Research on the Acoustic Attenuation Performance and Optimization of Split-Stream Rushing Exhaust Mufflers in the Presence of Acoustic–Structure Coupling Effects

Dear Reviewer,

We sincerely thank you for your review of our manuscript and the constructive criticisms offered. Regarding the concerns you have raised regarding a perceived lack of novelty, the limited relevance of the research findings, and an insufficient integration with existing literature, we have accorded these matters significant importance and engaged in thorough introspection. We understand that these concerns have impacted your overall assessment of the manuscript, and we earnestly accept the decision not to recommend publication at present. Nevertheless, we still hope to avail ourselves of this opportunity to offer a concise clarification of certain differing interpretations concerning the novelty of the research and overlap with existing literature, and to implement substantive revisions to the manuscript content.

Below, we provide point-by-point responses to your comments. The revised manuscript incorporates the theoretical framework and analysis of structural modes(Lines 119-145, Lines 449-493 ), the theoretical framework and analysis of acoustic cavity modes(Lines 146-180, Lines 494-537 ), the impact of two structural parameters on transmission loss(Lines 671-719), mesh generation(Lines 326-343), and muffler optimization(Lines 720-742). All remaining modifications made in the revised manuscript have been marked in red text. While not all of this material directly addresses the reviewers' feedback, it is intended to augment the depth of the manuscript and provide a response to the review process.

Response to reviewer's comments:

Comments 1: The authors claim that their design is "novel," but it is clearly not. The authors published their first paper on this type of muffler in 2018 (https://doi.org/10.1016/j.jsv.2018.04.025), and they have failed to reference it in Figure 1, where it is evident that the same image has been used.

Response 1:

Thank you for raising this important issue. Figure 1 is indeed the schematic of the split-stream rushing muffler conceived by our research group in prior investigations, with its initial publication appearing in our preliminary studies. The omission of a clear citation in Figure 1 within the present manuscript was an inadvertent oversight. We extend our sincere apologies for this oversight and have duly included the citation in the revised version of the manuscript. It is important to clarify that while the muffler configuration employed in the present study draws upon the fundamental principle previously introduced by our team, this manuscript presents substantial innovations and extensions building upon that foundation. Firstly, the present research systematically incorporated the effects of sound-structure coupling, leading to the development of a more realistic representative model. Secondly, the credibility of the simulation was validated through the establishment of an experimental platform. Finally, within the revised version of the manuscript, the optimization of the muffler was conducted based on the results of single-factor analysis. The aforementioned research exhibits marked methodological distinctions from prior work, thereby forming the principal novel aspects of the present investigation.

Comments 2: A substantial portion of the paper is devoted to the basic theory of acoustic-structure coupling. However, in the end, the authors use this theory only for mode calculations, which seem irrelevant as those calculations are not applied later in the paper. Additionally, I have numerous doubts about whether these derivations are original to the authors, as they lack sufficient references and explanations. This knowledge is well-established in the field.

Response 2:

Thank you for providing this insightful feedback. We acknowledge the reviewers' concern regarding the perceived inadequate linkage between the fundamental principles of acoustic-structure coupling presented within the manuscript and their subsequent applications. In response, we provide the following clarification: The fundamental principles of acoustic-structure coupling expounded within the manuscript serve predominantly to lay the theoretical groundwork for the ensuing coupled modal analysis. We acknowledge that certain sections of the manuscript reflect a synthesis of well-established derivation procedures for the governing equations of acoustic-structure coupling systems, and therefore do not represent entirely original theoretical developments. Given that this derivation procedure is prevalent in numerous acoustics textbooks and scholarly works, our initial manuscript did not provide an exhaustive list of all relevant references, resulting in a demonstrable inadequacy in the citation. The revised version of the manuscript now includes supplementary relevant classical literature:[20] Zhong, J.; Zhao, H.; Yang, H.,; Yin, J.; Wen, J. Effect of Poisson's loss factor of rubbery material on underwater sound absorption of anechoic coatings. J. Sound Vib. 2018, 424, 293-301.

