Analysing the Impact of 3D-Printed Perforated Panels and Polyurethane Foam on Sound Absorption Coefficients
Round 1
Reviewer 1 Report
Comments and Suggestions for AuthorsNew designs for absorbing materials combined with perforated panels are of interest, especially if the performance of different designs has been validated with, in this case, a numerical model.
However, there are some major and minor remarks for this paper.
- The FEA is a main topic of this paper. How does the Comsol model account for energy losses in the perforations? (not the losses in the foam). For instance, I did not see the use of a viscothermal acoustic domain.
- The comparison between measurements & calculations is not made directly (the agreement appears to be very good). Why not do this in one figure?
- Only in the Discussion, in Section 6.2, prior results are mentioned on perforation ratio’s (without reference). It would be better to introduce this earlier.
(i.e. this parameter is much more sensitive that the geometry of the pore).
- The paper addresses the literature extensively. In The Introduction, in Section 2.1, in Section 2.3, and at other sections. Would it be better to concentrate this, and use headers for different topics? In addition, it is not always clear where the contribution of this paper is meant.
- The results of the 6 samples, using forward and backward orientated perforations, provide quite similar results, with about 10% differences. For acoustics, using dBs, this is a very small difference. So a 10% higher result is not likely to be described as ‘superior’.
- In general, the authors use strong words like ‘unique’, ‘exceptional’, ‘excel’, ‘superior’, ‘crucial’, and ‘standout’. I would advise to omit these terms, as the discussed results, and small differences between the samples, do not support these terms.
Minor remarks:
- The model uses a poroacoustic domain for the foam, using the empirical Delany and Bazley model. Only the flow resistivity is needed. How is the parameters obtained at ‘exactyly’ 13498 Pa.s/m2? I guess 13.5 kPa.s/m2 is accurate enough?
- In general, can you measure the absorption coefficient for each one-third octave bands with a three digit accuracy?
- Line 101: replace ‘measure’ with ‘calculate’
- Line 123 section: suggestion to delete this section; statements are over the top.
- Section 1.1: suggestion to delete this section; this is more suitable for a textbook.
- Lines 266 & 267: delete?
- Line 283: why is the model mentioned as a ‘multiphysics-enabled environment’? As it is (only) the acoustic environment using normal acoustics and interaction with foam (via Delany & Bazley).
- Table 1 & 2: mention that these are calculated results.
Could the tables also be represented as figures?
- Conclusion, last Section. Suggestion to rephrase with more modest words.
Author Response
Thank you for your detailed review and constructive feedback on our manuscript. We have carefully revised the manuscript in response to each comment, with changes marked in red and highlighted in yellow in the updated version. Below, we provide point-by-point responses to your comments, also highlighted in red. We believe these revisions elevate our manuscript to meet the journal's standards and hope for its acceptance.
Comments 1: The FEA is a main topic of this paper. How does the Comsol model account for energy losses in the perforations? (not the losses in the foam). For instance, I did not see the use of a viscothermal acoustic domain.
Response 1: Thank you for pointing this out. We agree with this comment. As per your comment, we have made changes in the main manuscript.
In COMSOL, the energy losses in perforations are adeptly managed by the thermoacoustic interface, utilising complex impedance boundary conditions tailored to address both viscous shear and heat conduction losses effectively. These conditions are significant for capturing resistive and reactive energy dissipation within the perforations, ensuring an accurate and detailed simulation of the acoustic dynamics. Structurally, the solid mechanics interface for the perforated panels sets parameters such as material symmetry, Poisson's ratio, and Young's modulus under a linear elastic framework. The pressure acoustic model integrates the atmospheric attenuation domain to account for the effects of thermal and viscous attenuation and variations due to environmental conditions like atmospheric pressure, temperature, and relative humidity. This model is significant for the precise simulation of sound propagation, ensuring accurate modelling of atmospheric influences on sound propagation.
(These changes can be found on page number-9 and line numbers-329-340).
Comments 2: The comparison between measurements & calculations is not made directly (the agreement appears to be very good). Why not do this in one figure?
Response 2: Thank you for your comment. We agree that a comparison is crucial and have illustrated this with a figure in the manuscript.
