On the Crossing Bridge between Two Kirchhoff–Love Plates
Round 1
Reviewer 1 Report
In this paper, the structure consisting of two Kirchhoff-Love elastic plates and a bridge being in contact with the plates is analyzed. The variational and differential formulations of an equilibrium problem are presented. Passages to limits are investigated as a rigidity parameter of the bridge tends to infinity and to zero. Some useful theorems related to the solutions of the considered problem are proved. The existence of solution for inverse problem is also proved.
This is a very nice paper. The topic is very interesting and falls within the scope of the journal. The results are well presented. The language and grammar is generally good but there are some minor mistakes at some places.
The paper deserves to be published in Axioms after some minor issued are addressed.
1. A conclusion section should be added to sum up the study and present the concluding remarks.
2. The literature review does not seem satisfactory as there are a lot of citations by the same author. It would be better if the literature review is updated to cover the recent accomplishments by different researches.
3. The manuscript should be rechecked to correct all typo errors.
After the suggested changes I recommend to ACCEPT the manuscript for publication.
Author Response
I would like to thank the reviewer for helpful suggestions regarding the manuscript. I have reduced the number of references to Khludnev and made minor changes to Introduction. All typos corrected.
Reviewer 2 Report
Please find my detailed report in the attachment.
Comments for author File: 
Comments.pdf
Author Response
I would like to thank the reviewer for a very careful reading of the article and comments on the text. Almost all comments were taken into account, and appropriate changes were made to the text. I kept the +- characters at the end of each line despite the reviewer's recommendation, and I thank the reviewer for this suggestion.
Reviewer 3 Report
I tested the manuscript for plagiarism and the percentage is huge: 44%.
The author try to reduce the similarities until maximum 20%.
After that the manuscript can be resubmitted.
Author Response
I am well aware that in my articles one and the same sentences are repeatedly encountered regarding the formulation of elasticity problems and standard explanations of the notations used. This has no bearing on the various issues under consideration. In the manuscript, we find the new geometry of the problem , problem formulation itself is new, and results obtained are new. In principle, I could slightly change the phrases used in the text, but it does not seem to make much sense in this. However, I would like to thank the reviewer for his attention to this issue. I am well aware that I should think about it.
Round 2
Reviewer 3 Report
Before the Editor makes a decision, I suggest that the author must takes into account the following corrections:
1. The expression “Kirchhoff-Love plates” appears only in the introduction and in the conclusions. It seems to be just a pretext for some abstract calculations. A justification is required.
2. Author must argue how the relations (2) were obtained, or indicate a bibliographic reference for their original form.
3. Details on obtaining equation (3) are required.
4. What is the motivation of the estimate (13)?
5. The equation (20) is “bushy”. It is very difficult to check its correctness.
6. Details on obtaining equation (67) are required.
7. Some editing "glitches" need to be corrected.
8. I think the author need to emphasizes more clearly the contribution of the manuscript from a scientific point of view.
9. References are not uniformly written. In some references the name of the journal is written in full and in other it is incorrect abbreviated.
10. Also, I think, the author must strengthen the References section with some articles that use some similar techniques, to make the techniques used more plausible, for instance: New analytical method based on dynamic response of planar mechanical elastic systems, Boundary Value Problems, Vol. 2020, No.1, Art. No. 104, 2020.
If the author takes into account all these corrections, then this manuscript deserves to be published.
Author Response
I would like to thank the reviewer for the suggestions concerning the manuscript.
- I provided comments and suitable references to the Kirchhoff-Love model, below the formula (11)
- References concerning the formulas (2) and Green’s formula for $\Omega_i$ are given on the page 2
- The variational inequality (13) is equivalent to the minimization problem $\inf_S \Pi$
- Suitable comments concerning the derivation of (21) and (68) are provided
- In Conclusion, an additional sentence is given emphasizing a scientific contribution of the manuscript
- A small correction in References is provided. In particular, the reference recommended by the reviewer is given
Round 3
Reviewer 3 Report
The author considered all my proposed corrections, which led to an improved form of the manuscript.