Comments 3: The authors do not provide detailed explanations of the FEM models or reference the software used. Based on the analysis of the plots, I suspect they used COMSOL Multiphysics. As a result, the authors did not employ any of the equations presented in the theoretical section; they merely utilized some well-known software for FEM modeling.

Response 3:

Thank you for providing this meticulous feedback regarding our finite element modeling section. We acknowledge that in the initial draft, COMSOL software was only mentioned in the keywords. Therefore, relevant descriptions have been added to the revised manuscript(Lines 20-22, Lines 109-111, Lines 539-541). The theoretical derivation presented herein serves to systematically elucidate the foundational theoretical framework for such problems, elucidating the coupling mechanism between the acoustic and structural fields from a physical mechanism standpoint. This procedure furnishes the physical context and fundamental comprehension necessary for the ensuing modal analysis, notably providing crucial support for the analysis of modal coupling phenomena. We fully recognize the advanced state of coupling modeling functionalities offered by contemporary commercial software, but it is still necessary to enhance physical understanding through the presentation of the theory. Therefore, this section has been preserved to augment the integrity and comprehensibility of the manuscript, and not as a novel contribution. Within the revised manuscript, we shall further delineate that the principal novel contributions of this research reside in the acoustic-structure coupling performance assessment, transmission loss comparative analysis, and structural parameter optimization.

Comments 4: The FEM modal analysis for the muffler presented in chapter 5.1 is not meaningful since it does not contribute to performance or design improvements. For example, the assertion in line 492 that this design "enhances uniformity" lacks practical significance.

Response 4:

Thank you for providing this insightful recommendation regarding Section 5.1, the finite element modal analysis section. The section on modal analysis within the original Chapter 5.1 has been deleted, and the remaining pertinent content has been consolidated into the revised Chapter 5.3. The revised chapter redirects the analytical emphasis towards the coupling interrelations among acoustic-structure coupled modes, structural modes, and acoustic cavity modes, a focus that contributes to a deeper comprehension of the acoustic-structure coupling mechanism.

Comments 5: Considering the above points, the only original contribution of this paper appears to be the investigation of the influence of acoustic-structure coupling in FEM muffler simulations and the effect of wall thickness. However, even if we acknowledge these as original results, the findings are ultimately irrelevant, as the observed differences are nearly negligible, raising questions about model preparation. The same applies to the wall thickness study; while it may show differences in the range of 2600-2900 Hz, these variations have no implications since the noise produced by mufflers and engines occurs in entirely different frequency bands.

Response 5:

We appreciate you bringing this to our attention. In response, we have implemented the following modifications to the manuscript:

1. The section in the original manuscript about the impact of wall thickness variation has been abridged.

2. To augment the utility and rigor of the structural parameter analysis, we have incorporated an investigation into the impact of inner pipe diameter and inner pipe length variations on transmission loss (Pages 22-24, Lines 671-719).

3. Based on the preceding efforts, we performed a comprehensive optimization analysis encompassing the three pivotal parameters: wall thickness, inner pipe diameter, and inner pipe length (Page 25, Lines 720-742).

It is our conviction that the structural parameter analysis and optimization segment of this research has been enhanced in both engineering applicability and scientific rigor through the aforementioned revisions, and it more effectively addresses your judicious recommendations.

Thank you once again for your time, effort, and support.

Dear Reviewer,

We sincerely thank you for your comprehensive evaluation and affirmation of this study. We are highly gratified by the recognition of the innovative aspects of this research in acoustic-structure coupling modeling and the affirmation of its practical utility in transmission loss prediction and optimization analysis.

