Dynamic Analysis of Beams with Interval Parameters
Round 1
Reviewer 1 Report
Comments and Suggestions for AuthorsSummary:
In this paper, the dynamic analysis of beams with interval parameters is studied. A new dynamic analysis method is proposed to evaluate the transient vibration response of beams with uncertain structural parameters. The finite difference method and finite element method are used to solve the interval dynamic beam equation and optimize the solution. It provides a new perspective and method for the treatment of uncertainty in structural engineering. The thesis has important contributions in both theoretical and numerical analysis. The writing quality is high, and the focus is prominent. However, to further improve the academic quality and practicability of the paper, the following aspects need further attention and improvement:
1.Please further clarify the connection between this study and the existing literature, and clearly point out the innovation of this study and the expansion or improvement of the existing theory.
2.The finite difference method and finite element method are mentioned in the paper, and it is suggested that the author provide more detailed algorithm description and pseudo-code, so that readers can better understand and reproduce the method.
3. References [20] should be placed"."Before.
4.Figure 2 is relatively vague, and the replacement is clearer.
5. The color matching of the diagram is re-allocated. For example, Fig.4 and Fig.5 can select colors with higher discrimination.
6.Please unify the format of references according to the format requirements of journals, including year, issue number, volume number, page number and DOI number.
7. In the introduction, the some research content needs to be added. Useful information can be found in the following paper: https://ascelibrary.org/doi/10.1061/JSENDH.STENG-11767
The forced vibration part of the formula does not correspond to (4) and (5).
8. In the conclusion part, the significance of the research results to practical engineering problems and how to apply these results to structural design and risk assessment in the real world should be discussed in more depth.
9.The author should provide more in-depth analysis and explanation for the specific observation results or data in the paper, such as the sharp increase of peak displacement in the vertical direction.
Comments on the Quality of English LanguageCan be improved.
Author Response
Comment 1: Please further clarify the connection between this study and the existing literature, and clearly point out the innovation of this study and the expansion or improvement of the existing theory.
Response1: Additional information, highlighted in blue color, is added to the manuscript under the introduction section to answer the above question raised by the reviewer.
Comment2: The finite difference method and finite element method are mentioned in the paper, and it is suggested that the author provide more detailed algorithm description and pseudo-code, so that readers can better understand and reproduce the method.
Response 2: The manuscript is now modified to include steps involved in implementing finite difference method as well as finite element method. The modified portion is highlighted in blue color.
Comment 3:References [20] should be placed"."Before.
Response 3: All references are revised and formatted in accordance with the guidelines given in the template of the MDPI Modelling journal.
Comment 4: Figure 2 is relatively vague, and the replacement is clearer.
Response 4: Figure 2 is replaced with an enhanced version.
Comment 5: The color matching of the diagram is re-allocated. For example, Fig.4 and Fig.5 can select colors with higher discrimination.
Response 5: Figures 3,4 and 5 are replaced with enhanced versions.
Comment 6: Please unify the format of references according to the format requirements of journals, including year, issue number, volume number, page number and DOI number.
Response 6: All references are formatted in accordance with the template of the MDPI Modelling journal.
Comment 7: In the introduction, the some research content needs to be added. Useful information can be found in the following paper: https://ascelibrary.org/doi/10.1061/JSENDH.STENG-11767.
The forced vibration part of the formula does not correspond to (4) and (5).
Response 7: As mentioned in example 2, the beam is subjected to a sudden distributed load of 5 kilo Newtons per meter run over the entire span for 0.4 seconds and 5% damping is present. Thus, the results obtained correspond to forced vibration.
Comment 8: In the conclusion part, the significance of the research results to practical engineering problems and how to apply these results to structural design and risk assessment in the real world should be discussed in more depth.
Response 8: The Conclusions section is now revised to reflect the recommendations of the reviewer.
Comment 9: The author should provide more in-depth analysis and explanation for the specific observation results or data in the paper, such as the sharp increase of peak displacement in the vertical direction.
Response 9: A detailed explanation is now provided and is highlighted in blue color in the manuscript.
Reviewer 2 Report
Comments and Suggestions for AuthorsEven if this approach shows great potential it is not mature enough to be applied for real life structures, rendering it useful for research purposes only. Nevertheless, it has the potential to evolve in a great tool for structural experts and used to account for in-field uncertainties.
Author Response
Comment 1: Even if this approach shows great potential it is not mature enough to be applied for real life structures, rendering it useful for research purposes only. Nevertheless, it has the potential to evolve in a great tool for structural experts and used to account for in-field uncertainties.
