Complex Band Structure of 2D Piezoelectric Local Resonant Phononic Crystal with Finite Out-Of Plane Extension
Thanh-Canh Huynh
Round 1
Reviewer 1 Report
The work 'Complex band structure of 3D piezoelectric local resonant phononic crystal' by Zhongjian Miao et al. presents a new phononic crystal and a theoretical method in which the speed of sound can be complex. This method is useful for viscoelastic polymers and phononic crystals that contain liquids. The authors have certainly done a thorough investigation with reasonable results althought the reviewer is not able to check the calculations. However the work has some significant weaknesses.
The introduction needs to be improved. The band structure is defined as 'formed by the stopband and passband' when it is the relationships between momentum and frequency even if there is no bandgap. In the introduction it might be necessary to add references for instance in the quote about 'small size controlling large wavelength'.
About the research design: 1) if the phononic crystal has periodicity in the x-y plane then why is it called a 3D phononic crystal? The thickness matters of course but the structure looks having 2D translation symmetry.
2) The selected material properties do not include viscoelasticity. The authors should make more clear that they evaluate the attenuation performance inside the stopband and discuss better the motivation.
Generally about text: 1) The article contains many relationships that are basic or included in comsol. Some symmetric tensors are shown in full form making the article much longer. The Bloch-Floque periodicity could just be mentioned. 2) Some Figure captions must be improved. Like 'Attenuation characteristics' instead of saying precisely what is plotted or not discussing the circuits of Fig 8 in the caption. The Authors should explain more about the circuits in Fig 8 and make clear the role of piezoelectricity in their study.
Some recent works that might be useful for comparing methods are: 1) Acoustoelastic analysis of soft viscoelastic solids with application to pre-stressed phononic crystals. International Journal of Solids and Structures 241, 111529, 2022. 2) Phononic Crystal Sensors: A New Class of Resonant Sensors—Chances and Challenges for the Determination of Liquid Properties. Frontiers in Mechanical Engineering 7, 705194, 2021.
Author Response
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Author Response File: 
Author Response.pdf
Reviewer 2 Report
The paper is well prepared and has enough contributions to the field. Accept after addressing minor points, as follows:
1. Check size of text and equations according to the format of the journal, they are not equal now
2. The geometrical parameters of the crystal are listed in Table 2. Why how to determine those parameters.
Author Response
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Author Response File: Author Response.pdf
Round 2
Reviewer 1 Report
The authors have made significant revisions to the manuscript in accordance with all the comments from the previous review. Given the fact that the authors present in detail their methods, further strengths and/or weaknesses of this work can be judged by peers after publication.
However some points still remain unclear and thus the suggestion is acceptance after minor revisions.
For instance in Figures 4-5, isn't it neccesarry to provide also the wavevector of these modes and give the frequencies?
In Figure 12 the caption was simply rephrased. It might not be obvious for the reader that the 8 curves show the 4 bandgaps evolution as in Figure 13.
There are also some minor typos like (example) 'peizoelectric' in line 492 that should be corrected.
Author Response
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Author Response File: Author Response.pdf