We have carefully considered your comments and made the necessary revisions to enhance the manuscript. Below, we provide point-by-point responses to your comments. Below, we provide point-by-point responses to your comments. The revised manuscript incorporates the theoretical framework and analysis of structural modes(Lines 119-145, Lines 449-493 ), the theoretical framework and analysis of acoustic cavity modes(Lines 146-180, Lines 494-537 ), the impact of two structural parameters on transmission loss(Lines 671-719), mesh generation(Lines 326-343), and muffler optimization(Lines 720-742). All remaining modifications made in the revised manuscript have been marked in red text. While not all of this material directly addresses the reviewers' feedback, it is intended to augment the depth of the manuscript and provide a response to the review process.

Response to reviewer's comments:

Comments 1: The study acknowledges the need for further optimization in test accuracy, suggesting that future work could involve more refined measurement techniques or additional validation with different engine configurations.

Response 1:

We extend our sincere gratitude to you for this insightful feedback on the experimental section and fully appreciate your emphasis on the precision of the testing. Our research also acknowledges that the precision of the current experimental measurements could be subject to further refinement. Subsequent research endeavors will incorporate more sophisticated and high-accuracy measurement methodologies to enhance the acquisition quality and dependability of acoustic data.

Comments 2: The frequency range considered, spanning from 10 to 4000 Hz, is reasonable, but exploring additional frequency bands could provide further insights into effects beyond this range.

Response 2:

We are deeply grateful to you for the insightful recommendations offered. In this study, the frequency range of 10–4000 Hz is principally predicated on the classification of this muffler as a reactive type and its primary application in single-cylinder diesel engines. According to relevant literature, 4000 Hz is considered a suitable upper-frequency limit. Subsequent research endeavors will involve the application of this muffler to three-cylinder or four-cylinder diesel engines, whereupon we will further investigate acoustic phenomena within elevated frequency spectra.

Comments 3: Additionally, the study assumes a fixed material composition for the muffler shell, and investigating how different materials influence acoustic-structure coupling could enhance the practical applicability of the findings.

Response 3:

We are deeply grateful to you for the insightful recommendations offered. We fully agree with the reviewers' viewpoint, and this will contribute to the enhancement of the real-world applicability of the research. Subsequent research endeavors will incorporate the introduction of diverse material parameters (e.g., elastic modulus and density) as variables to systematically investigate the influence of material property variations on coupled modes and acoustic performance, to augment the model's versatility and engineering applicability.

Comments 4: Given the computational demands of finite element method analysis, discussing the trade-offs between computational cost and accuracy would also add value to the study.

Response 4:

We are very grateful for this forward-looking suggestion you have provided. The matter of the "trade-off between computational cost and analysis accuracy" is indeed a critical consideration in finite element method-based engineering acoustics modeling, bearing significant implications for enhancing the model's practical utility and scalability. To ensure the fidelity of the acoustic-structure coupling simulation outcomes in this research, we implemented a relatively refined mesh discretization strategy and coupling solution parameters, consequently leading to comparatively elevated computational resource demands. During the simulation procedure, we have endeavored to optimize the equilibrium between solution precision and computational efficiency, exemplified by the application of a sweep meshing technique to the cylindrical ducts upstream and downstream of the muffler(Lines 337-340). In future research, we will conduct further research on this issue.

Comments 5: This paper presents a valuable and original contribution to muffler design and acoustic-structure coupling analysis. While some refinements could enhance its impact, the research is methodologically sound and well-supported by numerical and experimental data.

Response 5:

We sincerely thank you for recognizing the contributions of this study in the areas of muffler design and acoustic-structure coupling analysis. We are highly gratified that the reviewers acknowledge a degree of originality and value in the methodology employed by this research and recognize the well-established correlation between the numerical simulation and the experimental validation. In response to the reviewers' feedback, the pertinent content has been augmented and revised, with the inclusion of a single-factor optimization section in the revised manuscript, thereby aiming to elevate the academic influence of the paper.

Thank you once again for your time, effort, and support.