Response 1: As a part of ongoing research, attempts are being made to correlate the field observations of structural response with the response obtained using interval finite element approach. In this connection, the kind attention of the reviewer is drawn to the paper:
Francesco Fedele, Rafi L. Muhanna, Naijia Xiao, Interval-based Inverse Problems with Uncertainties, IFAC Proceedings Volumes, Volume 45, Issue 16, 2012, Pages 1079-1084.
https://doi.org/10.3182/20120711-3-BE-2027.00319
In this paper, the authors solve inverse problems in science and engineering by estimating model parameters of a physical system using observations of the model's response. Variational least square type approaches are adopted for solving the forward model, The resulting modeled data was then compared with the actual measured data. The data mismatch is minimized, and the process is iterated until the best match is achieved. The authors present an interval-based iterative solution to predict such errors, using adjoint-based optimization and the containment-stopping criterion. It is hoped that such methods pave the way for the eventual integration of interval uncertainty into field problems.
Reviewer 3 Report
Comments and Suggestions for AuthorsThe work is of high value, however the reviewer has the following recommendations to enhance the work further:
- There are no citations within the first three paragraphs of the introduction which include information that must be acquired from some source. Please cite the source(s) of information.
- The research gap is not mentioned, it is highly recommended to mention the research gap within the introduction.
- Using the active tense isn't appropriate in academic writing, the authors used the term "we" which isn't recommended at all. It is highly recommended to use the passive tense.
- In subsection 5.1.2, the direct method was very briefly mentioned. A description of this method is needed.
- The two examples mentioned in section 7 are very similar in terms of scale and boundary conditions which may result in them causing a similar behavior. To validate the results, it is recommended to have a third example of different scale and boundary conditions (may be a short cantilever or a deep beam).
- Only two of the 24 references are recent. All the other references are old. More updated references are recommended especially that the reviewer is aware of recent work in this area.
Author Response
Comment 1: There are no citations within the first three paragraphs of the introduction which include information that must be acquired from some source. Please cite the source(s) of information.
Response 1: The introduction is now revised. The first three paragraphs now contain citations.
Comment 2: The research gap is not mentioned, it is highly recommended to mention the research gap within the introduction.
Response 2: New paragraphs, highlighted in blue color, are added to the introduction to mention the research gap clearly.
Comment 3: Using the active tense isn't appropriate in academic writing, the authors used the term "we" which isn't recommended at all. It is highly recommended to use the passive tense.
Response 3: Now the sentence is rewritten in passive tense and is highlighted in blue color.
Comment 4: In subsection 5.1.2, the direct method was very briefly mentioned. A description of this method is needed.
Response 4: A brief description of the direct method is now outlined in the manuscript.
Comment 5: The two examples mentioned in section 7 are very similar in terms of scale and boundary conditions which may result in them causing a similar behavior. To validate the results, it is recommended to have a third example of different scale and boundary conditions (maybe a short cantilever or a deep beam).
Response 5: In Figure 4, uncertainty of Young’s modulus as well of mass density is ±0.5% whereas load is deterministic. This induces uncertainty in natural frequencies of the beam. As mentioned in the manuscript, the temporal shift observed in the response peaks is attributable to the escalating uncertainty in dis-placement over time. This phenomenon arises from the propagation of uncertainties in mass and stiffness, culminating in a broader range of uncertainty in the beam's natural frequencies. However, in Figure 5, load alone has uncertainty while Young’s modulus and mass density are deterministic. Because of this, the peaks occurring at various levels of uncertainty do not exhibit any shifting.
As per the suggestion of the reviewer, example 3 considers the vibration of a cantilever beam owing to the application of a sudden load at its tip. Here also, uncertainty is present in Young’s modulus and mass density while load is deterministic. Time history response is depicted in Figure 7. Shifting of peaks, similar to Figure 4, is observed in Figure 7.
Comment 6: Only two of the 24 references are recent. All the other references are old. More updated references are recommended especially that the reviewer is aware of recent work in this area.
Response 6: References are now updated. A total of 8 references correspond to the period 2020-2024.
Round 2
Reviewer 1 Report
Comments and Suggestions for AuthorsThe authors have amended their paper in accordance with the reviewers comments and I recommend the paper for acceptance in Modelling.
Reviewer 3 Report
Comments and Suggestions for AuthorsThe authors applied all of the items recommended previously by the reviewer. The manuscript is now acceptable for the reviewer.