5.1. Comparative Analysis of Sound Absorption Coefficients from FEA and Experimental Data for Case 1 in the Forward Scenario
The comparison has been made using data from both FEA and experimental observations. This discussion specifically focuses on Case 1 of the forward scenario for simplicity. The subsequent Figure 9 illustrates a comparison of sound absorption coefficients as a function of frequency, ranging from 0 Hz to 4000 Hz. It presents two curves: one representing the FEA and the other obtained from experimental methods. Both curves reach a peak absorption at 630 Hz, where the coefficient nears a maximum of approximately 0.9. Following this peak, there is a consistent decline in absorption coefficients as the frequency continues to increase. This similar trajectory across the frequency spectrum indicates a strong correlation between the FEA predictions and experimental results, affirming the accuracy of the FEA model relative to the experimental conditions.
Figure 9. Comparison of results from FEA and experimental method for forward case 1.
(These changes can be found on page numbers-16-17and line numbers-484-498).
Comments 3: Only in the Discussion, in Section 6.2, prior results are mentioned on perforation ratio’s (without reference). It would be better to introduce this earlier.(i.e. this parameter is much more sensitive that the geometry of the pore).
Response 3: Thank you for your feedback. We agree that introducing this information earlier is essential. Accordingly, we have revised the manuscript to include this detail at an earlier point.
Yuvaraj et al. examined the impact of perforation ratio, air gap, and various porous layer configurations on sound absorption performance, a critical dependent variable. An increased perforation ratio reduces panel acoustic mass, leading to higher resonant frequencies for optimal sound absorption, while lower ratios yield peaks in the low-frequency range. The perforation ratio affects the absorption bandwidth: higher ratios expand the bandwidth due to enhanced sound interaction and increased viscous loss from the countersunk profile. Conversely, a lower perforation ratio increases the panel's resistance to sound waves and reduces acoustic hole mass, thereby influencing the peak absorption frequency. In this work, the center-to-center distances between holes are set at 5 mm, 10 mm, and 15 mm. Increasing this distance reduces the perforation ratio, thereby optimizing absorption in the lower frequency range [20].
(These changes can be found on page number-4, and line numbers-182-192 )
This study uses additive manufacturing techniques to produce acoustically relevant perforated panels with variable hole spacings. A Markforged 3D printer is precisely employed for this purpose, and onyx is selected as the material of choice for fabricating this one mm-thick panel. This material pairing plays a substantial role in fine-tuning sound control and elevating acoustic performance, offering versatile acoustic solutions adaptable to diverse environments. Increasing the center-to-center distance between holes (i.e., reducing the perforation ratio) improves low-frequency absorption. Due to production constraints, the center-to-center distance has been fixed at 18 mm.
(These changes can be found on page numbers-6-7, and line numbers-278-285 )
Yuvaraj et al. investigated the impact of hole spacing on the sound absorption coefficient.
(These changes can be found on page number-20, and line numbers-581-582 ).
Comments 4: The paper addresses the literature extensively. In The Introduction, in Section 2.1, in Section 2.3, and at other sections. Would it be better to concentrate this, and use headers for different topics? In addition, it is not always clear where the contribution of this paper is meant.
Response 4: Thank you for your comment. We acknowledge the importance of including the header in the introduction. The significance of the current work to the paper is also noted. Therefore, we have updated the manuscript to include this information.
1.1. Effect of Cavity Depth on Sound Absorption Coefficient
Mosa et al. investigated the effects of modifying the cavity depth behind sub-structures in a double-layer inhomogeneous micro-perforated panel (DL-iMPP) on sound absorption coefficients. Enhancing the back cavity depth of sub-MPPs with larger hole diameters and smaller perforation ratios boosts low-frequency absorption. Conversely, decreasing the inter-panel cavity depth shifts the absorption peak to higher frequencies, expanding the frequency bandwidth of absorption. While the front cavity depth has negligible effects on absorption characteristics, modulating the back cavity depth at certain sub-MPPs optimizes absorption amplitude and frequency response [13]. Chiang et al. noted that the cavity depth significantly impacts the sound absorption coefficients of the MPP (Micro-Perforated Panel) absorber array. Variations in the depths of sub-cavities within the array lead to different absorption coefficients, enhancing absorption at specific resonance frequencies. Changes in cavity depth alter local resonance effects and particle velocities, thereby impacting the acoustic resistance and overall absorption performance of the MPP absorber array. Adjusting these depths is essential for optimizing the acoustic properties and effectiveness of the absorber array in various acoustic environments [14].
