Locomotion of Self-Excited Vibrating and Rotating Objects in Granular Environments

Round 1

Reviewer 1 Report

The interactions of active objects with granular media have been analyzed by using the model of a self-excited spherical object immersed in a granular bed, by using a discrete elements method. The locomotion by the transverse vibration and the rotation around axes has been studied. The oscillations, the vibration and the angular velocity respect the model have been studied. Optimization performance results have been shown.

About the idea regarding a real-world problem and examples linked to the considered topic is strongly related to the journal.

I consider fundamental the coupling approach, used all along the paper.

Major remarks

• Abstract: the so technique and numerical description regarding the numerical values must be avoided.
• Introduction: I can't consider eq.s 1-2 as complete to really represent the problem, in particular they don't consider the temporal evolution of the problem in terms of time-space coupling.
• Eq. 1: the fractional exponent must be motivated, by considering the reality conditions.
• About the decision of using the NUMA architecture, this isn't so actual in terms of memory efficiency, it could be replaced by some more innovative structures, by making the factorization less heavy.
• Section 2.3: all the numerical values must be motivated. The problem is very linked to real dynamics, parameters must be chosen by using also experimental data.
• Line 98: the one-dimensional vibration sinus function can't represent completely the dynamic, it could be more adapt a vector parametric time function in more directions, the same for ω.
• Figures 1-2: the result is affected by the choice of the inner parameters, a more complete analysis must be carried on by varying the values into a certain set. 
• Figure 8: the result is clearly linked to the opposite sign values for Ω, it could be more interesting to consider different coupling by using very different values in terms of sign and modulus of the parameter.
• Line 140: it's fundamental a study about the velocity variation in time, by coupling the results with a differential equations which described the problem in a theoretical way, and then by comparing both. In effect the author proposes a certain function but this choice could be anew considered by comparing it with other kind of interpolating function, and then by comparing the discrepancies.
• Figues 6-7: describe and motivate the constants values behavior of the extreme dynamics.
• The discrete (finite) elements method used for the paper is never explicitly described.

Minor remarks:

• Abstract: avoid the word "simple".
• Line 9: write "analyze" instead of "analyse".
• Eq.4: write the right arrow only over the y and ω symbol.
• Ref 3: write "Oxford: Butterworth" instead of "Oxford:Butterworth".

Author Response

We are grateful for the encouragement about the relevance of this work to the journal and that this coupling approach is fundamental. Below we respond to the detailed comments.

Author Response File: Author Response.pdf

Reviewer 2 Report

The authors analyze the movement of a spherical object in granular media vibrating with periodic oscillations.
The paper is interesting and well written.
I found only some typos e.g.:
section 2.1 Capital letter
Section 2.3 lines 84 and 92 dimensions of the box do not agree. Please change!
Line 145 and 147 Do you mean figure 4?
line 153 erase doubled that
Section 4. For me "Conclusions and future research" sounds better.
Author contribution P.L. not L.P.

Author Response

Thank you for the supportive appraisal.

Author Response File: Author Response.pdf

Reviewer 3 Report

The submitted study presents a very interesting application of the discrete element method related to the locomotion of a spherical object embedded in a granular medium. The results are well-explained, and the text is well-written. Several minor comments are given below.

1- In section 2.1, the theoretical background of DEM is explained super short. So, please provide additional info regarding how did you conduct the analysis (dynamic or quasi-static). If the results are obtained in a real-time domain, how did you manage to assign appropriate damping, and what kind of damping has been used.

2-How the contact stiffnesses are estimated? Please explain in detail. It would be interesting to see the effect of contact stiffnesses on the overall response of the SO.

3- Could you provide the required time (min. or hours) to complete one analysis using the system given in the article.

4- I am not sure, the considered boundary conditions are representative enough. Could you provide one more analysis by considering a larger medium (e.g., double the one that you have used) to better observe the influence of boundaries on the response of SO?

5- I believe that future studies are acceptable and appropriate. To what extend the spherical representation of the discrete particle estimate the real problem. What do you think about the irregular polyhedral blocks to be utilized in this kind of simulation? Please, provide several sentences regarding these issues in the manuscript.

Author Response

We are grateful for this encouraging appraisal.

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

I consider the author's reply sufficient about my remarks.