Fractional Dynamical Behavior of an Elastic Magneto Piezo Oscillator Including Non-Ideal Motor Excitation

Round 1

Reviewer 1 Report

In this paper, the authors have investigated the influence of fractional Bouc-Wen damping in an energy harvesting collection device under the action of a nonideal motor coupled to the structure. The non-ideal motor considering the two parameters $a_0$ and $b_0$, which are defined by the active interaction between the oscillating system and the excitation source. Authors have used the Riemman-Liouville fractional derivative operator to describe the Bouc-Wen fractional damping, which can express the vicoelastivities of the piezoceramic material coupled to the beam and to an electrical circuit for energy harvesting. Further, the parameter of the fractional derivative operator that showed changes in the hysteresis curve of the Bouc-wen damping; and other analyzes carried out were the non-linear dynamics of the system with the variation of the fractional derivative parameter for a range of values, which showed the chaotic and periodic behavior of the system. 

The fractional Bouc-Wen hysterical damping and observed that it dissipates mechanical energy in the oscillator that cannot be harvested. On the other hand, it flatters the resonance of the oscillator (mechanical resonator) by amplifying the frequency bandwidth effect. And it can additionally influence the resonance curve causing its frequency-dependent deformation which can be useful for energy capture. The Bouc-Wen fractional hysterical damping enriches the dynamics by changing the way it dissipates mechanical energy in the oscillator. In one hand, it flatters the resonance of the oscillator (mechanical resonator) by amplifying the frequency bandwidth effect. On the other hand, it can influence the resonance curve causing its frequency-dependent deformation, which is useful for energy capture. The Fractional Bouc-Wen damping changed the beam vibration and, therefore, the displacements in the piezoceramic ma- 375 terial, allowing a higher average power, which establishes that the changes observed in the fractional hysteresis can characterize the piezoelectricity of the material for materials.

In the present paper, the given results seem correct and all the figures are at appropriate place. The given results can be used for further studies in the field of Mathematical Modeling by using Fractional Calculus operators.

For improvement, the authors are suggested few modifications/suggestions:

1. In the line 382, the project name DIALOG picture should be removed (the name of project is already given).

2. Some recent work related to present paper should be given and cited.

3. The references which are not cited should be removed from the list of references.

Thanks 

Author Response

Dear Editor and Reviwers

Thank you for your observations, the answers to the questions are in the attached document

The author

Author Response File: Author Response.docx

Reviewer 2 Report

See the attached file for the comments 

Comments for author File: Comments.pdf

Author Response

Dear Editor and Reviwers 

Thank you for your observations, the answers to the questions are in the attached document

The authors

Author Response File: Author Response.docx

Reviewer 3 Report

 Our work analyzed the behavior of the fractional model with an external force de scribed in Equation 2 and the fractional BW damping. 1. a) Strong points:
   - The proposed mathematical model is a complex one and it generates,
 through simulation, feasible results.
   - The mathematical procedures used in the manuscript have a relevant> research aspect.

Good paper!

   - The references are consistent as number and relevance.

 b) Weak points:
   - The text from some Figures is not understandable .
   - The applied numerical simulation algorithm is not detailed.
   - Some assumptions are made in the research, but their validity is explained.  2. Some recommendations:
    1. The text from some Figures is not understandable (for example,
 in the Figures 1,5, and 6). This problem must be solved.
    2. The applied numerical simulation algorithm is not detailed. It
 has to be detailed.
    3. Some assumptions are made in the research, but their validity is
 not explained. These aspects should be clarified.

Author Response

Dear Editors and Reviewers 

Thank you for your observations, the answers to the questions are in the attached document

Author Response File: Author Response.docx

Reviewer 4 Report

The reference list needs an update. More recent works should be cited to provide the integration of the subject in the present state of the art and justify that the research topic is worth pursuing.

What is the physical relevance of the results?

Can the setup from Fig 1 be physically built? If yes, please include a guide to reproduce it.

How are figures 2,3,4 generated? Measurements or simulations?

Author Response

Dear Editors and Reviewers 

Thank you for your observations, the answers to the questions are in the attached document

Author Response File: Author Response.docx