Parameter Optimization for Composite Structures of Microperforated Panel and Porous Metal for Optimal Sound Absorption Performance

Round 1

Reviewer 1 Report

In this work, the authors constructed a theoretical model for the composite structure of the microperforated panel and porous metal based on Maa’s theory and Johnson-Champoux-Allard model. Factors optimisation using cuckoo search algorithm was carried out. The model was simulated and experimentally validated. The presented work is interesting and well written. 

 

These are my comments:

Section 3.2. Validation of the optimal composite structure:

This section should include photos of the setup and the fabricated samples.

Author Response

Response to reviewer 1’s comments

Summary: In this work, the authors constructed a theoretical model for the composite structure of the microperforated panel and porous metal based on Maa’s theory and Johnson-Champoux-Allard model. Factors optimisation using cuckoo search algorithm was carried out. The model was simulated and experimentally validated. The presented work is interesting and well written.

Response: Thanks a lot for your kind comments. We aimed to develop the optimal composite structure of microperforated panel and porous metal for industrial noise reduction, and it sound absorption performance was optimized by through parameter optimization. Corresponding modifications had been conducted in the revised paper according to your comments, which we wished to meet your requirements.

Point 1: Section 3.2. Validation of the optimal composite structure: This section should include photos of the setup and the fabricated samples.

Response 1: Thank you so much for your kind suggestion. Physical pictures of the used AWA6128A detector and the fabricated samples of optimal composite structures were added in the revised paper, as shown in the Figures 7b and 8 respectively. Meanwhile, preparation of the composite structures were introduced in the revised paper, and these modifications were highlighted in yellow.

We appreciate for your warm work and hope that the correction will meet with approval. We are looking forward to the result of final acceptance.

Once again, thank you very much for your comments and suggestions.

Author Response File: Author Response.docx

Reviewer 2 Report

The paper deals with the optimization of the sound absorption coefficient of multilayered systems (under various configurations) including cavities, porous materials, and perforated panels.

The approach combines theorical developments, as well as numerical and experimental results.

The paper is interesting but not strong novelty/originality is published here.

Remarks are attached in the annotated pdf file.

I would suggest going deeper in the analysis of the uncertainty of the approach.

Comments for author File: Comments.pdf

Author Response

Response to reviewer 2’s comments

Summary: The paper deals with the optimization of the sound absorption coefficient of multilayered systems (under various configurations) including cavities, porous materials, and perforated panels. The approach combines theorical developments, as well as numerical and experimental results. The paper is interesting but not strong novelty/originality is published here. Remarks are attached in the annotated pdf file. I would suggest going deeper in the analysis of the uncertainty of the approach.

Response: Thanks a lot for your kind comments. We aimed to develop the optimal composite structure of microperforated panel and porous metal for industrial noise reduction, and it sound absorption performance was optimized by through parameter optimization. Corresponding modifications had been conducted in the revised paper according to your comments, which we wished to meet your requirements.

Point 1: Line 28, In the abstract, ‘AWA6128A detector’ is not necessary at the abstract level.

Response 1: Thank you so much for your kind reminder. The presentation of ‘AWA6128A detector’ is deleted in the abstract in the revised paper.

Point 2: Line 88-90, ‘porous metal + cavity + microperforated panel + cavity, microperforated panel + cavity + porous metal + cavity, and porous metal + cavity + microperforated panel + cavity + porous metal + cavity.’, Please itemize on the various configuration.

Response 2: Thank you so much for your kind suggestion. The presentations of ‘porous metal + cavity + microperforated panel + cavity’, ‘microperforated panel + cavity + porous metal + cavity’, ‘porous metal + cavity + microperforated panel + cavity + porous metal + cavity’, ‘porous metal + cavity’, and ‘microperforated panel + cavity’ are labelled as PCMC, MCPC, PCMCPC, PC, and MC respectively, and the marks in the Figures 2, 3, 4, 6, 8, and 9 are also modified, which aims to make the presentation more readable. Meanwhile, these modifications are highlighted in yellow.

