Effective Frequency Range and Jump Behavior of Horizontal Quasi-Zero Stiffness Isolator
Round 1
Reviewer 1 Report
The submitted manuscript is well organized, and describes a very interesting topic. The authors have proposed the effective frequency range and failure mechanism of a horizontal quasi-zero stiffness (QZS) isolator subject to harmonic excitations in two cases. In addition, the jump phenomena in the response amplitude induced by the strong nonlinearity of the isolator are analyzed. These are very good.
However, the following questions and comments need to be considered before the paper can be accepted for publication.
1. The authors mentioned “The results indicate that the solutions obtained via the complexification-averaging method and the Runge-Kutta method are in good agreement” in line 144. This is very good. However, the peak points of the two methods do not agree on Fig. 3 (b). Please be careful and make a much more precise description.
2. The information on Fig.8-10 is a bit single. It is recommended that the pictures be combined to reduce the length of the page.
3. The parametric study sections all consider the effect of a single variable only. However, could the authors further discuss/mention the simultaneous changes of multiple variables?
4. The authors mentioned “this finding indicates that the elongation of the springs should not be too large” in line 244. This description would be much better if it combines further discussion with a proper and reasonable conclusion.
5. In the introduction section, much more recent and related studies can be briefly mentioned. Moreover, as tensegrity, origami and auxetic structures have been verified to have high energy absorption, the authors are advised to briefly mention their design and potential applications. Please mention these interesting works: Zero stiffness tensegrity structures. International Journal of Solids and Structures. 2007; Structural symmetry recognition in planar structures using convolutional neural networks. Engineering Structures. 2022; Intelligent computational design of scalene-faceted flat-foldable tessellations. Journal of Computational Design and Engineering. 2022; Selective hinge removal strategy for architecting hierarchical auxetic metamaterials. Nature Communications Materials. 2022; Computational modeling and energy absorption behavior of thin-walled tubes with the Kresling origami pattern. Journal of the International Association for Shell and Spatial Structures. 2021; Energy absorption of origami inspired structures and materials. Thin-Walled Structures. 2020.
6. The abstract and conclusion should be revised to be concise and clear. Moreover, the authors should be carefully check the whole manuscript and avoid typos.
Author Response
We would like to thank the reviewer for their comments. Those comments are helpful for revising and improving our paper. Below we provide our detailed responses to these comments and the corresponding revisions made in the manuscript.
The submitted manuscript is well organized, and describes a very interesting topic. The authors have proposed the effective frequency range and failure mechanism of a horizontal quasi-zero stiffness (QZS) isolator subject to harmonic excitations in two cases. In addition, the jump phenomena in the response amplitude induced by the strong nonlinearity of the isolator are analyzed. These are very good.
However, the following questions and comments need to be considered before the paper can be accepted for publication.
1. The authors mentioned “The results indicate that the solutions obtained via the complexification-averaging method and the Runge-Kutta method are in good agreement” in line 144. This is very good. However, the peak points of the two methods do not agree on Fig. 3 (b). Please be careful and make a much more precise description.
Answer: Thank you for the reviewer’s suggestion. The relative statement has been modified to “The results indicate that the solutions obtained via the complexification-averaging method and the Runge-Kutta method are in good agreement under most excitation frequencies and the deviation between the solutions of peak point is acceptable, which verifies the correctness of the theoretical derivation”.
2. The information on Fig.8-10 is a bit single. It is recommended that the pictures be combined to reduce the length of the page.
Answer: Figure 8 shows the effect of the external excitation and Figures 9 and 10 show the effect of isolator parameters. Therefore, Figures 9 and 10 have been combined into one figure, please see Figure 9 in the current version. Meanwhile, Figures 18 and 19 have also been combined into one figure, please see Figure 17 in the current version.
3. The parametric study sections all consider the effect of a single variable only. However, could the authors further discuss/mention the simultaneous changes of multiple variables?
Answer: This study aims to show some common conclusions of the horizontal quasi-zero stiffness isolator. Therefore, those conclusions mainly provide qualitative guidance for engineering applications. Considering the qualitative results of the simultaneous change of multiple variables are the same as those of the change of a single variable, we only show the accessible results of changing a single variable.
4. The authors mentioned “this finding indicates that the elongation of the springs should not be too large” in line 244. This description would be much better if it combines further discussion with a proper and reasonable conclusion.
Answer: The reason for the conclusion mentioned by the reviewer has been further explained in the manuscript. The linear natural frequency of the isolator increases with the elongating of the two springs. Consequently, the resonance peak is increased, which leads to the effective frequency range becoming narrower.
5. In the introduction section, much more recent and related studies can be briefly mentioned. Moreover, as tensegrity, origami and auxetic structures have been verified to have high energy absorption, the authors are advised to briefly mention their design and potential applications. Please mention these interesting works: Zero stiffness tensegrity structures. International Journal of Solids and Structures. 2007; Structural symmetry recognition in planar structures using convolutional neural networks. Engineering Structures. 2022; Intelligent computational design of scalene-faceted flat-foldable tessellations. Journal of Computational Design and Engineering. 2022; Selective hinge removal strategy for architecting hierarchical auxetic metamaterials. Nature Communications Materials. 2022; Computational modeling and energy absorption behavior of thin-walled tubes with the Kresling origami pattern. Journal of the International Association for Shell and Spatial Structures. 2021; Energy absorption of origami inspired structures and materials. Thin-Walled Structures. 2020.
Answer: The recommended articles have been cited, please see the red part in this section. Thank you for recommending these valuable papers.
6. The abstract and conclusion should be revised to be concise and clear. Moreover, the authors should be carefully check the whole manuscript and avoid typos.
