy;
(12) F. Bosia, Department of Applied Science and Technology, Politecnico di Torino, Torino, Italy and a Corresponding Author (federico.bosia@polito.it). Table of Links Abstract and 1 Introduction Abstract and 1 Introduction 2 Unit cell design and analysis 2 Unit cell design and analysis 3 Unit cell experimental and numerical characterization 3 Unit cell experimental and numerical characterization 4 Rainbow AM labyrinthine panel 4.1 Panel design and fabrication 4.1 Panel design and fabrication 4.2 FE model of the AM panel 4.2 FE model of the AM panel 4.3 AM panel characterization 4.3 AM panel characterization 4.4 AM panel sound absorption results 4.4 AM panel sound absorption results 5 Numerical evaluation of different labyrinthine sound absorption panel solutions 5.1 Macrocell with backing cavity 5.1 Macrocell with backing cavity 5.2 Results 5.2 Results Conclusions, Acknowledgements, and References Conclusions, Acknowledgements, and References Appendix I Appendix I 4.3 AM panel characterization The measurement of the sound absorption of the complete panel is performed in a small-scale reverberation room at the Politecnico di Torino. A full validation of the performance of the room is presented in [21], highlighting the 400-5000 Hz general validity frequency range. The mean reverberation time of the empty room between 100 Hz and 5000 Hz is of 0.95 s with a Schroeder frequency fs of 1152 Hz [45]. In order to ensure a high diffusivity of the sound field, the room is equipped with 8 diffusers on the ceiling, covering 13.5% of the total room area. The panel characterization procedure consists in using the integrated impulse response method [41] for simultaneous measurements on six different microphone positions in two conditions, i.e. with and without the sample on the floor of the room. The measurement chain includes a set-up of six 1/4" BSWA Tech MPA451 microphones and ICP104 (BSWA Technology Co., Ltd., Beijing, China), two ITA High-Frequency Dodecahedron Loudspeakers with their specific ITA power amplifiers (ITARWTH, Aachen, Germany) and a Roland OctaCapture UA-1010 sound card (Roland Corporation, Japan) in order to perform 12 measurements (the minimum number required by ISO 354 [41]). We use a Matlab code combined with the functions of the ITA-Toolbox (an open-source toolbox from RWTH-Aachen, Germany) for sound generation, recording and signal processing. We perform a spatial averaging considering all the 12 sources and microphone combinations, checking the temperature (≥ 15 °C) and humidity (between 30-90 %) conditions. In accordance with ISO 354, before measurements the equivalent specimen absorption area is calculated (in square meters), using the formula 4.4 AM panel sound absorption results As shown in Fig. 7, the panel has a flat upper surface and an uneven lower surface. The upper surface is equipped with apertures from which the sound waves access the UCs, while the lower surface is fully sealed. Fig. 10a displays the experimental test configuration of the panel: the flat surface is facing the sound source. This configuration corresponds to the configuration in which the panel has an attenuating effect on sound waves. In Fig. 10b, the comparison of analytically, numerically and experimentally predicted absorption spectra is shown. Frequencies of interest are reported as thirdoctave bands in the range of interest (250-5000 Hz). The orange line shows the effective sound absorption of the upper surface, which is close to the ideal value of 1 in the desired frequency range between 800 and 1300 Hz. Additionally, an analytical absorption curve (in blue) is obtained for a fine band spectrum computing the overall impedance of the panel considering the UCs working in parallel, as detailed in [37]. Although the pressure field of the analytical and numerical model impinges normally on the surface, while in experimental testing conditions of the reverberation room there is a diffused field, the two absorption spectra show good agreement, in the main absorption peak range, indicating the effectiveness of the panel also in non-normal conditions. Numerical results, calculated with the model described in the previous Section (again for normal incidence), are also included in the plot in Fig. 10b, showing excellent agreement with analytical and experimental results. Some discrepancy emerges at higher frequencies (above 3 kHz) between experimental and predicted results, probably due to the greater influence of a non-normal incidence angle. This paper is available on arxiv under CC BY-NC-ND 4.0 DEED license. This paper is available on arxiv under CC BY-NC-ND 4.0 DEED license. available on arxiv Authors: (1) F. Nistri, Department of Applied Science and Technology, Politecnico di Torino, Torino, Italy and Politecnico di Milano, Milano, Italy; (2) V. H. Kamrul, Politecnico di Milano, Milano, Italy; (3) L. Bettini, Politecnico di Milano, Milano, Italy; (4) E. Musso, Politecnico di Milano, Milano, Italy; (5) D. Piciucco, Politecnico di Milano, Milano, Italy; (6) M. Zemello, Politecnico di Milano, Milano, Italy; (7) A.S. Gliozzi, Department of Applied Science and Technology, Politecnico di Torino, Torino, Italy; (8) A.O. Krushynska, Faculty of Science and Engineering, University of Groningen, Groningen, The Netherlands; (9) N. M. Pugno, Laboratory for Bioinspired, Bionic, Nano, Meta Materials & Mechanic, University of Trento, Trento, Italy and School of Engineering and Materials Science, Queen Mary University of London, United Kingdom; (10) L. Sangiuliano, Phononic Vibes s.r.l., Milano, Italy; (11) L. Shtrepi, Department of Energy "Galileo Ferraris", Politecnico di Torino, Torino, Italy; (12) F. Bosia, Department of Applied Science and Technology, Politecnico di Torino, Torino, Italy and a Corresponding Author (federico.bosia@polito.it). Authors: Authors: (1) F. Nistri, Department of Applied Science and Technology, Politecnico di Torino, Torino, Italy and Politecnico di Milano, Milano, Italy; (2) V. H. Kamrul, Politecnico di Milano, Milano, Italy; (3) L. Bettini, Politecnico di Milano, Milano, Italy; (4) E. Musso, Politecnico di Milano, Milano, Italy; (5) D. Piciucco, Politecnico di Milano, Milano, Italy; (6) M. Zemello, Politecnico di Milano, Milano, Italy; (7) A.S. Gliozzi, Department of Applied Science and Technology, Politecnico di Torino, Torino, Italy; (8) A.O. Krushynska, Faculty of Science and Engineering, University of Groningen, Groningen, The Netherlands; (9) N. M. Pugno, Laboratory for Bioinspired, Bionic, Nano, Meta Materials & Mechanic, University of Trento, Trento, Italy and School of Engineering and Materials Science, Queen Mary University of London, United Kingdom; (10) L. Sangiuliano, Phononic Vibes s.r.l., Milano, Italy; (11) L. Shtrepi, Department of Energy "Galileo Ferraris", Politecnico di Torino, Torino, Italy; (12) F. Bosia, Department of Applied Science and Technology, Politecnico di Torino, Torino, Italy and a Corresponding Author (federico.bosia@polito.it).

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