Dear Reviewer,

We extend our sincere gratitude to the reviewers for their attention to and positive acknowledgment of this research endeavor. We are highly gratified that you deemed the article to be innovative and possess readability. Regarding the issues you identified for further scrutiny, we have undertaken a meticulous analysis of each point and have addressed and modified them systematically within the revised manuscript. Presented below are our comprehensive responses and elucidations related to the aforementioned issues.

Below, we provide point-by-point responses to your comments. The revised manuscript incorporates the theoretical framework and analysis of structural modes(Lines 119-145, Lines 449-493 ), the theoretical framework and analysis of acoustic cavity modes(Lines 146-180, Lines 494-537 ), the impact of two structural parameters on transmission loss(Lines 671-719), mesh generation(Lines 326-343), and muffler optimization(Lines 720-742). All remaining modifications made in the revised manuscript have been marked in red text. While not all of this material directly addresses the reviewers' feedback, it is intended to augment the depth of the manuscript and provide a response to the review process.

Response to reviewer's comments:

Comments 1: While the article explains the acoustic-structure coupling phenomenon well, it would be beneficial to elaborate on its relevance for specific industrial applications.

Response 1:

We extend our sincere gratitude to you for this insightful recommendation concerning " elaborate on its relevance for specific industrial applications." We fully agree with this viewpoint. While the acoustic-structure coupling analysis in the present research primarily employs numerical and experimental approaches, a key objective is to elucidate the impact patterns of the reciprocal coupling between the acoustic field and the structure on the variations observed in the transmission loss curve. This coupling phenomenon holds considerable importance in real-world engineering applications, particularly within representative strongly coupled scenarios characterized by substantial structural vibration and acoustic field interaction, such as engine exhaust systems, wherein it can induce shifts or degradation in the acoustic performance of the muffler, consequently impacting the overall noise mitigation efficacy of the system. Therefore, a thorough investigation into the impact patterns of acoustic-structure coupling on acoustic performance holds significant reference value for enhancing the accuracy and engineering applicability of muffler design in complex operational scenarios.

Comments 2: The study presents experimental tests to validate simulations. Were measurement uncertainties considered? Including an error analysis would enhance the robustness of the results.

Response 2:

We sincerely thank you for this critical suggestions. Indeed, the analysis of measurement uncertainty is of considerable importance for augmenting the trustworthiness of experimental findings and the stringency of the research. In the present research, meticulous measures were undertaken during the experimental testing phase to mitigate potential sources of measurement error, including the implementation of standardized testing protocols, the execution of repeated trials, and the utilization of calibrated microphones for data acquisition. We reiterate our sincere gratitude to the reviewers for their meticulous scrutiny and expert guidance on this research.

Comments 3: The article states that the new design improves prediction accuracy. Could a quantitative comparison with previous approaches be added?

Response 3:

Thank you for the important suggestion. The present research primarily evaluates the predictive accuracy of the proposed coupling model by assessing the extent of agreement between simulation outcomes and experimental measurements, which has provided a degree of evidence for the efficacy of the acoustic-structure coupling approach. Moreover, inherent limitations in the experimental apparatus and modeling techniques employed in prior investigations resulted in comparatively lower data precision and substantial disparities in experimental conditions, thereby rendering the comparative analysis less compelling and potentially undermining the reader's judgment of the present model's reliability. Therefore, we have not presented that part of the data in the current manuscript.

Comments 4: The study analyzes only the influence of wall thickness. How do other factors, such as perforation geometry or muffler material, impact performance?

Response 4:

Thank you for this professional suggestion. We fully comprehend that beyond wall thickness, the performance of the muffler can be subject to the integrated influence of a multitude of structural parameters. Therefore, by the reviewers' recommendations, we have incorporated an analysis of two pivotal structural parameters, namely inner pipe diameter and inner pipe length, into the revised manuscript to systematically investigate the impact patterns of their variations on transmission loss, and these parameters have been jointly employed with wall thickness for optimization analysis.