Point 3: Line 111-113, ‘porous metal + cavity + microperforated panel + cavity, microperforated panel + cavity + porous metal + cavity, and porous metal + cavity + microperforated panel + cavity + porous metal + cavity.’, idem: itemize to avoid confusion.

Response 3: Thank you so much for your kind suggestion. The overlong presentation has been simplified in the revised paper, and these modifications are highlighted in yellow.

Point 4: Equations (5) and (6), these are not equations derived from Johnson, Champoux and Allard theory. I do not see these equations in Kino and Ueno modifications. Please clarify where this model comes from and specify clearly the associated references.

Response 4: Thank you so much for your kind reminder. The Equations (5) and (6) are generated from the classical Johnson-Champoux-Allard model, and some symbols are changed in the reference [8,9,36,37] from the original in the reference [27]. Thus, the reference [8,9,27,36,37] are also added in deriving the transfer matrix for the porous metal in the revised paper, and these modifications are highlighted in yellow.

Point 5: Eqs 16 to 18: TT11 to TT22 multiply defined, use subscript a to d.

Response 5: Thank you so much for your kind suggestion. The Equations  (16) to (20) are modified according to your comments in the revised paper, and these equations are highlighted in yellow.

Point 6: In Table 1, This is not experimental! Please use another term here.

Response 6: Thank you so much for your kind reminder. The ‘Experimental serial’ is replaced by ‘Serial number’ in the Table 1, and the marks in the Figure 2 are also corresponding modified.

Point 7: In Figure 3, do not use line between markers.

Response 7: Thank you so much for your kind suggestion. The lines between marks in the Figure 3 are deleted, as shown in the revised paper.

Point 8: In Line 330, ‘The selected porous metal was porous copper,’, Please detail how this materiel is produced. Detail also the origin of the perforated panel. Photos are welcome here.

Response 8: Thank you so much for your kind reminder. As mentioned in the paragraph 4 of section 1, we point out that the required microperforated panels are fabricated by precision laser beam machining [32], and the porous metals are prepared by the electrodeposition [33]. Meanwhile, Physical pictures of the used AWA6128A detector and the fabricated samples of optimal composite structures are added in the revised paper, as shown in the Figures 7b and 8 respectively. Moreover, preparation of the composite structures were introduced in the revised paper, and these modifications were highlighted in yellow.

Point 9: In Line 340-348, A systematic review of the uncertainities is necessary here to discuss the validation of the approaches:

- uncertainty about material design (thicknesses, diameter of perforation, ...)

- uncertainty about charaterisation (sound absorption coeff)

Response 9: Thank you so much for your kind suggestion. Uncertainties are not taking into consideration in our original research. It is our pleasure to receive such constructive suggestions from you. We have added systematic review of the uncertainties in the paragraph 3 of the section 3.2 in the revised paper, and these modifications were highlighted in yellow.

We appreciate for your warm work and hope that the correction will meet with approval. We are looking forward to the result of final acceptance.

Once again, thank you very much for your comments and suggestions.

Author Response File: Author Response.docx

Reviewer 3 Report

Review of the manuscript « Parameter optimization of composite structure of microperforated panel and porous metal for optimal sound absorption performance » by H. Duan, X. Shen, F. Yang, P. Bai, X. Lou and Z. Li, sent to Applied Science.

The manuscript proposes a parameter optimization for some arrangements of porous metal panels, cavities and microperforated panels, in the context of sound absorption.  Globally, it is well built and scientifically accurate. I have no major objection for the publication. I however have some minor remarks and questions, which follow:

Although the English along the manuscript is globally good, most of the paper is written in the past tense. Please rewrite it in the present tense, as it is classical in the scientific literature. Figure 2 proposes several examples of the structure “porous metal + cavity + microperforated panel + cavity”, which is useful. Can the author provide the average sound absorption coefficient in the [2000 – 6000] Hz range? It would provide more highlights on the performance of the optimized cases. Section 3.1 : What software package have been used in the finite element simulation ? What element and what number of dof ? Section 3.2 : In the experimental section, Figure 8 shows similar tendencies for experiment and theoretical results, attributed to manufacturing errors. Can the authors find in the literature similar discrepancies between Maa’s and JCA’s model and experiments?

