Static Bending and Vibration Analysis of a Rectangular Functionally Gradient Piezoelectric Plate on an Elastic Foundation
Round 1
Reviewer 1 Report
References are scarce. The introduction must include a deeper state of art review to contextualize and justify the contribution/ addition of knowledge of this paper.
In lines 46-49, «PZT-5 has a high piezoelectric constant and dielectric coefficient, so 47 it has good mechanical and electrical conversion characteristics and electrical properties. PZT-4 has good 48 mechanical properties but poor electrical properties. When these two materials are combined together, mechanical 49 components can achieve a good electromechanical coupling effect in work.»:
I presume the authors mean (and if that is the case the authors must make it clear) “In this paper” or “In the present formulation”.
Equation (17) is introduced with a reference to itself.
Line 123 replaced “maked” -> “made”.
When I finish reading the paper, the sensation was “that’s it? Just this?” It felt so empty. I know this is not objective, but still. The authors should improve the conclusion with possible future work to be developed or open questions in the area or suggestions for the design of PGPM’s or …
Author Response
Static Bending and Vibration Analysis of A Rectangular Functionally Gradient Piezoelectric Plate on An Elastic Foundation
Wei Wang 1,3 , Haonan Li 1,2 and Linquan Yao 1,2,*
1 School of Mathematical Sciences , Soochow University , Suzhou 215006 , Jiangsu, China
2 School of Rail Transportation , Soochow University , Suzhou 215131 , Jiangsu, China
3 Soochow College, Soochow University , Suzhou 215006 , Jiangsu, China
* Correspondence: [email protected]
Response to Comments of Reviewer 1
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.
1.Query:References are scarce. The introduction must include a deeper state of art review to contextualize and justify the contribution/ addition of knowledge of this paper.
Reply:Thank you for reminding us the problem. I have added the relevant contents in the introduction and a deep description.
2.Query:In lines 46-49, PZT-5 has a high piezoelectric constant and dielectric coefficient, so 47 it has good mechanical and electrical conversion characteristics and electrical properties. PZT-4 has good 48 mechanical properties but poor electrical properties. When these two materials are combined together, mechanical 49 components can achieve a good electromechanical coupling effect in work:
I presume the authors mean (and if that is the case the authors must make it clear) “In this paper” or “In the present formulation”.
Reply:Thank you for reminding us the problem. I have revised the contents of this part.
Since most scholars in the past studies have used these two materials when studying the mechanical properties of composite piezoelectric structures, and therefore comparison can be made during the analysis of the data, and the two materials can be used to study the change of the material gradient index. The resulting conclusions have guided significance for the mechanical properties of the plates formed by other materials.
3.Query:Equation (17) is introduced with a reference to itself.
Reply:Thank you for reminding us the problem. I have revised and expand the content of this part.
According to Hamilton principle, the variation in the total energy is divided into zero, i.e.,
(16)
Substituting Eqs.(11), (12) and (13) into Eq. (16), the governing equation of rectangular plate is
(17)
and the boundary condition of the four-sided simply supported plate is deduced as follows:
(18)
4.Query:Line 123 replaced “maked” -> “made”.
Reply:Thank you for reminding us the problem. I have revised and expand the content of this part.
To facilitate data processing, each quantity is made dimensionless first
Reviewer 2 Report
My comments for the manuscript titled: “Static Bending and Vibration Analysis of A Rectangular Functionally Gradient Piezoelectric Plate on An Elastic Foundation”
*Minor comments:
-"Hamiltonian" or "Hamilton principle" should be used. "Hamiltonian principle" is wrong.
- “the governing equations and corresponding boundary conditions of the model are derived, and then the equations are discretized and solved by the differential quadrature method”
This sentence is wrong. DQM transfers the differential equations into algebraic ones only, not solving them. To solve the obtain algebraic equations, the eigenvalue process will be applied.
-The most important result of the work should be mentioned at the end of the abstract.
-A very weak introduction and literature review. There are plenty of published works on this topic that were ignored by authors.
*Major comments:
-What is the reason for mixing the two mentioned ceramics as an FG structure? To increase its mechanical, thermal, or electric properties? So then where is the result for this? How it is possible to practically mix them? And etc.
