Nonlinear Analyses of Porous Functionally Graded Sandwich Piezoelectric Nano-Energy Harvesters under Compressive Axial Loading

Round 1

Reviewer 1 Report

This is a very interesting article which nevertheless needs in my opinion some improvement which will be appreciated by a potential reader.  For example in page 9 you mention that Galerking procedure is followed to obtain the critical buckling force.  It would be good to include a brief reminder of this procedure (eqs. 33, and 34).   Some equations are quite complicated (e.g. 37), where they obtained using a program of symbolic manipulation such as Mathematica by Wolfram or any other?  If this is the case it must be so specified and, if this is not the case, then a more detailed description of the mathematical procedure must be given.  It would be good to include a more careful description of the measure of porosity, the average size of the porous is not used or is it assumed that all the porous are the same size and homogeneously distributed? This also applies to the mechanical to electrical conversion efficiency.  

In page 20-21 it is stated that It can be seen that the RMS voltage output is independent of the total beam thickness 
when only piezoelectric effect (PE) is considered. While the RMS voltage output 
decreases with the increase of the total beam thickness when the piezoelectric and 
flexoelectric effects are considered simultaneously, which indicates that the flexoelectricity has a significant effect on the performance of the small-scale energy harvester.  This must be explained in more detail.

Finally I believe that it is fundamental for this article to discuss the PRECTICAL USE of this device. How will this practical use relate to the theoretical assumptions here discussed?  What is the relation between the real use of this device and the data here analized?  I believe that the authors could provide some practical examples and discuss them.

 

Author Response

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Author Response File: Author Response.pdf

Reviewer 2 Report

The research focuses on nonlinear analyses of porous functionally graded sandwich piezoelectric nano-energy harvesters under compressive axial loading.

The existent experience and knowledge are well systemized and described. The research aim is clearly stated in the introduction. The paper is well-structured and well-presented.

The paper has a scientific novelty. A mathematical formulation of the research problem was presented in section 2. Several solution procedures were applied, particularly static buckling analyses, natural frequency analysis, electromechanical responses. The proposed model was validated, and results were presented in section 4. The effects of the different types of distribution, porosity coefficients, length scale parameters, nonlocal parameters excitation frequency, and axial loads on the nanobeam's vibration frequency and output voltage were discussed. The results are well-presented in graphical form.

I recommend a paper for publication, but the following drawbacks should be solved.

• It is unclear why L=50 nm and ht=1 nm were used in the paper text (Table 1). Would you please provide the appropriate justification?
• Quantitative data should be added to the conclusions to prove the achieved research tasks.
  

  I do not recommend duplicating words (phrases) from the title in the keywords. To expand the web visibility, try to find other terms (phrases).

  It is recommended to place figures/tables (Fig. 2, Table 1) after linking them in the text.

  Missed letter “S” in the word “Sketch” – please see figure caption (Fig. 1).

Author Response

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Author Response File: Author Response.pdf

Reviewer 3 Report

Interested analytical study of nonlinear porous functionally graded sandwich piezoelectric nano-energy harvesters under compressive axial loading. The paper contain large introduction that can help to clearly explain background of analysis. The main chaptures contain matamatical derivation all effects that can impact to investigated phisical phenomen. The results are clear and present the sensitivity on the most important dynamic parameters. I have only one question (recomandation) Can be this interestd matematicaly derivated solution verified experiemtally?   

Author Response

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Reviewer 4 Report

A sandwich piezoelectric nano-energy harvester model under compressive axial loading is presented in this manuscript. Minor revision is required before publication.

 

In explanation of mathematical model, there are many equations. This flow is quite complex for the readers. The reviewer recommend the addition of a flow chart or image.

 

In Figure 17, the enlarged inset is shown. However, the scale ranges of vertical and horizontal axes. The authors should add such information.

Author Response

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Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

I do believe the manuscript has been
sufficiently improved to warrant publication in Applied Sciences.