Author Response

Response to reviewer 3’s comments

Summary: Review of the manuscript « Parameter optimization of composite structure of microperforated panel and porous metal for optimal sound absorption performance » by H. Duan, X. Shen, F. Yang, P. Bai, X. Lou and Z. Li, sent to Applied Science. The manuscript proposes a parameter optimization for some arrangements of porous metal panels, cavities and microperforated panels, in the context of sound absorption.  Globally, it is well built and scientifically accurate. I have no major objection for the publication. I however have some minor remarks and questions.

Response: Thanks a lot for your kind comments. We aimed to develop the optimal composite structure of microperforated panel and porous metal for industrial noise reduction, and it sound absorption performance was optimized by through parameter optimization. Corresponding modifications had been conducted in the revised paper according to your comments, which we wished to meet your requirements.

Point 1: Although the English along the manuscript is globally good, most of the paper is written in the past tense. Please rewrite it in the present tense, as it is classical in the scientific literature.

Response 1: Thank you so much for your kind suggestion. Most of the paper is rewritten in the present tense, except the literature review in the section ‘1. Introduction’ in the revised paper.

Point 2: Figure 2 proposes several examples of the structure “porous metal + cavity + microperforated panel + cavity”, which is useful. Can the author provide the average sound absorption coefficient in the [2000 – 6000] Hz range? It would provide more highlights on the performance of the optimized cases.

Response 2: Thank you so much for your kind suggestion. Average sound absorption coefficients in the [2000 – 6000] Hz range of the investigated composite structures in the Figure 2 are calculated and added in the Table 1, which is highlighted in yellow in the revised paper.

Point 3: Section 3.1 : What software package have been used in the finite element simulation ? What element and what number of dof ?

Response 3: Thank you so much for your kind suggestion. The used software is Virtual. Lab Acoustics for the finite element simulation. Size of each element in this simulation model is 5 mm, and it is triangular mesh in the thickness direction, which indicate that there utilize 897 points in the calculation process. These information are added in the revised paper, and these modifications are highlighted in yellow.

Point 4: Section 3.2 : In the experimental section, Figure 8 shows similar tendencies for experiment and theoretical results, attributed to manufacturing errors. Can the authors find in the literature similar discrepancies between Maa’s and JCA’s model and experiments?

Response 4: Thank you so much for your kind suggestion. In our former researches, such as the references [29, 35, 36, 41], we have compared the theoretical results with the experimental results for multilayer microperforated panel, microperforated compressed porous metal panel, gradient compressed porous metal, and combination of porous metal and microperforated panel respectively, which show similar tendencies for the theoretical data and experimental data. In these studies, sound absorption performance of the porous metal is theoretical modelled according to JCA model, and that of the microperforated panel is built based on the Maa’s theory. Therefore, effectiveness and feasibility of the Maa’s and JCA’s model are certified and proved.

We appreciate for your warm work and hope that the correction will meet with approval. We are looking forward to the result of final acceptance.

Once again, thank you very much for your comments and suggestions.

Author Response File: Author Response.docx

Reviewer 4 Report

The paper was read with interest.

The previous paper by Xinmin Shen was also considered. Published in MDPI Applied sciences, April 2019. It can be seen that there is a remarkable overlap between both papers.  For the present paper it is suggested to compress the content and make use of references to the previous paper.

The following remarks and questions are given:
- A small change for the title is suggested: Parameter optimization "for" composite structure"s" of ...
- The frequency range between 2000 and 6000 Hz is considered. Industrial noise in a workshop is mentioned for the application. It seems that this frequency range is rather high, in general. Can the authors explain a bit more on the application?
- There is little information on the AWA6128A detector. Fro instance what size is the cross section? For example, for a small cilinder with a 4 cm diameter the cut-off frequency is already at 5000 Hz.
- An accuracy of two digits after the decimal point for the absorption coefficient is not likely, both for experiments and simulations. It is mentioned that measurements were carried out more than 10 times. So it would be interested to see the spread in the results.
- Results and discussions, section 3.1. It is unclear at this stage how it is demonstrated that the optimal structural parameters obtained by the chuckoo search algorithm were reasonable and accurate.
- There is a conclusion for an optimal structure with a width of 36.8 mm and 98% absorption. But there is also a structure with 37 mm and 97% absorption, with a layer of porous metal and a cavity less. Perhaps the use of an average sound absorption coefficient is not suitable here to reach this conclusion? Some further explanation is welcome.