Lin et al. studied that perforation depth affects the sound absorption coefficients of PU foam plates by altering the resonance chamber size and consequently the sound absorption properties. Specifically, perforation depths of 50 mm and 75 mm optimize absorption at 2500 Hz, whereas a depth of 100 mm reduces absorption due to enhanced sound wave penetration. Additionally, larger resonance chamber sizes, particularly with a perforation depth of 100 mm, shift absorption peaks to lower frequencies. The varying perforation depths in PU foam plates result in distinct sound absorption coefficients, with peak absorption effectiveness occurring at specific frequencies determined by both perforation depth and rate [15]. Bravo et al. studied that the cavity depth is critical in micro-perforated panel structures for establishing Helmholtz-type resonances, significantly influencing sound absorption coefficients. Optimal cavity depths not only enhance the maximum absorption values but also broaden the effective bandwidth of absorption without compromising performance. This depth directly affects the absorption characteristics, making the selection of appropriate cavity dimensions essential for achieving desired acoustic outcomes [8].
Min et al. explored how the depth sequence of sub-cavities critically affects the sound absorption coefficients of micro-perforated panel (MPP) absorbers. Their research highlights that the depth ratio and arrangement of these cavities are pivotal in optimizing absorption performance. By tuning the cavity depth sequence, the absorption characteristics are enhanced, resulting in broader absorption bandwidths and higher coefficients than those observed in single MPP absorbers [16]. Sound absorption in materials involves reflection, absorption, and transmission of sound waves, influenced by material properties and wave incidence. Porous absorbers are designed to minimize reflection and maximize energy dissipation as heat, enhancing noise control and acoustic quality in various environments.
(These changes can be found on page numbers-2-3, and line numbers-87-128 )
2.1.1. Natural materials
Hong et al. evaluated the sound absorption by using bio-composite micro-perforated panels (BC-MPP) with polypropylene and natural fillers (rice husk, coconut coir) using an impedance tube. BC-MPP with rice husk showed maximum sound absorption coefficients (SAC) over coconut coir. Increases in filler content, perforation distance, and air gap size shifted SAC peaks to lower frequencies [22]. Cao et al. made an outstanding review on noise pollution mitigation through porous sound-absorbing materials, summarising recent advancements in design and fabrication. It covers absorption mechanisms, predictive models, and developments in foams and fibrous materials, offering future perspectives [23]. Taban et al. studied coconut fiber composites as sound absorbers by measuring their absorption coefficients using impedance tubes. MATLAB-based models confirm that increasing material thickness and air gap boosts low-frequency sound absorption, aligning with experimental data [24].
(These changes can be found on page numbers-4-5, and line numbers-197-209 )
2.3.1. Contribution of current work
The study conducted a quantitative evaluation of sound absorption performance across a frequency spectrum of 100 to 4000 Hz, tailored for typical acoustic engineering scenarios. This assessment utilized impedance tube measurements and experimental validation of the structure, with further verification provided through COMSOL Multiphysics simulations. Utilizing a Multiphysics-enabled acoustics module, the research offered a comprehensive platform for sound propagation analysis, enhancing material behavior understanding within the stipulated frequency range. The research parameters were explicitly defined, considering resource availability and specific limitations. Detailed analyses were also performed to examine the effects of variations in perforated panel hole geometry and the integration of polyurethane foam on the Sound Absorption Coefficient (SAC) and Noise Reduction Coefficient (NRC). This research contributes to a better understanding sound absorption mechanisms in complex acoustic systems, potentially guiding advancements in noise control and acoustic design methodologies.
(These changes can be found on page number-6, and line numbers-257-271 ).
