A Hyperbolic Shear Deformation Theory for Natural Frequencies Study of Functionally Graded Plates on Elastic Supports

Round 1

Reviewer 1 Report

The present work presents an analytical study of the vibrational behaviour of simply supported FGM structures resting on Winkler-Pasternak type foundations through a high-order hyperbolic theory. This manuscript is well presented. However, the authors need to improve this manuscript in some areas. The following are the points that need to be addressed.

 

The introduction is not sufficient. Many references are accumulated at the end of paragraphs. Refer to the literature precisely. 

 

The constitutive equations part can be significantly reduced. 

 

In this work, the authors mainly focused on the observations in the results section. However, it would help the reader to report the critical assessment of the obtained results.

Author Response

Responses to Reviewer # 1

General comment: The present work presents an analytical study of the vibrational behaviour of simply supported FGM structures resting on Winkler-Pasternak type foundations through a high-order hyperbolic theory. This manuscript is well presented. However, the authors need to improve this manuscript in some areas. The following are the points that need to be addressed.

Response: The authors are very grateful to the reviewer for his positive feedback.

Comment 1: The introduction is not sufficient. Many references are accumulated at the end of paragraphs. Refer to the literature precisely.

Modification: thank you for this relevant remark. However, the authors did not want to go into excessive details to avoid making it lengthy and challenging to read. They wanted to concentrate on relevant works related to each theory.

Comment 2: The constitutive equations part can be significantly reduced.

Modification: Thank you. This had been revised as recommended.

Comment 3: In this work, the authors mainly focused on the observations in the results section. However, it would help the reader to report the critical assessment of the obtained results.

Response: Thank you for this relevant comment. As mentioned in the conclusion, the use of limited number of unknows has enabled us to easily implement the present theory mathematically. The results for this type of analyses were found to be in very agreement with other theories.  To assess critically the results of the present theory, it would be very interesting to study the influence of manufacturing defects, namely porosity, on the overall response of functionally graded plates under different stresses and different support conditions.

Author Response File: Author Response.docx

Reviewer 2 Report

This study presents the Navier’s approach for free vibration of simply supported functionally graded plates on elastic foundations based on a hyperbolic shear deformation theory. The accuracy of the framework is verified by other higher order shear deformation theories. The effects of the power law index, the thickness ratio, and the foundation parameters are well investigated.

 

Some issues have to be improved in order to enhance the quality of the manuscript.

 

1. “FG” and “FGM” should have their full names.

2. Indentation in some sentences should be re-evaluated.

3. Some symbols should be in italics.

4. The usage of the words should be consistent throughout the manuscript, e.g., “non-dimensional/dimensionless”.

5. Grammar mistakes should be avoided, e.g., “singular/plural”.

6. Figure 1 should be clearer.

7. The novelty should be demonstrated. Please clearly state which one is new in the article: theory or solution method or others?

Author Response

Response to Reviewer # 2

General Comments: This study presents the Navier’s approach for free vibration of simply supported functionally graded plates on elastic foundations based on a hyperbolic shear deformation theory. The accuracy of the framework is verified by other higher order shear deformation theories. The effects of the power law index, the thickness ratio, and the foundation parameters are well investigated.

Some issues have to be improved in order to enhance the quality of the manuscript.

Response: Thank you for your comments. We have gone through your comments carefully and tried our best to address them one by one. We hope the manuscript has been improved accordingly.

Comment 1: “FG” and “FGM” should have their full names.

Response: Thank you for the asked comment. I inform you that the paper has been revised as suggested.

Comment 2: Indentation in some sentences should be re-evaluated.

Response: Thank you for this recommendation. The authors have re-evaluated all indentations.

Comment 3: Some symbols should be in italics.

Response: As recommended, the paper has been revised.

Comment 4: The usage of the words should be consistent throughout the manuscript, e.g., “non-dimensional/dimensionless”.

Response: We thanks for this remark. As requested by the reviewer, the text was revised.

Comment 5: Grammar mistakes should be avoided, e.g., “singular/plural”.

Response: thank you for this comment. The authors try to make their best to avoid all the grammar mistakes.

Comment 6: Figure 1 should be clearer.

Response: the figure 1 has been modified.

Comment 7: The novelty should be demonstrated. Please clearly state which one is new in the article: theory or solution method or others?

Response: the novelty of this theory resides in the limited number of unknow variable (just four) taken into account. The assumptions of this method are that the transverse displacement includes bending and shear components which leads to a reduction in the number of unknowns, and consequently, makes the present theory much easier to implement mathematically. Also, this theory uses a shear strain shape function that considers an adequate distribution of the transverse shear strains across the plate thickness and tangential stress-free boundary conditions on the plate boundary surface without introducing a shear correction factor.

Author Response File: Author Response.docx

Round 2

Reviewer 1 Report

I am not satisfied with the authors' reply regarding the "Many references are accumulated at the end of paragraphs. Refer to the literature precisely."

 

Moreover, comment 3 has not been answered correctly. There is no critical assessment of the obtained results in the manuscript.

 

Comment 3: In this work, the authors mainly focused on the observations in the results section. However, it would help the reader to report the critical assessment of the obtained results.

Author Response

Manuscript Number:  jcs-1850901

 

Title: A hyperbolic shear deformation theory for natural frequencies study of functionally graded plates on elastic supports

Responses to Reviewer # 1

Response: Thank you for your comments. We have gone through your comments carefully and tried our best to address them one by one. We hope the manuscript has been improved accordingly.

Comment A: I am not satisfied with the authors' reply regarding the "Many references are accumulated at the end of paragraphs. Refer to the literature precisely."

Modification: The Introduction has been modified by detailing the literature as recommended.

Comment B: Moreover, comment 3 has not been answered correctly. There is no critical assessment of the obtained results in the manuscript.

Modification: Thank you. This was revised as recommended.

Comment C: In this work, the authors mainly focused on the observations in the results section. However, it would help the reader to report the critical assessment of the obtained results.

Response:

We have added additional comments in yellow to provide further clarification.

 

Author Response File: Author Response.docx

Reviewer 2 Report

My comments have been addressed. Publication of the paper is recommended.

Author Response

Everything had been answered during the first round.

 

Thank you

Author Response File: Author Response.docx