Analysis of Floquet Waves in Periodic Multilayered Isotropic Media with the Method of Reverberation-Ray Matrix
Round 1
Reviewer 1 Report
Review of the manuscript "Analysis of Floquet Waves in Periodic Multilayered Isotropic Media with the Method of Reverberation-Ray Matrix".
The manuscript investigates the dispersion equation for analyzing the propagation characteristics of in-plane waves in general periodically multilayered isotropic media.
The basic model of general periodic multilayered isotropic media with considering the arbitrarily-directed in-plane wave propagation is described. The state equation and its solution of the constituent isotropic layers are given according to the theories of elastodynamics and differential equations.
The dispersion equation governing the propagation characteristics of in-plane Floquet elastic waves in general periodically multilayered isotropic media is derived by combining the MRRM and the Floquet theorem.
The verifications are conducted by numerical examples about the correctness and the numerical stability of the proposed MRRM as compared to the method of transfer matrix.
In my opinion the manuscript is interesting, well organized and discussed.
English is fine.
It can be accepted for publication after the following minor revisions:
References 27 and 30 are not called in the main text.
References all are quite ancient and should be up to date.
Author Response
Please see the attachment.
Author Response File: 
Author Response.pdf
Reviewer 2 Report
Reviewer Report
In this manuscript, the authors combine the method of reverberation-ray matrix (MRRM) with the Floquet theorem, thus the dispersion equation for analyzing the propagation characteristics of in-plane waves in general periodically multilayered isotropic media is derived. All kinds of dispersion curves of the Floquet in-plane waves propagating perpendicularly, parallelly and obliquely to layering are provided through a periodic octal-layered media. Besides, the dispersion surfaces and the slowness curves reflecting the propagation characteristic of the Floquet in-plane waves in all directions are given. Among the other results, authors show that the proposed MRRM is validated to be numerically stable within all the considered frequency ranges and in cases of all considered periodic laminated media with unit cell containing various constituent layers such as two and eight layers
This research is of great importance in the field. Overall, the whole article is a good-written one with consecutiveness, strict logic, affluent datum, and clear consecution. The following suggestions are supplied:
1. Authors should mention why they choose to consider lead (Pb), aluminum (Al), epoxy (Ep) and steel (St) as materials for the unit cell which compose the form of periodically multilayered isotropic media. Are there some other materials which should also be (at least) mentioned as potentially interesting ones, from practical point of view.
2. Check English language in order to improve it. For example, Instead of “State Equations and Its Solutions for Constituent Isotropic Layers”, you should write “State Equations and Their Solutions for Constituent Isotropic Layers”.
So, the present manuscript is suitable for publication in Crystals, subject to the above mentioned minor revision points.
Author Response
Please see the attachment.
Author Response File: Author Response.pdf
Reviewer 3 Report
The article is well written and can be of significance in the field of isotropic media.
However, this manuscript is lacking of novelty.
The reviewer found several similar papers on this topic (even some from the authors). Therefore, it is important to highlight the novelty and compared the results with the other papers. The authors published several papers based on numerical analysis. Therefore, the real experiment can be significant for validation.
Also, the reviewer will be excited to see the point-by-point analysis compared to the published one in the result section.
Author Response
Please see the attachment.
Author Response File: Author Response.pdf
Round 2
Reviewer 3 Report
The manuscript can be publishable. The future work could be more interesting.