Comments 5: The results of the 6 samples, using forward and backward orientated perforations, provide quite similar results, with about 10% differences. For acoustics, using dBs, this is a very small difference. So a 10% higher result is not likely to be described as ‘superior’.
Response 5: Thank you for pointing this out. We agree with your comment and have made the necessary changes in the main manuscript as per your suggestion.
In this analysis, the Noise Reduction Coefficient (NRC) values for the forward configuration exhibit a range from 0.371 to 0.441 across various setups. Correspondingly, for the reversed configuration, NRC values span from 0.371 to 0.421. The proximity of these measurements indicates minimal variation. The configuration that includes tapered holes demonstrates improved performance in the forward case compared to all other cases.
(These changes can be found on page number-12, and line numbers-389-393).
Comments 6: In general, the authors use strong words like ‘unique’, ‘exceptional’, ‘excel’, ‘superior’, ‘crucial’, and ‘standout’. I would advise to omit these terms, as the discussed results, and small differences between the samples, do not support these terms.
Response 6: Thank you for highlighting this. In response to your suggestions, we have replaced these words, and the manuscript has been revised accordingly.
This study introduces a new approach to exploring sound absorption mechanisms in engineered materials.
(These changes can be found on page number-1, and line numbers-31-32)
Case 5's design, featuring two stepped portions, delivers peak sound absorption coefficients in the 630 to 1000 Hz range in the reverse case but underperforms the forward Case 5 for other frequencies.
(These changes can be found on page number-20, and line numbers-566-568)
Figure 7 demonstrates proficiency in producing durable carbon fiber composite parts utilizing continuous fiber reinforcement (CFR).
(These changes can be found on page number-13, and line numbers-410-411)
Case 3 and Case 6 perform well in the 630 to 800 Hz frequency range, boasting the maximum Sound Absorption Coefficient values within this spectrum.
(These changes can be found on page number-18, and line numbers-514-516)
It performs well across all frequencies in forward and reverse conditions.
(These changes can be found on page number-20, and line numbers-554-555)
Case 6, a configuration with a tapered portion and a step, performs well in the 630 to 800 Hz range in forward and reverse conditions.
(These changes can be found on page number-20, and line numbers-569-570)
This analysis highlights the effectiveness of the tapered hole design in enhancing both sound absorption and noise reduction coefficients, particularly in higher frequency ranges.
(These changes can be found on page number-18, and line numbers-520-522).
Comments 7: The model uses a poroacoustic domain for the foam, using the empirical Delany and Bazley model. Only the flow resistivity is needed. How is the parameters obtained at ‘exactyly’ 13498 Pa.s/m2? I guess 13.5 kPa.s/m2 is accurate enough?
Response 7: Thank you for bringing this to our attention. Following your suggestions, we have made the necessary updates to the manuscript.
The flow resistivity was measured using an airflow resistivity meter, adhering to the DIN EN 29053 standard.
(These changes can be found on page number-10, and line numbers-350-352).
Comments 8: In general, can you measure the absorption coefficient for each one-third octave bands with a three digit accuracy?
Response 8: Thank you for your comment. In this study, we calculated the sound absorption coefficients to five decimal places for one-third octave bands and rounded them to three decimal places. Accordingly, the values are presented in the manuscript with three decimal places.
Comments 9: Line 101: replace ‘measure’ with ‘calculate’.
Response 9: Thank you for your comment. We agree that "calculate" is the appropriate term to use. Therefore, we have replaced "measure" with "calculate" in the manuscript.
(These changes can be found on page number-3, and line number-133)
Comments 10: Line 123 section: suggestion to delete this section; statements are over the top.
Response 10: Thank you for bringing this to our attention. We agree with your comment and have accordingly made revisions to the main manuscript.
(These changes can be found on page number-3).
Comments 11: Section 1.1: suggestion to delete this section; this is more suitable for a textbook.
Response 11: Thank you for highlighting this important point. We agree with your suggestion and have made changes to the manuscript accordingly.
(These changes can be found on page number-4).
Comments 12: Lines 266 & 267: delete?
Response 12: Thank you for this comment. We agree with your suggestion. The lines you mentioned have been removed from the manuscript.
