An Analytical Method for Elastic Seismic Response of Structures Considering the Effect of Ground Motion Duration
Round 1
Reviewer 1 Report
In this manuscript (ms), the authors present an analytical method for elastic seismic response of structures considering the effect of ground motion duration. The method is interesting, original and the results indeed show that the dynamic time duration of the structure's seismic reaction is quantified by time-domain seismic reaction spectrum thus obtaining a more accurate analysis method for the seismicreaction of the structure. Hence, the paper deserves publication in Applied Sciences. However, the presentation in the current version of the ms needs improvement mainly in the following points so that the general reader of Applied Sciences to be appropriately informed:
1)First, in line 74 in page 4, the authors write:
“… different natural vibration periods at each time”.
Here, the authors should clarify that they do not refer to natural time analysis which is widely used by adding the following:
“… different natural vibration periods at each time (This should not be confused with the analysis in natural time which is a new view of time [Natural Time Analysis: The new view of time. Precursory Seismic Electric Signals, Earthquakes and other Complex Time-Series (Springer-Verlag, Berlin Heidelberg) 2011; Europhysics Letters (EPL) 91, 59001, 2010; J. Geophys. Res. Space Physics 119, 9192-9206, 2014]”
2)Second, in page 4, the system of coordinates in Figure 2 does not comply with the discussion in the lines 79 to 81, or does it? Please explain the axis better in the text or redraw the Figure so that the reader understands clearly the allocation of indices in a(m,n). This should be consistent with the interpretation given in lines 88 to 93 and the rest of the paper.
3)Third, in page 5, line 118. The ms reads “as 0.02s in the text”, where in the text exactly?
4)Fourth, in lines 127-129, in page 6 the authors write: “… the Great East Japan Earthquake on March 11, 2011 (with a recording duration 300s, … and a damping ratio J of 0.05).”
The following point should be added here for the sake of readers’ better information:
“(Note that an estimation of the epicentral location of this Great Earthquake could be achieved a few months in advance by means of natural time analysis of the Japanese seismicity [Proc Natl Acad Sci USA 112, 986-989, 2015])”
5)Fifth, in page 7, the understanding of the curve shown in Figure 6 as well as of the method suggested will be improved if the curve of Fig.6 appears somehow in Figure 5.
The authors should additionally check their manuscript for typos, for example:
l.49 Please explain ξ (xsi) and decide whether to use ξ (xsi) or ζ (zeta) throughout the ms
l.59 There is an obvious mistype in the Equation just below line 59
l.61 “its differentiation by time t” -> “its time derivative”
l.63 “accelerations’” -> “acceleration”
l.64 “system’s” -> “system”
l.78 “system’s” -> “system”
l.110 “ζ” (zeta) -> “ξ” (xsi), if the authors keep ξ (xsi) see the first typo above
l.111 Define acronym JSTN
Figure 4, in page 6, “datas” -> “data” throughout the figure
l.136 “α0Τ” -> “α_{0T}” (make 0T subscript)
l.147 “data and” -> “data acceleration and”
l.213 “follow:” -> “follows”
Thus, in summary if the authors address appropriately the points mentioned above I will be glad to suggest the publication of the revised version.
Author Response
please see the attached file.
Author Response File: 
Author Response.doc
Reviewer 2 Report
Reviewer comments and conclusion on the manuscript entitled
An analytical method for elastic seismic response of structures considering the effect of ground motion duration
submitted by Qianqian Liang, Chen Zhao, Jun Hu, and Hui Zeng
General
The objective of the paper is to provide some methodology for accounting the earthquake ground motion duration in the response analysis of structures.
For this reason, in the Introduction the response of the damped single degree of freedom (SDF) system has been analyzed and an analytical solution is proposed that consists of the base motion of SDF system at the time t in a form of linear interpolation of the excitation at time points ti and ti+1.
The Method (Section 2) itself is based on the digital decomposition of the time-history response record into SDF responses with given periods (Section 2.1 and Figure 2). The practical performance of this is shown in Section 3. Practically, it seems, that the basis of decomposition is the dividing the time-history into m intervals, and calculation of responses of the series of SDF systems with periods Tc for each of m intervals of time.
Case study for the implementation of the decomposition is presented in the Section 4. The application of the procedure is discussed in Section 5. The research conclusions are given in Section 6.
The research objective is devoted to important practical issue that has interesting theoretical aspects, too.
Major comments
The most important deficiency of the manuscript is the insufficient linkage between the parts and different results of the research. The Sections are practically autonomous, they are not presented as elements of a system, or steps of consecutive logical action.
The theoretical introduction concluded in the derivation of Equations 6-8. These results are even not mentioned in the remaining part of the manuscript.
Main result of the research is the proposed method of the decomposition of the acceleration time-history. However, the novelty of the proposed method is not demonstrated by appropriate review of the literature.
Application of the method of the decomposition of the acceleration time history is presented and discussed.
The Sections Method and Application are not logically linked either to the Introduction or to the Discussion.
It seems that the Discussion is intended to show the application of the proposed method in the structural analysis. However, a verbal connection of this with the previous sections is insufficient for convincing the reader on the applicability of the proposed decomposition.
The Conclusion gives appropriate summary of the research.
Minor comments
Minor comments are given in the annotated manuscript.
Comments for author File: 
Comments.pdf
Author Response
please see the attached file.
Author Response File: Author Response.doc
Reviewer 3 Report
This paper deals with the elastic response spectrum analysis, trying to include the effect of the ground motion duration in the definition of response spectra.
The topic is surely interesting and fits with the topics of the journal.
The paper is generally clear and well organized, nevertheless some remarks should be addressed.
- In the title and abstract, the duration of earthquake ground motion is remarked as one of the most important contributions to the seismic behavior of structures, and its inclusion in the proposed analytical method is presented as the most original contribution of the paper. Nevertheless, duration is already included in common elastic spectra. In fact, as pointed out also by the authors, elastic spectra are basically the alpha(0,T) projection of the time-domain spectra. It is opinion of the reviewer that the paper should be better rewritten stressing out that the aim of the paper is to include the time-domain decomposition instead of the ground motion duration.
- Section 1: It is opinion of the reviewer that the readability of this section could be improved by expressing the first and second order derivatives of the displacements with the dot notations instead using dx/dt, resulting in more compact equations and shorter text.
- Section 2.1, lines 79-80: Given the definition of the seismic coefficient alpha(x,y), it is suggested to consider time t on the X-axis and natural period T on the Y-axis (X with x, and Y with y).
- The benefits of time-domain decomposition are well presented in section 5. However, the introduction of the time domain, and the consequent repetition of several conventional mode decomposition over time steps, impair the strongest point of conventional spectral analysis which is the easiness and quickness of the method. The authors are kindly invited to give some comments (and possibly examples) of the computational cost comparison between the proposed time-domain decomposition method and a standard step-by-step dynamic analysis. Furthermore, comments on the opportunity to adopt this simplified linear methodology instead of a full non-linear step-by-step analysis (required to include the damaging of the structure over time during the earthquake) are necessary.
Author Response
please see the attached file.
Author Response File: Author Response.doc
Round 2
Reviewer 3 Report
Please, check the attached file
Comments for author File: Comments.pdf
Author Response
Please see the attached file.
Author Response File: Author Response.doc
