Analysis of the Vibration Behaviors of Rotating Composite Nano-Annular Plates Based on Nonlocal Theory and Different Plate Theories
Round 1
Reviewer 1 Report
The paper presents thermomechanical analysis of FG plate using different plate theories. According to the reviewer’s opinion, the paper is well-structured and clear. The topic is interesting and falls within the aim of the journal. In addition, the results are well-presented and could be helpful to further develop the same topic. Thus, the paper can be accepted for publication with minor revisions:
(1) The authors used Kirchhoff, Midlin, and Reddy’s plate theory for the research. However, since the last decade, these theories have been expanded by many authors having analyzed FG plates under to mechanical / thermal loads”. Authors may discuss recent activities in this regard, for example: Applied Sciences 2020, 10, 4190; Material 2018, 11, 2381; B. Mechab, I. Mechab, S. Benaissa, "Analysis of thick orthotropic laminated composite plates based on higher order shear deformation theory by the new function under thermo-mechanical loading," Compos Part B-Eng, vol. 43, no. 3, pp. 1453-1458, 2012. In your opinion, would it be possible to apply shear deformation theories based on shape functions?
(2) The authors gave diagrammatic, but not tabular presentation of the results. The authors say “When studying the vibration problems of the nano-annular plates based on the three plate theories, the differences of the numerical results calculated by the three theories become apparent as the thickness to radius ratio increases. " In this sense, it would be desirable to give the most representative tabular presentation of the results, which would contain values ​​from the paper by which the procedure was verified, as well as values ​​for all three applied theories. In this way, the author's claim would be more convincing.
(3) „For the derived governing equations (21), it is difficult to solve high-order variable coefficient differential equations due to the existence of nonlocal parameter, rotational velocity and other parameters, so in this paper uses, the differential quadrature method (DQM) is used to discretize the governing equations…” It would be desirable for the authors to further clarify the procedure for obtaining numerical results. This would further highlight the contribution of the paper.
(4) In the conclusion, you must state more clearly the contribution of your work. What are the advantages and disadvantages of the proposed procedure compared to the existing ones?
Comments for author File: 
Comments.pdf
Author Response
We thank the reviewer very much for the insightful comments and constructive suggestions, which are of great value for further improving the quality of our manuscript. We have revised our manuscript in full compliance with the reviewer’s comments and suggestions. In the following, we respond to the comments point-by-point. All the changes are also highlighted in the revised manuscript in RED color.
The paper presents thermomechanical analysis of FG plate using different plate theories. According to the reviewer’s opinion, the paper is well-structured and clear. The topic is interesting and falls within the aim of the journal. In addition, the results are well-presented and could be helpful to further develop the same topic. Thus, the paper can be accepted for publication with minor revisions:
1.Query: The authors used Kirchhoff, Midlin, and Reddy’s plate theory for the research. However, since the last decade, these theories have been expanded by many authors having analyzed FG plates under to mechanical/thermal loads. Authors may discuss recent activities in this regard, for example: Applied Sciences 2020, 10, 4190; Material 2018, 11, 2381; B. Mechab, I. Mechab, S. Benaissa, “Analysis of thick orthotropic laminated composite plates based on higher order shear deformation theory by the new function under thermo-mechanical loading.” Compos Part B-Eng, vol. 43, no. 3, pp. 1453-1458, 2012. In your opinion, would it be possible to apply shear deformation theories based on shape functions?
Reply: Thank you for reminding us the problem.The three theories used in this article have been used by many scholars to analyze plates vibration, but the aim of this paper is to unify these three theories and express them in a mathematical form. This is also the purpose and character of this paper. Applying the new shear theory and shape functions to analyze the vibration behaviors of the plate. This is the author's next task and work. I have described the relevant content in the prospect part of the discussion in detail.