(These changes can be found on page number-8).
Comments 13: Line 283: why is the model mentioned as a ‘multiphysics-enabled environment’? As it is (only) the acoustic environment using normal acoustics and interaction with foam (via Delany & Bazley).
Response 13: Thank you for your feedback. We acknowledge the importance of using the correct terminology. Therefore, we have revised the manuscript to reflect this consideration.
The acoustics module in our simulation framework provides an environment with normal acoustics and interaction with an acoustic absorber for sound propagation analysis.
(These changes can be found on page number-9, and line numbers-342-343).
Comments 14: Table 1 & 2: mention that these are calculated results. Could the tables also be represented as figures?
Response 14: We acknowledge that providing specific information is very important, so frequency-dependent sound absorption for different cases in Forward and Reversed Configurations has been added and shown with the help of a figure in the manuscript. Thank you for pointing this out.
3.3. Frequency-Dependent Sound Absorption Characteristics of Various Cases
The following Figure 6 visualizes sound absorption coefficients as a function of frequency, ranging from 0 to 4000 Hz, for six cases in both forward and reversed configurations, represented by twelve curves. The coefficients, varying between 0 and 1.0, peak between 500 and 1000 Hz, highlighting optimal absorption. Post-peak, the curves decline, indicating reduced efficacy at higher frequencies. This pattern reflects how material properties or setup variations impact the sound absorption characteristics, providing a clearer understanding of the data presented in Tables 1 and 2.
Figure 6. Frequency-Dependent Sound Absorption for Different Cases in Forward and Reversed Configurations
(These changes can be found on page numbers-12-13, and line numbers-395-407).
Comments 15: Conclusion, last Section. Suggestion to rephrase with more modest words.
Response 15: Thank you for your suggestion to rephrase the conclusion. We recognize the importance of precise wording and the need to present our findings in the appropriate way. Accordingly, we have updated the manuscript.
Through both computational simulations using COMSOL Multiphysics 6.0 and experimental validations, the influence of diverse hole geometries and panel orientations on the sound absorption coefficient and noise reduction coefficient was assessed.
Our results show that the perforated panel with a tapered hole geometry achieved the maximum noise reduction coefficient of 0.444, performing better than other configurations. The geometry and orientation of the holes are vital for effective sound absorption.
The study provides insights into sound absorption in porous and perforated materials, offering a framework for material and design selection in noise-sensitive settings. It highlights rapid prototyping for panel fabrication as a promising area for further research and application in acoustic engineering. This research advances the understanding of complex acoustic structures, setting a foundational base for future innovations in noise control and acoustic design. Exploration of diverse hole geometries with varying depths in perforated panels is essential to assess their impact on sound absorption, advancing understanding of acoustic properties.
(These changes can be found on page numbers-21-22, and line numbers-607-621).
Reviewer 2 Report
Comments and Suggestions for AuthorsThis paper investigates the noise attenuation properties of open-pore polyurethane foam and perforated onyx panels. While in the foam, the energy of the sound is converted into heat; in the panels, it is dissipated by resonant behavior. The impact of hole geometries and panel orientations on sound absorption and noise reduction was assessed by COMSOL Multiphysics 6.0 and impedance tube experiments according to ISO 10534-2. In this work, six 3D-printed perforated panel configurations were tested with different hole diameters and backed by a 24 mm foam layer. A tapered hole design from 4 mm down to 2 mm showed the highest absorption in the range from 100 to 4000 Hz frequency, which corresponded to a noise reduction coefficient of 0.444. Overall, forward configurations showed better performance compared to reverse configurations, proving the importance of hole geometry and orientation. Experimental results matched FEA simulations, thus verifying the computational model.
The novel contribution of this manuscript should be better highlighted, mostly from a conceptual/methodological point of view, compared to the present relevant literature and, more specifically, with reference to bibliographic entries [32] and [33] from the same authors. Furthermore, some detailed comments are pointed out in the attached review; however, it should be underlined that acceptance is not conditional upon agreeing to the proposed bibliography enrichment suggestions.
Comments for author File: 
Comments.pdf
From a stylistic point of view, this manuscript is quite well written and only needs a minor language revision.
