Non-Proportionality Indices and Error Constraint in Modal Analysis of Viscously Damped Linear Structures

Round 1

Reviewer 1 Report

The paper entitled “Non-proportionality Indices and Error Constraint in Modal Analysis of Viscously Damped Linear Structures” presents a study to quantify the errors deriving from ignoring off‐diagonal coefficients of the modal damping matrix and to correlate the error with the level of non‐proportionality of the damping matrix measured by different literature-based indices. Finally, recommendations are made regarding the value of existing indices.

The paper is well written and well organized. The use of English language is very good, and the sections follow clearly. In general, the body of the text could be shortened. In general, as a minor improvement, it is recommended to reduce some of the results (Figures and Tables) that are somewhat repetitive in favor of cumulative and more representative results.

Also, others minor improvements are suggested in the attached manuscript file.

Comments for author File: Comments.pdf

Author Response

Thanks for the review. Please find attached the detailed reply to the comments. 

Author Response File: Author Response.pdf

Reviewer 2 Report

The paper presents relations between the indices to quantify non-proportionality of damping and the error due to modal analysis based on proportional damping. The manuscript provides useful detailed information on the topic. The reviewer can't find any logical problem in the description. Therefore, the reviewer recommends the publication of the paper in its present form.

Author Response

Thanks for the review. Please find attached the detailed reply.

Author Response File: Author Response.pdf

Reviewer 3 Report

The paper is easy to understand, but I could not observe new findings and originality. Too much calculated results are shown in the paper. The authors should summarize them simply and point out the highlights.

I am glad to help your revising the paper. My comments are shown as below, even with my weak understanding.

 

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Pages 1-2, Introduction

What is the study for? What type of buildings has a difficulty in modal analysis with considering non-proportional damping, instead of using time domain method (time history step-by-step analysis)?

Time domain methods are already utilized widely because their calculation speeds and costs have been improved in the last 30 years.

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Page 3, lines 105-107

Are the words “neglecting off-diagonal terms” correct, instead of “neglecting diagonal terms”?

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Page 5, line 216

"pp. 367 ff."

 

What does it mean?

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Page 10, line 368

"Acceptability Range (EAR) [-0.15; +0.25]"

 

Could you add comments about relationship between the EAR and structural performance of buildings, from a view of structural design? Is the EAR reasonable for evaluating dynamic responses during an earthquake? Why do you think so?

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Page 35, lines 715-716

"These conclusions are limited to linear systems with added linear viscous dampers within the range of structural parameters defined in the parametric study."

 

I agree the conclusions are depend on the structure and conditions shown in the paper, however they are weak/poor for an academic paper. Could you add comments about the applicability to other structures and conditions?

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Page 35, line 718

"field motions recorded on firm soil conditions"

 

Why did you think the trends would change on the soft ground?

Author Response

Thanks for the review. Please find attached the detailed reply.

Author Response File: Author Response.pdf

Round 2

Reviewer 3 Report

I have checked the revised version. It has been much improved.