Two New Models for Dynamic Linear Elastic Beams and Simplifications for Double Symmetric Cross-Sections
Round 1
Reviewer 1 Report
In this manuscript, the author proposed two new models for dynamic linear elastic beams and then carried out some simplifications for double symmetric cross-sections. The work has some scientific merit. The reviewer can, therefore, recommend its publication, providing the following comments are well addressed.
- -In the Introduction Section, the scientific problem is not clear. Please state the scientific problem and the objectives of the work and provide an adequate background, avoiding a detailed literature survey or a summary of the results.
--Every parameter and operator shall be defined in equations, avoiding any undefined or unspecified references.
--The assumption should be listed for the modeling process.
--It is suggested to add some schematic illustrations.
Author Response
I Thank you for your suggestion of improvement. My reply is written in red in the manuscript
reviewer: in the introduction section....
reply see introduction and the reference 20 is added.
reviewer: every parameter..
marqued (reply 1) in the manuscript
reviewer the assumption should be...
marqued (reply 2) in the manuscript
reviewer: it suggested to add..
marqued (reply 3) in the manuscript and I add figure 1
Author Response File: 
Author Response.pdf
Reviewer 2 Report
The paper addresses the derivation of dynamic equations within the linear theory of beams using and extending the approach used previously for static problems. Presented new models could be useful in applications.
The paper is well-written. Nevertheless, there are a few critical comments which should be addressed before publications.
- Statement that the positive definiteness of strain energy and strong ellipticity condition are equivalent is wrong. It is enough to consider an isotropic material to see it. Indeed, both restrictions will lead to different inequalities for Lame moduli.
- In dynamics of beams one can meet a rotatory inertia. Here this matter does not discuss. On the other hand, it could be nice to have formulas for it within this rigorous approach.
- I may propose also to consider 1D initial data, how they could be derived from the 3D formulation.
As a result, I recommend the paper for publication after minor revision.
Author Response
I thank for your suggestion of improvement. My reply is written in red in the manuscript.
reviewer: Statement that the positive...
reply: marqued (reply 4) in the manuscript
reviewer: in dynamics of beams...
reply: marqued (reply 5) in the manuscript
reviewer: I may propose also ....
reply (reply 6) in the manuscript. The work 19 is now submitted with minor revisions and should be published soon.
Author Response File: Author Response.pdf