Author Response
Thank you for your detailed review and constructive feedback on our manuscript. We have carefully revised the manuscript in response to each comment, with changes marked in red and highlighted in yellow in the updated version. Below, we provide point-by-point responses to your comments, also highlighted in red. We believe these revisions elevate our manuscript to meet the journal's standards and hope for its acceptance.
Comments 1: At the end of this section, I suggest to add the outline of the contents of this manuscript in a detailed manner, eg.: “In Sec.2…In Sec3…etc”.
Response 1: Thank you for pointing this out. We agree with this comment. As per your comment, we have made changes in the main manuscript.
This information provides an outline of the contents. Section 1 presents a technical overview of existing literature relevant to our research, focusing on sound absorption mechanisms and analyzing the influence of panel cavity depth on the sound absorption coefficient. Section 2 details the materials employed for sound absorption, including a morphological analysis of polyurethane foam, methods for assessing sound absorption coefficients, contributions of this research and the details of acoustic structures. Section 3 outlines the computational model and parameters implemented for acoustic analysis using COMSOL Multiphysics 6.0, and presents the corresponding simulation results. Section 4 describes the experimental validation process, detailing the 3D printing of acoustic samples and the configuration of measurement setups for acoustic testing. Section 5 interprets both computational and experimental results. Section 6 analyzes the impact of different hole geometries on acoustic performance, incorporating comparative studies with prior research. Section 7 summarizes the entire research, outlining key findings and implications.
(These changes can be found on page number-4 and line number-155-168).
Comments 2: Authors should be cited by only using surnames. Please check and eventually fix this aspect in the whole manuscript.
Response 2: Thank you for pointing this out. We agree with your comment and have made the necessary changes in the main manuscript as per your suggestion.
Comments 3: In the context of Helmholtz acoustic resonators, it may be worth citing the following relevant researches: https://doi.org/10.1080/15376494.2023.2237699.
Response 3: Thank you for highlighting this. In response to your suggestions, we have added this paper, and the manuscript has been revised accordingly.
(These changes can be found on page number-2 and line number-58-61)
(These changes can be found on page number-22 and line number-648-649).
Comments 4: Generally, a section is divided into subsections only if there are two or more of them. Please check and eventually fix this aspect in the whole manuscript.
Response 4: We acknowledge the importance of precise information and have updated and revised the manuscript accordingly.
Sound absorption in materials involves reflection, absorption, and transmission of sound waves, influenced by material properties and wave incidence. Porous absorbers are designed to minimize reflection and maximize energy dissipation as heat, enhancing noise control and acoustic quality in various environments.
(These changes can be found on page number-3 and line number-124-128).
Comments 5: Captions should always end with a dot. Please check and eventually fix this aspect in the whole manuscript.
Response 5: Thank you for pointing this out. We agree with your comment and have made the necessary changes in the main manuscript as per your suggestion.
Comments 6: Further information about the finite element model are required to be reported or better discussed, such as the number and /or type of DoFs, nodes, elements, constraints, loads, etc.
Response 6: Thank you for highlighting this. In response to your suggestions, we have added the information related to the above points, and the manuscript has been revised accordingly.
The mesh is complete with 49,513 vertices and a total of 286,629 elements, which include 285,925 tetrahedra, 704 prisms, 33,848 triangles, and 160 quads. There are also 1,913 edge elements and 120 vertex elements. Element quality varies, with a minimum quality of 0.1316 and an average quality of 0.649. Mesh parameters include a maximum element size of 0.0515 and a minimum size of 0.00374. The curvature factor is 0.4, the resolution of narrow regions is 0.7, and the maximum element growth rate is 1.4. The predefined size is finer.
(These changes can be found on page number-10 and line number-354-360).
Comments 7: It may be interesting to predict and discuss possible further developments of the present research at the end of this section.
Response 7: Thank you for bringing this to our attention. Following your suggestions, we have made the necessary updates to the manuscript.
Exploration of diverse hole geometries with varying depths in perforated panels is essential to assess their impact on sound absorption, advancing understanding of acoustic properties.
(These changes can be found on page number-22 and line number-619-621).