Discussion
However, the three plate theories and nonlocal constitutive relations used in this paper to study the vibration behaviors of the nano plates have been applied by a large number of scholars in previous studies. In recent years, the new plate theories and shape functions have been proved and applied by many scholars. Good numerical results have been obtained, such as literature [29, 30]. At the same time, when studying the mechanical properties of micro-nano structures and choosing physical constitutive relations, in addition to the nonlocal theory used in this paper, there are strain gradient theory and nonlocal strain gradient theory, etc. However, the nonlocal theory and the strain gradient theory get some different or even completely opposite conclusions in practical applications. The nonlocal strain gradient theory considers both nonlocal effects and strain gradient effects, and resolves the confusion and controversy caused by the two theories [31]. Therefore, the author's next work is to study the mechanical characteristics of micro-nano structures based on the nonlocal strain gradient theory and the new shear plate theories.
29 Mechab, B.; Mechab, I.; Benaissa S.; et al. Analysis of thick orthotropic laminated composite plates based on higher order shear deformation theory by the new function under thermo-mechanical loading. J. Composites, Part B, 2012, 43, 1453-1458.
30 Radakovic, A.; Cukanovic, D; Bogdanovic G; et al. Thermal buckling and free vibration analysis of functionally graded plate resting on an elastic foundation according to high order shear deformation theory based on new shape function. J. Appl. Sci. 2020, 10, 4190.
31 Lim, C.W.; Zhang G , Reddy, J.N. A higher-order nonlocal elasticity and strain gradient theory and its applications in wave propagation. J. Mech. Phys. Solids, 2015, 78, 298-313.
2.Query: The authors gave diagrammatic, but not tabular presentation of the results. The authors say “When studying the vibration problems of the nano-annular plates based on the three plate theories, the differences of the numerical results calculated by the three theories become apparent as the thickness to radius ratio increases.” In this sense, it would be desirable to give the most representative tabular presentation of the results, which would contain values from the paper by which the procedure was verified, as well as values for all three applied theories. In this way, the author's claim would be more convincing.
Reply: Thank you for reminding us the problem.The datas analysis of the main text part 3.7 is displayed in the form of images with better intuitiveness. The differences between the datas can be clearly seen from the images. The accuracy and validity of the relevant datas have been described by the author in the section 3.1.validation.
3.Query: “For the derived governing equations (21), it is difficult to solve high-order variable coefficient differential equations due to the existence of nonlocal parameter, rotational velocity and other parameters, so in this paper uses, the differential quadrature method (DQM) is used to discretize the governing equations...” It would be desirable for the authors to further clarify the procedure for obtaining numerical results. This would further highlight the contribution of the paper
Reply: Thank you for reminding us the problem. The introduction of numerical methods and related discrete forms of motion equations have been added in Appendix A
4.Query: In the conclusion, you must state more clearly the contribution of your work. What are the advantages and disadvantages of the proposed procedure compared to the existing ones?
Reply: Thank you for reminding us the problem, I have described the relevant contents in the discussion and conclusions.
Discussion
However, the three plate theories and nonlocal constitutive relations used in this paper to study the vibration behaviors of the nano plates have been applied by a large number of scholars in previous studies. In recent years, the new plate theories and shape functions have been proved and applied by many scholars.
Conclusions
The contribution of this paper is to unify the vibration equations of rotating nano annular plates based on the three plate theories and establish a unified mathematical model, which is a feature of this paper. Then the differences of the calculation results about the three plate theories are compared.
Author Response File: 
Author Response.doc
Reviewer 2 Report
See the attached file.
Comments for author File: Comments.pdf
Author Response
We thank the reviewer very much for the insightful comments and constructive suggestions, which are of great value for further improving the quality of our manuscript. We have revised our manuscript in full compliance with the reviewer’s comments and suggestions. In the following, we respond to the comments point-by-point. All the changes are also highlighted in the revised manuscript in GREEN color.
The artical entitled “Vibration Analysis of Rotating Functionally Graded Nano-Annular Plates Based on Different Plate Theories” by Haonan Li, Linquan Yao and Wei Wang is very similar to paper [1].
[1] Guo, X.-F.; Ma, L. Vibration analysis of rotating functionally gradient nano annular plates in thermal environment, Applied Mathematics and Mechanics. 2020; 41(11): 1224-1236.