-The explanations of results are not readable. Furthermore, there are no scientific and in-depth descriptions of the results.
-Tabulating the numerical results by different tables is interesting. However, plotting diagrams would be much more valued.
-The paper has been submitted to the SI titled: "Nonlinear Analysis of Static and Dynamic Problems in Mechanical Engineering".
Why did the authors employ linear strains and solve a linear static bending?
Moreover, the solved frequency analysis is linear as well. Thus, the paper does not match the SI scope.
Based on the above-mentioned comments, I have no doubt to recommend rejecting the manuscript.
Author Response
Static Bending and Vibration Analysis of A Rectangular Functionally Gradient Piezoelectric Plate on An Elastic Foundation
Wei Wang 1,3 , Haonan Li 1,2 and Linquan Yao 1,2,*
1 School of Mathematical Sciences , Soochow University , Suzhou 215006 , Jiangsu, China
2 School of Rail Transportation , Soochow University , Suzhou 215131 , Jiangsu, China
3 Soochow College, Soochow University , Suzhou 215006 , Jiangsu, China
* Correspondence: [email protected]
Response to Comments of Reviewer 1
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 Yellow color.
Minor comments:
"Hamiltonian" or "Hamilton principle" should be used. "Hamiltonian principle" is wrong.
“the governing equations and corresponding boundary conditions of the model are derived, and then the equations are discretized and solved by the differential quadrature method”
This sentence is wrong. DQM transfers the differential equations into algebraic ones only, not solving them. To solve the obtain algebraic equations, the eigenvalue process will be applied.
The most important result of the work should be mentioned at the end of the abstract.
A very weak introduction and literature review. There are plenty of published works on this topic that were ignored by authors.
Reply:Thank you for reminding us the problem. I have revised the contents according to your requirements.
*Major comments:
1.Query:What is the reason for mixing the two mentioned ceramics as an FG structure? To increase its mechanical, thermal, or electric properties? So then where is the result for this? How it is possible to practically mix them? And etc.
-The explanations of results are not readable. Furthermore, there are no scientific and in-depth descriptions of the results.
Reply:Thank you for reminding us the problem. I have revised the contents of this part.
Since most scholars in the past studies have used these two materials when studying the mechanical properties of composite piezoelectric structures, and therefore comparison can be made during the analysis of the data, and the two materials can be used to study the change of the material gradient index. The resulting conclusions have guided significance for the mechanical properties of the plates formed by other materials.
2.Query:Tabulating the numerical results by different tables is interesting. However, plotting diagrams would be much more valued.
Reply: Thank you for reminding us the problem. Some parameters of this paper on the influence of static curvature deflections and frequencies are not obvious, so the differences in the image cannot be obvious, and the datas are more convincing in the form of tables.
3.Query:The paper has been submitted to the SI titled: "Nonlinear Analysis of Static and Dynamic Problems in Mechanical Engineering".
Why did the authors employ linear strains and solve a linear static bending?
Moreover, the solved frequency analysis is linear as well. Thus, the paper does not match the SI scope.
Reply: Thank you for reminding us the problem. Linear bending and vibration is the basis for non-linear bending and vibration. Research on nonlinear mechanics behaviors are the author's next work and has been introduced in the prospects of the conclusions.
Conclusions
In this paper, a FGPM plate on an elastic foundation composed of two different piezoelectric materials bonded together in the form of plate is studied, we explore the influence of various physical parameters on the static bending and fundamental frequencies of the plate. However, in the process of research, we only consider the linear mechanics behaviors of the plate, and so we study the contents of nonlinear mechanics behaviors on next work.
Author Response File: 
Author Response.pdf
Reviewer 3 Report
The manuscript by the authors describes a differential quadrature method for analysing the static bending and vibration of a rectangular functionally gradient piezoelectric plate on an elastic foundation. The work is interesting, but I have some notes concerning clarity of the presentation: (1) It would be very nice if a Nomenclature illustrating all the parameters appeared in the manuscript is added, for papers focusing on theory. (2) The current introduction is quite short, more references are needed, among others, it would be better to include the applications of FGMs in different areas: 10.1016/j.jallcom.2015.04.216; 10.1016/S1003-6326(15)63996-6; 10.1016/j.compstruct.2015.08.113; 10.1016/j.compositesb.2015.07.018. (3) The model assumptions can be more explicitly presented by summarizing them in the beginning. (4) The results can be better presented if some of the results in ‘Table’ can be shown in the format of ‘Figure’.
