A Numerical Method for Simulating Viscoelastic Plates Based on Fractional Order Model

Round 1

Reviewer 1 Report

The paper deals with an interesting topic. The discussion is acceptable. The results are quite interesting and worthy. The contents are relevant to this journal. I recommend this article for publication after revision. The following suggestions should be taken into account. 1. English should be improved throughout the manuscript. 2. Quantitative information should be provided in the abstract. 3. Check that all symbols are used correctly in the text. 4. Check all equations used. 5. The introduction section needs to be updated with more relevant research. 6. More physical description is required in the discussion section. 7. The quality of the figures should be improved. 8. The original points must be explained well. 9. A comparison with other published results is necessary to validate the results obtained 10. More recent references must be add. Please check that all references used are well written. 11. The conclusion should be concise and to the points indicating the application of the work.

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 2 Report

I recommend accepting the manuscript after the authors do the minor revisions.
Please outline every change made in response to comments and provide suitable rebuttals for any comments not addressed.
An efficacious method for solving three-dimensional fractional viscoelastic plates in the time domain is proposed in this paper. The governing equation of the plate is approximated by the derived differential operator matrices of different orders of Bernstein polynomials. The obtained matrix equation is transformed into algebraic equations for solution. In addition, it is proved that the proposed method is feasible and effective through error analysis and mathematical examples. Finally, the effects of external load, side length of plate and boundary condition on the displacement of the square plate are studied. The stress variation of the viscoelastic plate with different thickness is discussed. The result was perfect to relative literature, which further verifies that the Bernstein polynomials algorithm can supply a favorable basis for the numerical solution of viscoelastic plates.
Decision:
I have completed my evaluation of your manuscript. There are some places in the manuscript should be improved.
I recommend that the manuscript should be revised before its publication in the journal.
Comments and Suggestions for improvement:
1. Please clarify the novelty of this paper with respect to the published paper.
2. In organizing the introduction, it is not good to only pile the related references together, it will be better
to give the relationship between these references. Motivation is not sufficiently stated in the introduction part.
It should be clarified why they consider this problem and what advantages of the proposed technique are. The
organization of the under review paper is very weak. The original contributions need to be much better presented
in the last paragraph of section “INTRODUCTION”. All improvements, if they are, and new results must be
described in this paragraph.
3. Please rewrite the paper in journal template . The references of this paper should be rewritten accordingly
to style of journal.
4. All acronyms should be defined. The reviewer would also like the authors to carry out a final editing of the
paper to correct any typos and grammatical errors.They should double check the mathematical formulations. A
professional proofreading revision is required.
5. The Abstract should be written in a well-written structure.
6. In general, equations should be regarded as parts of a sentence and treated accordingly with the appropriate
grammatical convention and punctuation. Sentences introducing equations should, with the inclusion of the
equation, constitute a complete sentence. More editing for writing is needed (Commas, Semicolons, Colons, and
point in equations)

7. How can you guarantee the consistent and stability of the proposed method?
9. Pleas report the numerical results in suitable tables.
10. Please provide Matlab code.
11. The authors can cite some newest references related to their work for a best presentation of the manuscript:
https://doi.org/10.1016/j.jocs.2021.101394
https://doi.org/10.1016/j.camwa.2020.11.003

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

No comment

Author Response

We appreciate your positive and constructive comments on this manuscript.

Reviewer 2 Report

The opinion of the reviewer: Minor Revision.
Decision:
Although, this manuscript is modified, but is required, other aspects of the subject are examined in the manuscript.

Minor Comments

1. In section Introduction , Line 19 Please delete "in"  

"Plate and plate structure are widely used in in many realms of mechanical, building"
2. There is no need for previous texts to be included in the  revised paper since it will confuse the referee.

3. In the equations such as  2, 8, 9, 11, 13 , 15,...

Please use  "\ldots" insted of  "\cdots"   in order to show "....".

4. I suggest the authors to keep up to date with the relevant literature such as:

https://doi.org/10.1016/j.jocs.2021.101394

Author Response

Please see the attachment.

Author Response File: Author Response.pdf