Characterization of the Vibration and Strain Energy Density of a Nanobeam under Two-Temperature Generalized Thermoelasticity with Fractional-Order Strain Theory

Round 1

Reviewer 1 Report

The manuscript is recommended to be accepted for publication after clarifying the following points

• The language of the paper should be improved by a native English speaker. Grammar and typo mistakes are all over the article.
• The fractional-order strain theory has been applied to construct a novel model that is a novel model introduced.
• The difference between the present work with other published work is vague. The authors must clearly express the novelty of the manuscript.
• The novelty of the work should be highlighted to real physics phenomena in the introduction.
• In my opinion, the paper does not bring substantial novelty to the state-of-the-art. Indeed, the authors just adopt the concept of fractional derivatives to a given problem. No new algorithm nor procedure is really given.
• There should be a technical application explained and the results should give a solution for it.
• There should at least be a comparison with experimental results or theoretical ones already published.
• The author, therefore, needs to provide more discussion on his results- What do the results mean? What do they tell us of the interactions among Phenomena present?
• This model (fractional-order strain) is nothing but a scientific lie and not a new model. This model for correcting the concepts of the author is nothing but a model for the fractional derivative Kelvin–Voigt model of viscoelasticity. And it was derived a long time ago.
• Half of the references belong to one author. Most of them have nothing to do with the research topic. The list of references needs updating.
• It is sufficient to cite one reference to Equation 17, especially since it has been used by many other authors.
• It is not clear how to obtain the analytical formulas for the different physical fields. Was it numerically or analytically obtained?
• The section of the conclusion seems abstract. This section needs to be revised by giving the main conclusions of the study and the significance of the obtained results.
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Author Response

Reviewer 1

Comments and Suggestions for Authors

The manuscript is recommended to be accepted for publication after clarifying the following points.

The author response

• The language of the paper should be improved by a native English speaker. Grammar and typo mistakes are all over the article.

Reply: The English writing has been revised and corrected by using Grammarly software with a complete version.

• The fractional-order strain theory has been applied to construct a novel model that is a novel model introduced.

Reply: Yes, this model in which a fractional-order strain in the context of two-temperature heat conduction is a novel model and has not been solved or discussed before.

• The difference between the present work with other published work is vague. The authors must clearly express the novelty of the manuscript.

Reply: The novelty of the work has been added at the end of the introduction section.

• The novelty of the work should be highlighted to real physics phenomena in the introduction.

Reply: the paragraph which contains the references [20-22] in the introduction section is about the physics phenomena of the fractional order strain which you need to know.

• In my opinion, the paper does not bring substantial novelty to the state-of-the-art. Indeed, the authors just adopt the concept of fractional derivatives to a given problem. No new algorithm nor procedure is really given.

Reply: I think that to construct the model in the context of fractional-order strain and two-temperature heat conduction model together and to discuss the effects of each parameter in the thermal and mechanical wave is a novel to the state-of-the art.

• There should be a technical application explained and the results should give a solution for it.

Reply: I do not think so. Many applications has been solved theoretically without  a certain technical application

• There should at least be a comparison with experimental results or theoretical ones already published.

Reply: a comparison with the results of the reference [24] has been added at the end of the discussion.

• The author, therefore, needs to provide more discussion on his results- What do the results mean? What do they tell us of the interactions among Phenomena present?

Reply: I think in the discussion section the interactions among phenomena present of the fractional-order strain and the two-temperature parameters have been written.

• This model (fractional-order strain) is nothing but a scientific lie and not a new model. This model for correcting the concepts of the author is nothing but a model for the fractional derivative Kelvin–Voigt model of viscoelasticity. And it was derived a long time ago.

Reply: Yes, Kelvin–Voigt model of viscoelasticity was derived a long time ago, but no one has constructed the governing equations of the thermoelasticity models by using this consideration which makes the model is new. Maybe you do not believe by the fractional-order strain, but many authors believe by it and solved and discussed many applications.