Reply:Thank you for reminding us the problem.The research contents of this paper are very different from that of literature [1]. The Kirchhoff plate theory is used to analyze the vibration behaviors of rotating nano annular plates in literature [1], while three plate theories are applied in this paper. At the same time, a unified mathematical model is established to analyze the vibration behaviors of the nano annular plate, which is a feature of this paper. Then the differences of the calculation results about the three plate theories are compared. At the same time, in order to avoid similarities, the author has revised the title.
Title
Analysis of the vibration behaviors of the rotating composite nano-annual plates based on the nonlocal theory and the three plate theories
Author Response File: Author Response.doc
Reviewer 3 Report
This paper is focused on the free vibration behavior of rotating nano annular plates exploiting different plate theories based on nonlocal elasticity theory. In particular the paper aims at analyzing the influence of rotary speed, temperature and other parameters on the vibration frequencies.
The paper could be interesting but it must be revised trying to clarify the aims and research design, because some parts are unclear.
Other concerns:
- English grammar and style must be revised.
- In the introduction authors state that the nonlocal strain gradient theory is the best one to study the mechanical behavior of nanostructures, but then they use the nonlocal theory. Please clarify.
- Chapter 2 should be entitled: Materials and Methods.
- The first part of chapter 3 should be put in a different chapter named "Validation".
Author Response
We thank the reviewer very much for the insightful comments and constructive suggestions, which are of great value for further improving the quality of our manuscript. We have revised our manuscript in full compliance with the reviewer’s comments and suggestions. In the following, we respond to the comments point-by-point. All the changes are also highlighted in the revised manuscript in BLUE color.
Comments and Suggestions for Authors
This paper is focused on the free vibration behavior of rotating nano annular plates exploiting different plate theories based on nonlocal elasticity theory. In particular the paper aims at analyzing the influence of rotary speed, temperature and other parameters on the vibration frequencies.
The paper could be interesting but it must be revised trying to clarify the aims and research design, because some parts are unclear.
Reply: Thank you for reminding us the problem, I have described related contents in the last paragraph of the introduction.
The rotating nano annular plates are of great application value in micro-nano structures (such as the disk on the upper shaft of the nanomotor). At the same time, the nano annular plates are affected by the surrounding physical environment and vibrate freely during the working process. Therefore, the main purpose of the paper is to study the influence of the changes of various physical parameters on the natural frequencies of the nano annular plates based on three different plate theories. The actual working conditions of the nano annular plates are affected by temperature. At the same time, compared with the inner and outer diameter surfaces, the upper and lower surfaces of the nano annular plates have more contact with the working environment and are more affected by external factors. Therefore, functionally graded materials are used to manufacture the equipments. The physical properties of the materials are designed according to the law of power function changes along the thickness of the annular plates.
Other concerns:
- English grammar and style must be revised.
Reply:Thank you for reminding us the problem, I have modified the relevant content in text.
- In the introduction authors state that the nonlocal strain gradient theory is the best one to study the mechanical behavior of nanostructures, but then they use the nonlocal theory. Please clarify.
Reply:Thank you for reminding us the problem. This paper is based on the nonlocal theory to study the vibration behaviors of the plates. The author has put the contents of the nonlocal strain gradient theory in the discussion for description. This is the next work for the author. At the same time, in order to avoid ambiguity, the title has been revised.
Title
Analysis of the vibration behaviors of the rotating composite nano-annual plates based on the nonlocal theory and the three plate theories
Discussion
At the same time, when studying the mechanical properties of micro-nano structures and choosing physical constitutive relations, in addition to the nonlocal theory used in this paper, there are strain gradient theory and nonlocal strain gradient theory, etc. However, the nonlocal theory and the strain gradient theory get some different or even completely opposite conclusions in practical applications. The nonlocal strain gradient theory considers both nonlocal effects and strain gradient effects, and resolves the confusion and controversy caused by the two theories [31]. Therefore, the author's next work is to study the mechanical characteristics of micro-nano structures based on the nonlocal strain gradient theory and the new shear plate theories.
31 Lim, C.W.; Zhang G , Reddy, J.N. A higher-order nonlocal elasticity and strain gradient theory and its applications in wave propagation. J. Mech. Phys. Solids, 2015, 78, 298-313.