Comments 5: Reducing exhaust flow resistance is a key objective in muffler design. Was the impact of this design on engine performance analyzed?

Response 5:

Thank you for raising this critical question. We concur entirely that minimizing exhaust flow resistance constitutes a primary objective in muffler design, and aerodynamic performance is directly correlated with the engine's output efficiency and stability, thereby holding considerable importance in real-world applications. The present research primarily concentrated on the acoustic-structure coupling investigation of the muffler and the impact of structural parameters on its acoustic performance within the context of acoustic-structure coupling. Owing to space constraints, a systematic analysis of flow resistance or engine performance was not undertaken. This constitutes a limitation of our present study. We intend to investigate this matter further in subsequent research endeavors.

Comments 6: Was a mesh convergence study performed to ensure that the results do not depend on mesh refinement in the simulations?

Response 6:

Thank you for raising this key question. We concur entirely that a mesh convergence analysis is of paramount importance for guaranteeing the stability and reliability of the simulation outcomes. Within the scope of this research, a mesh independence verification has been performed, predicated on the acoustic mesh generation formula (35). Employing average transmission loss as the metric, ten sets of simulations were conducted across a mesh range of 100,000 to 300,000 elements; however, the resulting variations were not substantial. Therefore, in response to the reviewers' recommendations, we have exclusively incorporated the acoustic mesh generation section (Lines 325-343) within the revised manuscript, providing supplementary details regarding the mesh discretization strategy, selection rationale, and convergence control methodology, thus enhancing the comprehensiveness and reproducibility of the model description.

Comments 7: The study mentions that coupling effects may cause unexpected resonances. How can these effects be mitigated in practical applications?

Response 7:

Thank you for raising this professional question. Indeed, as elucidated in the manuscript, the acoustic-structure coupling phenomenon can induce unforeseen resonance responses or localized sound pressure amplification within specific frequency bands, potentially compromising the stability of the muffler in real-world applications and therefore necessitating careful consideration. The primary objective of this research is to ascertain and elucidate the variation patterns in transmission loss resulting from acoustic-structure coupling. While a comprehensive exploration of engineering control strategies for resonance phenomena falls outside the scope of this manuscript, we posit that this study establishes a theoretical foundation for the identification of potential resonance frequencies and the determination of key structural modes. We intend to investigate this matter in subsequent work.

Comments 8: Were different flow speeds or temperatures considered to evaluate the robustness of the design under various conditions?

Response 8:

Thank you for this constructive comment. We fully concur that the assessment of muffler performance across varying flow rates or temperatures holds considerable importance for validating the design approach in real-world applications. Owing to manuscript length constraints, the present research primarily addressed acoustic-structure coupling modeling and analysis under steady-state operating conditions at ambient temperature and pressure and did not incorporate multi-flow rate or thermo-acoustic coupling effects. We intend to address this matter in more detail in subsequent research endeavors. We reiterate our sincere gratitude to the reviewers for their profound attention to the extensibility of this research.

Comments 9: Improve the quality of figures, font size, etc.

Response 9:

Thank you for this pertinent suggestion regarding image quality. All figures within the original manuscript have been reprocessed, encompassing enhancements such as increased resolution, enlarged font sizes, and improved readability of legends and axis labels, to ensure enhanced clarity and identifiability of the information presented therein.

Comments 10: References should be updated.

Response 10:

Thank you for the important suggestion regarding updating the references. We have observed that several references in the original manuscript have earlier publication dates and may not adequately represent the most recent advancements in fields such as acoustic-structure coupling analysis and muffler structural optimization in recent years. By the reviewers' recommendations, the references in the revised manuscript have been updated and augmented with the inclusion of several high-impact research outcomes representative of the pertinent domains within the last five years(e.g., [15] ,[16]and [34]). This will serve to augment the frontier nature and scholarly reference value of the manuscript.

Thank you once again for your time, effort, and support.