Experimental and Numerical Analysis of Triply Coupled Vibration of Thin-Walled Beam with Arbitrary Closed Cross-Section
Round 1
Reviewer 1 Report
A new thin-walled beam dynamic transfer matrix method, named TDTMM, has been proposed in the frequency domain for the thin-walled beam in the paper. The new TDTMM method takes into account the influence of warping effect and coupled bending and torsional vibration of the thin-walled beam. The TDTMM model shows high accuracy compared with the general dynamic transfer matrix method (GDTMM), which has been verified by the FE simulation and experimental results. The work of this paper is impressive and meaningful in this area. The paper is recommended to publish in Machines after answering following questions and finishing corresponding revision in the manuscript.
(1) Need to introduce the difference between the doubly and triply coupled vibration of the beam in the second paragraph of the Introduction.
(2) The authors mentioned that the transfer matrix method (TMM) is extensively used in the static analysis of solid beam or space frame structure in the Introduction. However, as far as my knowledge, TMM is also widely used in dynamic modelling.
(3) The Figure 1 is not clear. What do the dash curves refer to? Where is the section? You also need to illustrate the displacements u(s,x,t), ξ(s,x,t), et al. in the figure.
(4) In section 2.4, what does the bimoment B refer to? It should be illustrated in the figures of the paper.
(5) The FE model could be shown alongside the cross-section figures.
(6) What do the cyan dash curves in Figure 5 and 6 refer to? It should be explained in the legend or caption of the figures.
(7) Some mode shape figure results should be provided to give the evidence of the coupling between bend and shear in the vibration so that to verify the necessary to consider the coupling in vibration analysis. This is important.
(8) More figures about the test rig should be given in the paper, especially to shown how do you apply the fixed boundary condition.
(9) In the caption of Figure 10, results of 3 different boundary conditions are shown in figure (a), (b) and (c). However, only figure (a) and (b) are shown in Figure 10.
(10) What’s the difference of the curves with different colors in Figure 10? It should be given in the legend of the plot. The Figure 10 is not professional enough to appear in a paper, it should be replot. Try log scale y axis. Give x axis label name as Frequency.
(11) You compared the results form TDTMM proposed in this paper and the GDTMM method. You need to introduce the difference between the TDTMM and GDTMM in the introduction and conclusion of the paper.
(12) In Table 9 and 10, which columns of the table refer to experimental results? Whether the column heading GDTMM or S-FEM is given incorrectly?
(13) The English writing must be improved and polished. It is far from satisfactory at the moment.
Author Response
Please see the attachment.
Author Response File: 
Author Response.pdf
Reviewer 2 Report
1. As stated in the introduction (page 2, line 69), one of the purposes of this work is to establish the inherent relationship between the properties of the cross-section and the beam's dynamic behaviors. However, this is absent in the text of the work. After describing of the TDTMM method, it is immediately compared with other methods. Some useful dependencies of the resonant frequencies of beam on its cross-section parameters should be added, or this purpose of the work should be removed from the introduction and conclusion.
2. A description of the advantages of the newly proposed TDTMM method over the well-known and widely used S-FEM method should be added to the introduction. For example, the accuracy, computing time and memory costs can be compared.
3. In figures 5 and 7, dots should be used instead of lines, because modal index is a discrete value.
4. Tables 9 and 10 lacks experimental results. Perhaps this is a typo in the name of the GDTMM column.
Author Response
Please see the attachment.
Author Response File: Author Response.pdf
Round 2
Reviewer 1 Report
All the questions raised by the reviewer have been answered well. The manuscript is good enough for publication in Machines.
Author Response
Thank you very much for the comment and suggestion.
Reviewer 2 Report
The article has become much better and is acceptable for publication.
Only note: On (page 21, line 373), the description of table 9 "TDTMM, test and S-FEM" does not match the title of this table "TDTMM GDTMM Test"
Author Response
Thank you very much for the comment and suggestion. According to the reviewer's suggestion,the description of table 9 has been modified.
Author Response File: Author Response.pdf