Author Response
Static Bending and Vibration Analysis of A Rectangular Functionally Gradient Piezoelectric Plate on An Elastic Foundation
Wei Wang 1,3 , Haonan Li 1,2 and Linquan Yao 1,2,*
1 School of Mathematical Sciences , Soochow University , Suzhou 215006 , Jiangsu, China
2 School of Rail Transportation , Soochow University , Suzhou 215131 , Jiangsu, China
3 Soochow College, Soochow University , Suzhou 215006 , Jiangsu, China
* Correspondence: [email protected]
Response to Comments of Reviewer 3
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 manuscript by the authors describes a differential quadrature method for analysing the static bending and vibration of a rectangular functionally gradient piezoelectric plate on an elastic foundation. The work is interesting, but I have some notes concerning clarity of the presentation: 1.Query: It would be very nice if a Nomenclature illustrating all the parameters appeared in the manuscript is added, for papers focusing on theory.
Reply:Thank you for reminding us the problem. I have described the relevant contents, e.g., Functionally graded materials (FGMs).
2.Query: The current introduction is quite short, more references are needed, among others, it would be better to include the applications of FGMs in different areas: 10.1016/j.jallcom.2015.04.216; 10.1016/S1003-6326(15)63996-6;10.1016/j.compstruct.2015.08.113; 10.1016/j.compositesb.2015.07.018.
Reply: Thank you for reminding us the problem. I have quoted the relevant contents.
4 Fan, G.F.; Tang, Y.Q.; Lu, W.Z. Reduce synthesis temperature and improve dispersion of YAG nanopowders based on the co-crystallization method. J. J Alloy Comped, 2015, 618, 1-6.
5 Entwistle, D.; Cole, E.H.; Wooding, N.S. Reduce synthesis temperature and improve dispersion of YAG nanopowders based on the co-crystallization method. J. J Alloy Compd, 2015, 618, 7-13.
6 De, F.; Wu; Yu, X. Crystallization Behavior of Polylactide/Graphene Composites. J. Ind Eng Chem Res, 2013, 52, 6731-6739.
7 Lim, J.W.; Lee, D.G. Carbon fiber/polyethylene bipolar plate-carbon felt electrode assembly for vanadium redox flow batteries (VRFB) J. Compos Struct, 2015, 134, 483-492.
8 Daugherty, M.C.; Siyong, G.; Aaron, D.S. Graphene quantum dot-decorated carbon electrodes for energy storage in vanadium redox flow batteries J. Nanoscale, 2020, 12, 7834-7842.
9 Zhou, W.B. Preparation and thermodynamic analysis of the porous ZrO2/(ZrO2+Ni) functionally graded bolted joint J. Compos Part B-Eng, 2015, 82, 13-22.
3.Query: The model assumptions can be more explicitly presented by summarizing them in the beginning.
Reply: Thank you for reminding us the problem. I have summarized the contents of the model assumptions in the introduction part.
The functional gradient plate structure composed by a variety of materials combines excellent performance of a variety of component materials, so the functional gradient plates are important in the fields of aerospace, transportation engineering, construction and other fields. The interference of the plate structure is taken from external conditions in the process of work, and many mechanics such as bending and vibration, so many scholars have made a lot of research on the mechanical behaviors of the plates and have achieved rich research results [10-16]
4.Query: The results can be better presented if some of the results in ‘Table’ can be shown in the format of ‘Figure’.
Reply: Thank you for reminding us the problem. Some parameters of this paper on the influence of static curvature deflections and frequencies are not obvious, so the differences in the image cannot be obvious, and the datas are more convincing in the form of tables.