Author Response

Response to reviewer 4’s comments

Summary: The paper was read with interest. The previous paper by Xinmin Shen was also considered. Published in MDPI Applied sciences, April 2019. It can be seen that there is a remarkable overlap between both papers.  For the present paper it is suggested to compress the content and make use of references to the previous paper.

Response: Thanks a lot for your kind comments. We aimed to develop the optimal composite structure of microperforated panel and porous metal for industrial noise reduction, and it sound absorption performance was optimized by through parameter optimization. Corresponding modifications had been conducted in the revised paper according to your comments, which we wished to meet your requirements.

Point 1: A small change for the title is suggested: Parameter optimization "for" composite structure"s" of ...

Response 1: Thank you so much for your kind reminder. The title is modified according your comment in the revised paper, and this modification is highlighted in yellow.

Point 2: The frequency range between 2000 and 6000 Hz is considered. Industrial noise in a workshop is mentioned for the application. It seems that this frequency range is rather high, in general. Can the authors explain a bit more on the application?

Response 2: Thank you so much for your kind inquiry. There are many apparatuses working with the high-frequency vibration mode in the target workshop in this study, so major noise with the frequency range [2000 Hz, 6000 Hz] is detected by the testing equipment. Therefore, we aim to develop the optimal composite structure of microperforated panel and porous metal for reduction of this noise in the frequency range [2000 Hz, 6000 Hz].

Point 3: There is little information on the AWA6128A detector. Fro instance what size is the cross section? For example, for a small cilinder with a 4 cm diameter the cut-off frequency is already at 5000 Hz.

Response 3: Thank you so much for your kind suggestion. Diameter of cross-sectional of the AWA6128A detector is 96 mm, and its measurable frequency range is [1500 Hz, 6640 Hz]. Length of the slideway is 1000 mm, which can support motion of the pulley to detect peak value and valley value of the reflected sound wave. These information on the AWA6128A detector are added and highlighted in yellow in the revise paper.

Point 4: An accuracy of two digits after the decimal point for the absorption coefficient is not likely, both for experiments and simulations. It is mentioned that measurements were carried out more than 10 times. So it would be interested to see the spread in the results.

Response 4: Thank you so much for your kind comment. The sound absorption coefficient in the simulation data is obtained from the finite element simulation process, so its accuracy of two digits after the decimal point is reasonable, because the simulation process can be considered as a visualized and modularized theoretical analysis. Meanwhile, in order to reduce the accidental measuring error, each sound absorber is measured by more than 10 times, and the final sound absorption coefficient in the experimental data is average value of all the corresponding experimental values. It have been proved in our former research (such as references [29, 35, 36, 41]) that for one certain sound absorber, differences among experimental data for each measuring process in the multiple measurements are tinny, and their evolutions along with the sound frequency are exactly same.

Point 5: Results and discussions, section 3.1. It is unclear at this stage how it is demonstrated that the optimal structural parameters obtained by the chuckoo search algorithm were reasonable and accurate.

Response 5: Thank you so much for your kind inquiry. The optimal structural parameters are obtained by the cuckoo search algorithm based on the constructed theoretical sound absorption model, which indicate that the obtained optimal structural parameters can achieve best sound absorption performance under the given constraint conditions. In section 3.1, through input the optimal structural parameters into the finite element simulation model, the corresponding simulation data are achieved. Meanwhile, in section 3.2, through standing wave tube measurement, the corresponding experimental data are obtained. Consistence among theoretical data, simulation data, and experimental data proves that the optimal structural parameters obtained by the cuckoo search algorithm are reasonable and accurate.