- Chapter 2 should be entitled: Materials and Methods.
Reply:Thank you for reminding us the problem, I have modified the relevant content in text
- The first part of chapter 3 should be put in a different chapter named "Validation".
Reply:Thank you for reminding us the problem, I have modified the relevant content in text
Author Response File: Author Response.doc
Round 2
Reviewer 2 Report
Reviewer Comments to Authors
Review of Manuscript applsci-1491437
Analysis of the Vibration behaviors of the Rotating Composite Nano-Annular Plates Based on the Nonlocal Theory and Different Plate Theories
The article entitled “Analysis of the Vibration behaviors of the Rotating Composite Nano-Annular Plates Based on the Nonlocal Theory and Different Plate Theories” by Haonan Li, Linquan Yao and Wei Wang was improved after first review. The authors answered the questions correctly. In the opinion of this referee, this study is worthy of publication, following revisions and alterations outlined below.
MAIN POINTS/COMMENTS/ADDITIONS
- The Fig. 1 is the same of Fig. 1 in [1]. The authors have to change this figure.
[1] Guo, X.-F.; Ma, L. Vibration analysis of rotating functionally gradient nano annular plates in thermal environment, Applied Mathematics and Mechanics. 2020; 41(11): 1224-1236.
- There are some results that are similar to those reported in [1], for instance in Fig. 2 (a,d) for Kirchhoff plate. These results should be referenced in order to highlight that they have already been published in [1].
- For the equations, the authors should use bold and lower case letter for vectors, and bold and capital letter for matrices. They must also include the punctuation after the equations.
- The author must improve the figures of the article. Use vector graph when possible.
- I have noticed minor corrections to the text. The whole article should be carefully proof-read for adjustments.
Author Response
We thank the reviewer very much for the insightful comments and constructive suggestions, which are of great value for further improving the quality of our manuscript. We have revised our manuscript in full compliance with the reviewer’s comments and suggestions. In the following, we respond to the comments point-by-point. All the changes are also highlighted in the revised manuscript in Blue color.
The article entitled “Analysis of the Vibration behaviors of the Rotating Composite Nano-Annular Plates Based on the Nonlocal Theory and Different Plate Theories” by Haonan Li, Linquan Yao and Wei Wang was improved after first review. The authors answered the questions correctly. In the opinion of this referee, this study is worthy of publication, following revisions and alterations outlined below
1.Query: The Fig. 1 is the same of Fig. 1 in [1]. The authors have to change this figure.
Reply: Thank you for reminding us the problem. I have modified the model diagram in the paper.
Figure 1. Schematic diagram of of the cross section rotating functionally graded nano-annular plate
2.Query:There are some results that are similar to those reported in [1], for instance in Fig. 2 (a,d) for Kirchhoff plate. These results should be referenced in order to highlight that they have already been published in [1].
[1] Guo, X.-F.; Ma, L. Vibration analysis of rotating functionally gradient nano annular plates in thermal environment, Applied Mathematics and Mechanics. 2020; 41(11): 1224-1236.
Reply: Thank you for reminding us the problem.
The research contents of 3.1 to 3.6 subsubsections are the influence of various physical parameters on the natural frequencies of the rotating nano-annular plates. The results obtained through Kirchhoff's theory are the same as the conclusions of the literature [28].
28 Guo, X.F.; Ma, L. Vibration analysis of rotating functionally gradient nano annular plates in thermal environment. J. Appl. Math. Mech. 2020, 41, 1224-1236.
3.Query:For the equations, the authors should use bold and lower case letter for vectors, and bold and capital letter for matrices. They must also include the punctuation after the equations.
Reply: Thank you for reminding us the problem. I have modified the relevant contents.
4.Query:The author must improve the figures of the article. Use vector graph when possible.
Reply: Thank you for reminding us the problem. I have adjusted some pictures.
5.Query:I have noticed minor corrections to the text. The whole article should be carefully proof-read for adjustments
Reply: Thank you for reminding us the problem. I have adjusted the details in this paper.
Author Response File: Author Response.doc
Reviewer 3 Report
Authors addressed all my comments
Author Response
There is no second revision