• Half of the references belong to one author. Most of them have nothing to do with the research topic. The list of references needs updating.

Reply: The references have been modified and updated.

• It is sufficient to cite one reference to Equation 17, especially since it has been used by many other authors.

Reply: It has been modified

• It is not clear how to obtain the analytical formulas for the different physical fields. Was it numerically or analytically obtained?

Reply: The solutions have been obtained in the Laplace transforms domain analytically, while its inversions have been obtained numerically by using the iteration in (31).

• The section of the conclusion seems abstract. This section needs to be revised by giving the main conclusions of the study and the significance of the obtained results.

Reply: It has been modified

Author Response File: Author Response.docx

Reviewer 2 Report

This paper studied the characterization of the vibration and strain energy density of a nanobeam under the two-temperature generalized thermoelasticity with fractional order strain theory. The author derived the governing equations and analyzed the characteristics by using numerical method. However, there are some questions should be addressed before publication.

1. There are some minor problems with English writing, such as “conducive” in Line 76.
2. In Figure 1, the coordinate system is a left-hand Cartesian. This usage may not affect the results, but it is not common.
3. The organization structure of Section 3 is not clear and the readability is poor.
4. The units in the paper should not be italicized, which is unprofessional.
5. At the beginning of the Section 3 “Problem Formulation”, author should give a clear statement about the boundary conditions, external excitation and the beam vibration.
6. In figures 2(a), 2(b), 4(a) and 5(c), it looks like there's only one blue curve. The author should provide unambiguous pictures.
7. The paper discussed the numerical results, such as deflection, strain and stress. However, the vibration of nanobeam is not specified in this paper.
8. The authors need to clarify whether there are some properties in the vibration or heat conduction of nanobeams that can be explained by fractional strain theory. In addition, is the correctness of the conclusion verified by other theories or experimental data?

Author Response

Reviewer 2

The author response

1. There are some minor problems with English writing, such as “conducive” in Line 76.

Reply: The English writing has been revised and corrected by using Grammarly software with a complete version.

1. In Figure 1, the coordinate system is a left-hand Cartesian. This usage may not affect the results, but it is not common.

Reply: It is not important to be the left-hand Cartesian where it is usual to use these directions of the x, y, and z- axis in a beam such that.

1. The organization structure of Section 3 is not clear, and the readability is poor.

Reply: The section 3 has been modified and equation (9) has been added to make it clear.

1. The units in the paper should not be italicized, which is unprofessional.

Reply: the units have been corrected.

1. At the beginning of the Section 3 “Problem Formulation”, author should give a clear statement about the boundary conditions, external excitation and the beam vibration.

Reply: It has been added.

1. In figures 2(a), 2(b), 4(a) and 5(c), it looks like there's only one blue curve. The author should provide unambiguous pictures.

Reply: It is very difficult where the three curves are identical.

1. The paper discussed the numerical results, such as deflection, strain and stress. However, the vibration of nanobeam is not specified in this paper.

Reply: The distribution of the deflection is the vibration distribution.

1. The authors need to clarify whether there are some properties in the vibration or heat conduction of nanobeams that can be explained by fractional strain theory. In addition, is the correctness of the conclusion verified by other theories or experimental data?

Reply: According to the current results and the results in similar papers, I declare that the fractional-order strain has no major effects on the heat conduction or the thermal waves in general.

For validation of the current results, I can compare the current results with the results in Youssef and El-Bary [24]. I can see that the distributions of the studied functions in figures 2-8 in [24] have the same behaviors of the figures in the current work. 

Author Response File: Author Response.docx

Round 2

Reviewer 1 Report

The authors made the required improvements. They also responded to the auditors' concerns. We now believe that the manuscript is accepted for publication

This manuscript is a resubmission of an earlier submission. The following is a list of the peer review reports and author responses from that submission.