Buckling Analysis of a Composite Honeycomb Reinforced Sandwich Embedded with Viscoelastic Damping Material
Round 1
Reviewer 1 Report
The paper is very interesting and relevant. The disadvantage of this paper lies the weak conclusions. I recommend supplementing the conclusions with estimates of the significance of the results.
«The composite structure’s dynamic equivalent effective stiffness is directly affected by the honeycomb reinforcement’s width, and furthermore, the structure’s buckling loads in the considered research are significantly influenced» (page. 14). Well, but how exactly do they affect? Why the buckling loads ratio is non-linear when changing the geometric parameter (Fig. 6)? Why in the frequency range from 100 to 700 hertz loads, the stability losses do not depend on frequency, and in the intervals up to 100 hertz and above 700 hertz they depend on frequency (Fig. 7)?
An analysis of the results should be given in conclusion.
Author Response
Reply to Reviewer #1:
Reviewer #1: Comments on Manuscript applsci-1942092
Q1: The paper is very interesting and relevant. The disadvantage of this paper lies the weak conclusions. I recommend supplementing the conclusions with estimates of the significance of the results.
Reply: Thank you for taking the time to review our manuscript. The conclusion section of this manuscript is rewritten and improved in the new version.
Q2: The composite structure’s dynamic equivalent effective stiffness is directly affected by the honeycomb reinforcement’s width, and furthermore, the structure’s buckling loads in the considered research are significantly influenced (page. 14). Well, but how exactly do they affect?
Reply: Thank you for the reviewer’s professional comment. This sentence is improved in the new version as:
The composite structure’s dynamic equivalent effective stiffness is directly affected by the honeycomb reinforcement’s width. By increasing the reinforcement’s width, the dynamic equivalent effective stiffness of the composite structure will be increased, and furthermore, the structure’s buckling loads in the considered research are significantly influenced.
Q3: Why the buckling loads ratio is non-linear when changing the geometric parameter (Fig. 6)?
Reply: Thank you for the reviewer’s professional comment. The buckling load's ratio shows non-linear indeed in our research, in the authors’ opinion, this phenomenon is mainly caused by that the length and width ratio ka in the buckling load calculate equation is non-linear, as shown in Eq. (24). When the ka gradually increased, the buckling load is not increased linearly, it’s increased speed shows gradually slow down.
Q4: Why in the frequency range from 100 to 700 hertz loads, the stability losses do not depend on frequency, and in the intervals up to 100 hertz and above 700 hertz they depend on frequency (Fig. 7)?
Reply: Thank so much for the reviewer’s professional comment. This reason is that this honeycomb sandwich layer is composed of viscoelastic material and reinforced elastic material. Physical parameters of elastic material, such as Young’s modulus and Poison’s ratio, will not be influenced by load’s frequency. However, the physical parameters of viscoelastic material will be affected by load frequency. The Young’s modulus of viscoelastic material will be increased fast in low frequency, and reach an approximate platform value in middle-frequency (as shown in Fig. 7, in 100 to 700 Hz), finally increased by frequency raise. This phenomenon leads to the same trend of the buckling load in this analysis.
Q5: An analysis of the results should be given in conclusion.
Reply: Thank you for your valuable comment. This section was modified.
Reviewer 2 Report
The paper concerns an analysis of the dynamic buckling loads of the composite sandwich structure. The paper includes in itself interesting aspects but it is hard to call present study that refers to “dynamic buckling” basing on load frequency. In my opinion, the paper provides only results of theoretical calculations (it would be difficult to verify scores of this approach in any way) and reading the text of manuscript there are many questions nevertheless maybe after major corrections paper could be suitable to be published in “Applied Sciences”.
Remarks/Questions:
1) English language and style in text should be corrected e.g.: “embeded”: to “ embedded”.
2) How durations of dynamic load were considered? It should be clearly given.
3) Where in equilibrium equation is a given density included?
4) How were taken material properties of middle solid based on orthotropic honeycomb structures? As isotropic ones?
5) What physically mean determined dynamic buckling loads? It is not clear in text. How are differences in dynamic bucking loads vs. static buckling loads? Authors took into consideration this aspect?
6) How dynamic criteria of structure behaviour were considered (displacements or material strengths)? Only based on calculated buckling loads? Why look the buckling modes of each case with respect to ratio of dimensions or thicknesses of detailed layers?
7) What with imperfections of sandwich? This parameter was taken under consideration?
8) In the title there are words “thermal environment”. How is analysis related to thermal approach? The title seems to be misleading.
9) What essential conclusions of obtained results were drawn with regard to reality (real structures)? Is some correlation? Authors should include these information in discussion paragraph and conclusions.
10) Sandwich structures can bear greater loads (than buckling load) in short time?
11) What is greatest contribution of paper?
Author Response
Reply to Reviewer #2:
Reviewer #2: Comments on Manuscript applsci-1942092
Q1: The paper concerns an analysis of the dynamic buckling loads of the composite sandwich structure. The paper includes in itself interesting aspects but it is hard to call present study that refers to “dynamic buckling” basing on load frequency. In my opinion, the paper provides only results of theoretical calculations (it would be difficult to verify scores of this approach in any way) and reading the text of manuscript there are many questions nevertheless maybe after major corrections paper could be suitable to be published in “Applied Sciences”.
