Differential Quadrature Method for Fully Intrinsic Equations of Geometrically Exact Beams
Round 1
Reviewer 1 Report
The authors apply DQM to Prof. Hodges' fully intrinsic beam theory. For publication, the followings should be considered.
1. The results should be compared with the original form by Prof. Hodges.
2. In Table, why do the authors use the root bending moment only ?
Blade deflections may be also good for validation.
3. The differences in Table 3 should be represented using percentages.
4. In Tables 1 and 4, the upper scripts should be used when the unit, Nm2, is represented.
5. The authors should describe more clearly the advantages of the method proposed in this work.
Author Response
Dear Reviewer,
Sorry so late reply to you. I got back to school from quarantine recently. I have provided a point-by-point response to your comments.
Please see the attachment.
Kind regards,
Lidao Chen
Author Response File: 
Author Response.docx
Reviewer 2 Report
The authors present a modification to the DQ method using high precision Pade approximation. Given a suitable choice of parameters (e.g. number of elements, number of discretisation points) improved accuracy and computational efficiency can be achieved compared with competing methods. The proposed method has potential application to the dynamic analysis of rotor blades. I can recommend publication provided the following issues are addressed.
1. The English needs to be improved throughout the manuscript. There are many grammatical errors. To give one example, in lines 73-78 there is confusion between singular and plural nouns and verbs; is there one equation or multiple equations?
2. The reference list needs to be tidied up. Author names are given incorrectly in references 3, 5 and 22-24. There are many inconsistencies in the capitalisation of article titles and journal abbreviations.
3. The introduction refers to the underlying beam problems in general terms. But the paragraph starting in line 120 seems to restrict attention to rotor blades, perhaps undermining the more general applicability of the proposed approach.
4. Section 3 gives the proposed theory and methodology. Some of this reports on work by previous authors such as Fung and Hodges. The novel features of the present work should be highlighted.
5. Some wording is rather obscure and needs to be clarified. Examples are: 'maximum nonlinearity' in line 47; the 'additional parameter' in line 181; 'fully matrix' in line 250; 'public point' in line 269. And the significance of the tilda symbols in Eq. (1) should be explained.
6. The loss of accuracy with increasing numbers of grid points (Figs. 3 and 4) is rather worrying. It would have to be addressed heuristically by anyone attempting to apply the method to new problems or new types of problem.
Author Response
Dear Reviewer,
Sorry so late reply to you. I got back to school from quarantine recently. I have provided a point-by-point response to your comments.
Please see the attachment.
Kind regards,
Lidao Chen
Author Response File: Author Response.docx
Round 2
Reviewer 1 Report
The authors have revised their manuscript considering the present reviewer's comments and requests.