Author Response File: Author Response.pdf
Round 2
Reviewer 2 Report
The scope of mixing two materials as FGM is to increase mechanical, chemical, electrical, etc. properties. In this case, normally, the two mixed materials are differently remarkable in some properties. For example, mixing steel and ceramic. Mixing them will lead to the new material including good properties together in one material. It is a strange and so weak idea to mix two similar materials. Authors by themselves mentioned this; "The FGPM plate composed of the two materials of PZT-4 and PZT-5, when the material component changes, the change on the equivalent stiffness of the plate is not large, which is because the physical properties and electrical properties of the two materials are relatively close." So, such the mix is not a novelty.
The revision is not convincing. This response is so strange "Linear bending and vibration is the basis for non-linear bending and vibration".
When the SI has been presented for nonlinear problems, it means they are looking for advanced analyses, not basic ones. This paper does not deserve to be published in this SI, in my opinion.
Undoubtedly, this paper should be rejected.
Author Response
Static Bending and Vibration Analysis of A Rectangular Functionally Gradient Piezoelectric Plate on An Elastic Foundation
Wei Wang 1,3 , Haonan Li 1,2 and Linquan Yao 1,2,*
1 School of Mathematical Sciences , Soochow University , Suzhou 215006 , Jiangsu, China
2 School of Rail Transportation , Soochow University , Suzhou 215131 , Jiangsu, China
3 Soochow College, Soochow University , Suzhou 215006 , Jiangsu, China
* Correspondence: [email protected]
Response to Comments of Reviewer 2
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 yellow color.
Query:The scope of mixing two materials as FGM is to increase mechanical, chemical, electrical, etc. properties. In this case, normally, the two mixed materials are differently remarkable in some properties. For example, mixing steel and ceramic. Mixing them will lead to the new material including good properties together in one material. It is a strange and so weak idea to mix two similar materials. Authors by themselves mentioned this; "The FGPM plate composed of the two materials of PZT-4 and PZT-5, when the material component changes, the change on the equivalent stiffness of the plate is not large, which is because the physical properties and electrical properties of the two materials are relatively close." So, such the mix is not a novelty.
Reply:Thank you for reminding us the problem. I have modified the reasons for choosing these two materials.
Since most scholars in the past studies have used these two materials when studying the mechanical properties of composite piezoelectric structures, and therefore comparison can be made during the analysis of the datas, and the two materials can be used to study the change of the material gradient index. The resulting conclusions have guided significance for the mechanical properties of the plates formed by other materials.
Query:The revision is not convincing. This response is so strange "Linear bending and vibration is the basis for non-linear bending and vibration".
Reply: Thank you for reminding us the problem. I have made a narrative part of the prospects in the conclusions.
However, in the process of research, we only consider the linear mechanics behaviors of the plate, and so we study the contents of nonlinear mechanical behaviors on next work.
Author Response File: Author Response.pdf
Reviewer 3 Report
Thanks for the response, please carefully check the newly added text, e.g., line 53, 'It is' should be 'There are...'; The tense should be past tense when introducing the literature, e.g. line 39, ..investigated..; Some typos exist in the Refs as well, e.g. There is an extra 'J.' for all the Journal names, Refs 4-5 have exactly the same title, Ref 9 author names are not complete.
Author Response
Static Bending and Vibration Analysis of A Rectangular Functionally Gradient Piezoelectric Plate on An Elastic Foundation
Wei Wang 1,3 , Haonan Li 1,2 and Linquan Yao 1,2,*
1 School of Mathematical Sciences , Soochow University , Suzhou 215006 , Jiangsu, China
2 School of Rail Transportation , Soochow University , Suzhou 215131 , Jiangsu, China
3 Soochow College, Soochow University , Suzhou 215006 , Jiangsu, China
* Correspondence: [email protected]
Response to Comments of Reviewer 3
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.
Query:Thanks for the response, please carefully check the newly added text, e.g., line 53, 'It is' should be 'There are...'; The tense should be past tense when introducing the literature, e.g. line 39, ..investigated..; Some typos exist in the Refs as well, e.g. There is an extra 'J.' for all the Journal names, Refs 4-5 have exactly the same title, Ref 9 author names are not complete.
Reply: Thank you for reminding us the problem. I have modified as your request. In all the cited literature, J represents the meaning of the journal, and I organize it according to the format of the Applied Sciences journal template.
Author Response File: Author Response.pdf