Reply: Thank so much for the reviewer’s professional and patient comments. We have tried our best to make the revised manuscript easier to read and to emphasize its impact on the topic. Due to that, the structure proposed in this manuscript is constructed in two phases material, viscoelastic material, and elastic material. The viscoelastic material can be applied to dissipate and absorb the mechanical energy generated by an external load, and the elastic material can be applied to resist the load that maybe lead to buckling. The physical behaviors of the viscoelastic material are influenced not only by the environmental properties, such as temperature and moisture but also the frequency and load amplitude. Therefore, the mechanics of the composite sandwich structure are also influenced by environment and load behaviors.
In order to minimise the reader’s confusion and show the main work performed in this analysis, the word “dynamics” and “thermal environment” are deleted in the tittle of this manuscript of the new version.
Q2: English language and style in text should be corrected e.g.: “embeded”: to “embedded”.
Reply: Thank so much for your comments. We checked carefully the whole manuscript about the language.
Q3: How durations of dynamic load were considered? It should be clearly given.
Reply: this is a professional comment, thanks a lot. The word “Dynamics” applied in this manuscript is mainly to demonstrate the physical behaviors of the composite sandwich structure that constructed by viscoelastic and elastic materials, and the mechanical parameters of viscoelastic material is frequency- and temperature-dependent. In order to make our work clear, the expression “dynamic buckling load” is modified as “buckling load”, and this load is static or quasi-static.
Q4: Where in equilibrium equation is a given density included?
Reply: Thank so much for your comments. The Halpin-Tsai model is applied in this manuscript, there, the density of the core sandwich layer can be determined according to the fraction volume of elastic and viscoelastic materials. In the new version, an equation numbered Eq. (22b) and some expression was added.
Q5: How were taken material properties of middle solid based on orthotropic honeycomb structures? As isotropic ones?
Reply: Thank so much for your professional comments. All elastic and viscoelastic materials are isotropic. After they are composed together, an orthotropic honeycomb composite structures are constructed, then, the homogenous asymptotic is applied to determine the stiffness of this structure in all directions. The 11 and 22 directions are the same, which is the difference from the parameters of 33 direction.
Q6: What physically mean determined dynamic buckling loads? It is not clear in text. How are differences in dynamic bucking loads vs. static buckling loads? Authors took into consideration this aspect?
Reply: This is a professional and shrewd question. This refers to the original starting point of our job, we had performed a static buckling loads analysis, even though the mechanics' parameters, such as the equivalent stiffness of the composite sandwich are dynamics with environment and load behaviors (Temperature and moisture of environment, and frequency and amplitude of external loads), we had changed our expression in the whole manuscript.
Q7: How dynamic criteria of structure behaviour were considered (displacements or material strengths)? Only based on calculated buckling loads? Why look the buckling modes of each case with respect to ratio of dimensions or thicknesses of detailed layers?
Reply: Thank so much for your professional comments. In this manuscript, the research is based on the calculated buckling loads through the von Karman large deformation.
We provide some figures to visualize the buckling modes of each case with respect to ratio of dimensions or thicknesses in the manuscript, the purpose is that we want to find the tendency and sensitivity of each parameter influence on the buckling load, that’s can help us to design a real structure in engineering application, or perform an optimization.
Q8: What with imperfections of sandwich? This parameter was taken under consideration?
Reply: This is a very good question indeed, thanks a lot. In our work, each layers of the sandwich are assumed to bond perfectly together. Imperfections of the sandwich extensive appear in engineering, such as delamination, fracture, warping, and locally buckling, we are now considering and trying to find a way to detect those imperfections.
Q9: In the title there are words “thermal environment”. How is analysis related to thermal approach? The title seems to be misleading.
Reply: Thank so much for your professional comments. The title of this manuscript is changed.
Q10: What essential conclusions of obtained results were drawn with regard to reality (real structures)? Is some correlation? Authors should include this information in discussion paragraph and conclusions.
Reply: Thank so much for your comments. We had improved our conclusion section. In fact, for an engineering structure, maybe a lot of factors should be considered, our research can be regarded as a new way to improve the buckling load of the structure.
Q11: Sandwich structures can bear greater loads (than buckling load) in short time?
Reply: Thank so much for your comments. The answer is yes, but with a condition that by the same macroscopic geometry parameters. The reason is that: under a load, before buckling appears, the viscoelastic material in the core layer can dissipate and absorb some energy (the value depends on the damping ratio, density, and shear elastic modulus of viscoelastic material.), that’s can increase the buckling load of the structure. However, the traditional elastic material structure can only generate permanent plastic deformation.
Q12: What is greatest contribution of paper?
Reply: The contribution of this work is that we construct a new composite sandwich structure, and analyze the factors that influence its buckling load, that’s can be considered as a way to design the real structure in engineering applications.
Round 2
Reviewer 2 Report
I have no more questions. My all remarks have been explained or taken into account.