Answer: The abstract and conclusion have been revised, and the manuscript has been checked thoroughly to avoid typos. Thanks again for the reviewer’s valuable suggestions.
Reviewer 2 Report
To the reviewer's point of view, the jump behavior of horizontal quasi-zero stiffness isolator has been theoretically studied much, not only the methods but also the phenomenon. There is nothing originality new of this manuscript compared to the existing literatures, both in method and results. Also this work is lack of experiment prove.
Author Response
To the reviewer's point of view, the jump behavior of horizontal quasi-zero stiffness isolator has been theoretically studied much, not only the methods but also the phenomenon. There is nothing originality new of this manuscript compared to the existing literatures, both in method and results. Also this work is lack of experiment prove.
Answer: This paper comprehensively studied the failure of a horizontal quasi-zero stiffness isolator by analyzing the differences in the jump behaviors in two installation cases, which takes a different view of the jump from other papers. Furthermore, the simulation method of the additional impact load has not been used before.
Reviewer 3 Report
The authors presented a study on the effective frequency range and jump behavior of horizontal quasi-zero stiffness isolator. In general, the manuscript is very well written. However, there are some technical issues that must be addressed. I, therefore, recommended a minor revision.
1. The beginning of the abstract is quite absurd. Such as “are studied in two cases.” Where are they studied? In this work? Not clear.
2. The objective of the work is to be mentioned at the beginning itself. The beginning of the abstract is not proper. It is nothing but a general discussion. Plz, revise.
3. Plz present some quantitative information in the abstract.
4. Use some innovative and impactful keywords. They should not match the words used in the title.
5. I want to see some strong literature review presentations and problem statement discussions. Use a tabular form to discuss the literature review.
6. Plz present a flowchart to discuss the methodology, it will be beneficial for a quick understanding.
7. Plz remove ‘we’, ‘I’, etc., Use passive voice instead.
8. Plz re-write the conclusion section as follows: Main objective, findings, advantages, limitations of the study, and the future scope of the study.
9. Follow proper grammatical arrangement as stated below:
Check the following para on how to apply the grammatical correction: Use the past tense to report what happened in the past: what the authors did, what someone reported, what happened in an experiment, and so on. Use the present tense to express general truths, such as conclusions (drawn by the authors or by others) and facts not limited by time (including information about what the paper does or covers). Reserve the future tense for perspectives: what will be done in the coming months or years
Author Response
We would like to thank the reviewer for the comments. Those comments are helpful for revising and improving our paper. Below we provide our detailed responses to these comments and the corresponding revisions made in the manuscript.
The authors presented a study on the effective frequency range and jump behavior of horizontal quasi-zero stiffness isolator. In general, the manuscript is very well written. However, there are some technical issues that must be addressed. I, therefore, recommended a minor revision.
1. The beginning of the abstract is quite absurd. Such as “are studied in two cases.” Where are they studied? In this work? Not clear.
Answer: In the first case, the isolator is subject to a base displacement excitation. In the second case, the isolator is installed on a linear primary structure that is subject to a harmonic force. Please see the fourth sentence of the abstract in current version, “the two cases” has been further explained.
2. The objective of the work is to be mentioned at the beginning itself. The beginning of the abstract is not proper. It is nothing but a general discussion. Plz, revise.
Answer: The beginning of the abstract has been revised. The objective of the work is highlighted in the beginning.
3. Plz present some quantitative information in the abstract.
Answer: The paper aims to study the common problems of the quasi-zero stiffness isolators, and thus the parameters of the studied systems are not taken from specific actual engineering. Considering the qualitative value of the paper is far more than its quantitative value, we only show the important qualitative conclusions in the abstract.
4. Use some innovative and impactful keywords. They should not match the words used in the title.
Answer: Three keywords have been replaced. The new keywords are strong nonlinearity, additional impact and lowest effective frequency.
5. I want to see some strong literature review presentations and problem statement discussions. Use a tabular form to discuss the literature review.
Answer: In the introduction section, we first present the significance of vibration isolation and then introduce some structures of the QZS isolator. After that, a typical problem, i. e. the jump phenomenon, is proposed and the research contents are briefly introduced. Please forgive us for our lack of knowledge, we have not seen the introduction in tabular form before. Therefore, we are very sorry for do not know how to rewrite the abstract in this form. Currently, the introduction section has been rewritten in an ordinary way, we hope it is acceptable.
6. Plz present a flowchart to discuss the methodology, it will be beneficial for a quick understanding.
Answer: A semi-analytical method and a numerical method were applied in this study. The semi-analytical method was mainly used to study the effective frequency range and the numerical method was used to study the jump behaviors. The results obtained from the two methods were compared for mutual verification. The reviewer is correct, a flowchart is beneficial for a quick understanding. However, the flowchart would be too simple if we use this way to discuss the methodology. Therefore, a description has been added below Figure 2 to introduce the methodology of the study instead of using the flowchart.
7. Plz remove ‘we’, ‘I’, etc., Use passive voice instead.
Answer: The active voice has been removed from the paper.
8. Plz re-write the conclusion section as follows: Main objective, findings, advantages, limitations of the study, and the future scope of the study.
Answer: The conclusion section has been rewritten according to the reviewer’s suggestion.
9. Follow proper grammatical arrangement as stated below:
Check the following para on how to apply the grammatical correction: Use the past tense to report what happened in the past: what the authors did, what someone reported, what happened in an experiment, and so on. Use the present tense to express general truths, such as conclusions (drawn by the authors or by others) and facts not limited by time (including information about what the paper does or covers). Reserve the future tense for perspectives: what will be done in the coming months or years
Answer: The correct grammatical arrangement has been adopted according to the reviewer’s suggestion.
Round 2
Reviewer 2 Report
This manuscript can be accepted in the present form.