Point 6: There is a conclusion for an optimal structure with a width of 36.8 mm and 98% absorption. But there is also a structure with 37 mm and 97% absorption, with a layer of porous metal and a cavity less. Perhaps the use of an average sound absorption coefficient is not suitable here to reach this conclusion? Some further explanation is welcome.

Response 6: Thank you so much for your kind suggestion. The composite structure of porous metal + cavity + microperforated panel + cavity (PCMC) with the limited total thickness of 50 mm is 37.04 mm (including the cavity with length of 10.77 mm), and its average sound absorption coefficient of 96.76% is close to that 97.65% of corresponding optimal porous metal + cavity + microperforated panel + cavity + porous metal + cavity (PCMCPC) with thickness of 36.8 mm. Therefore, taking complexity of the composite structure into account, the PCMC can also be treated as novel sound absorber with fewer utilized materials for reduction of the industrial noise. These contents are added in the revised paper, and these modifications are highlighted in yellow.

We appreciate for your warm work and hope that the correction will meet with approval. We are looking forward to the result of final acceptance.

Once again, thank you very much for your comments and suggestions.

Author Response File: Author Response.docx

Round 2

Reviewer 2 Report

The paper has been improved compared to last version.

However, details are still missing about uncertainties.

Please detail:

the uncertainty in length measurement (±1mm?; ±0.1mm?...) the uncertainty in sound absorption measurement (±5%?....). Provide references on this post.

And discuss the consequences on the interpretation of your results.

 

Author Response

Response to reviewer 2’s comments

Summary: The paper has been improved compared to last version. However, details are still missing about uncertainties. Please detail: the uncertainty in length measurement (±1mm?; ±0.1mm?...) the uncertainty in sound absorption measurement (±5%?....). Provide references on this post. And discuss the consequences on the interpretation of your results.

Response: Thanks a lot for your kind and rapid comments. We agree with you that there exists uncertainties in the validation process, one of which is about material design of the composite structure and the other is about characterization of the sound absorption coefficient. Thickness of the utilized porous metal samples has fabrication error, especially those special blocks, which is measured by the vernier caliper. It can be found that uncertainty of thickness of the used porous metal sample is ±0.01 mm and that of the microperforated panel is ±0.004 mm. Meanwhile, length of the rear cavity in the optimal sound absorber is controlled through the sample holder, and its control accuracy is ±0.01 mm. Thus, total uncertainty of the sound absorber is ±0.024 mm. It had been proved by Qian et al. [32,43] that the fabrication error within the submillimeter range had few influence to sound absorption performance of the sound absorber. Meanwhile, there is uncertainty in measuring the sound absorption coefficients, and each sound absorber is measured by more than 10 times. For example, when the limited thickness is 30 mm, evolutions of experimental data of sound absorption coefficients of the PCMC in the 10 times standing wave tube measurements are shown in the Figure 10 in the revised paper. It can be observed that undulation of the experimental data is in ±0.2%, which further prove that uncertainty in the measurement is tiny and it has few influence to the research results in this study. These presentations and the Figure 10 are added in the revised paper, and these modifications are highlighted in green, which aims to distinguish with the modified contents highlighted in yellow in the first round revision.

We appreciate for your warm work and hope that the correction will meet with approval. We are looking forward to the result of final acceptance.

Once again, thank you very much for your comments and suggestions.

Author Response File: Author Response.pdf

Reviewer 4 Report

My thanks to the authors for addressing most of the questions and remarks.

Author Response

Response to reviewer 4’s comments

Summary: My thanks to the authors for addressing most of the questions and remarks.

Response: Thanks a lot for your positive comments and kind support. Corresponding modifications had been conducted in the revised paper according to your and the other reviewers’ comments, which we wished to meet your and the other reviewers’ requirements.

We appreciate for your warm work and hope that the correction will meet with approval. We are looking forward to the result of final acceptance of our manuscript.

Once again, thank you very much for your comments and suggestions.

Author Response File: Author Response.pdf