Vortex-Induced Nonlinear Bending Vibrations of Suspension Bridges with Static Wind Loads
Round 1
Reviewer 1 Report
Journal: Buildings (MDPI)
Title: Vortex-induced Nonlinear Bending Vibrations of Suspension 2 Bridges with Static Wind Load
The author presents the investigation on the nonlinear vibrations of long-span suspension bridges under the combined effects of static and vortex-induced loads. The authors have tried to justify the novelty of the research by primarily focusing on linear problems related to wind-induced vibrations in suspension bridges. By highlighting the lack of profound consideration of nonlinear problems, the introduction establishes the novelty of the study.
However, still needs minor concerns to make it publishable as scientific research. The concerns are presented as follows.
Key comments
1. The initiation of introduction is satisfactory, however, it is advised to include a brief description of how the study intends to fill the research gap, such as by examining the impact of static wind loads on vortex-excited vibrations and analyzing the effect of structural factors on vibration amplitude. The significance and relevance of the findings will therefore be clear to the readers.
2. As the author mentioned about the Tacoma Bridge collapse, it would be helpful to provide a brief overview of the incident, including the factual data with the lessons learned from that event. This will encourage the readers and highlight the relevance of studying concerning the wind-induced vibrations in such cases.
3. Though the authors have clearly depicted the significance of the research by mentioning the previous studies, it would be clearer to the readers if there were more clarity on why considering nonlinear problems is important and what insights can be gained by doing so. Highlight the limitations of existing literature and the need for a more comprehensive.
4. Literature review is very limit , the authors should include discussion of the free vibration analyses, vehicle induced vibration and real case studies in the introduction, see the extensive work below:
· https://doi.org/10.1016/j.jweia.2021.104762
5. The variables in the equation need to be clearly defined.
6. The discretizing approach by using Galerkin method to obtain the nonlinear ordinary differential equation to describe vortex-induced nonlinear bending vibrations of suspension bridges with static wind load is impressive. However, it needs a comparison database to compare other approaches and prior work. Check this article:
· Dai, H. L., Abdelkefi, A., & Wang, L. (2014). Theoretical modeling and nonlinear analysis of piezoelectric energy harvesting from vortex-induced vibrations. Journal of Intelligent Material Systems and Structures, 25(14), 1861-1874.
7. It is suggested to make more specific conclusion linking to the problem of the statement,
8. There are minor typos in the manuscript; checking the typos and grammatical odds thoroughly is suggested.
9. Reference needs to be revised based on the journal guideline.
10. Besides these minor issues, overall, the article seems relevant for scientific publication.
The author presents the investigation on the nonlinear vibrations of long-span suspension bridges under the combined effects of static and vortex-induced loads. The authors have tried to justify the novelty of the research by primarily focusing on linear problems related to wind-induced vibrations in suspension bridges. By highlighting the lack of profound consideration of nonlinear problems, the introduction establishes the novelty of the study.
However, still needs minor concerns to make it publishable as scientific research.
Author Response
Comments: The author presents the investigation on the nonlinear vibrations of long-span suspension bridges under the combined effects of static and vortex-induced loads. The authors have tried to justify the novelty of the research by primarily focusing on linear problems related to wind-induced vibrations in suspension bridges. By highlighting the lack of profound consideration of nonlinear problems, the introduction establishes the novelty of the study.
However, still needs minor concerns to make it publishable as scientific research. The concerns are presented as follows.
Reply: Thank you for your comments. Your comments help us improve the quality of the manuscript. In the present revised manuscript, we added four references to extend some content related to this article (Refs. 9, 20, 21 and 22). Furthermore, we revised the manuscript according to the comments, and carefully proofread the manuscript to minimize typographical, grammatical, and bibliographical errors. Significant changes have been marked in blue font.
Key comments
Comments 1. The initiation of introduction is satisfactory, however, it is advised to include a brief description of how the study intends to fill the research gap, such as by examining the impact of static wind loads on vortex-excited vibrations and analyzing the effect of structural factors on vibration amplitude. The significance and relevance of the findings will therefore be clear to the readers.
Reply: We have added some content about the vortex-induced vibration in lines 38-44 and lines 53-57 in the revision. At the same time, two reference papers recommended by reviewers have been added to help readers understand the recent progress of vortex-induced vibration.
Comments 2. As the author mentioned about the Tacoma Bridge collapse, it would be helpful to provide a brief overview of the incident, including the factual data with the lessons learned from that event. This will encourage the readers and highlight the relevance of studying concerning the wind-induced vibrations in such cases.
Reply: Thank you for your advices. I added some content to describe the wind destruction of the Tacoma Bridge in lines 38-44. We also added a reference about the Tacoma Bridge (Ref.9).
Comments 3. Though the authors have clearly depicted the significance of the research by mentioning the previous studies, it would be clearer to the readers if there were more clarity on why considering nonlinear problems is important and what insights can be gained by doing so. Highlight the limitations of existing literature and the need for a more comprehensive.
Reply: Suspension bridge’s vibrations are sensitive to damping, excitation frequency, and structural stiffness, and this sensitive derives from the nonlinearity of the structure. The nonlinearity may cause some sudden changes of the suspension bridge’s vibrations even if the parameters are only slightly perturbed. Therefore, to accurately understand the wind-induced vibrations of suspension bridges, it is necessary to consider the nonlinearity caused by the finite deformations of the structure. We add the related content at the end of the fourth section (Lines 293-299).
Comments 4. Literature review is very limit , the authors should include discussion of the free vibration analyses, vehicle induced vibration and real case studies in the introduction, see the extensive work below:
https://doi.org/10.1016/j.jweia.2021.104762
Reply: Thank you for the references. We found that the paper is a good reference for readers to understand wind-induced vibration. We have added 4 references in the revision (Refs. 9, 20, 21 and 22). In addition, we have added a review of the vortex-induced vibrations that recently occurred at the Humen Bridge in China in the revised draft (lines 69-80).
Comments 5. The variables in the equation need to be clearly defined.
Reply: We re-derived the equations in the manuscript and checked the definitions of all variables. All variables in the revised version have been defined.
Comments 6. The discretizing approach by using Galerkin method to obtain the nonlinear ordinary differential equation to describe vortex-induced nonlinear bending vibrations of suspension bridges with static wind load is impressive. However, it needs a comparison data base to compare other approaches and prior work. Check this article:
Dai, H. L., Abdelkefi, A., & Wang, L. (2014). Theoretical modeling and nonlinear analysis of piezoelectric energy harvesting from vortex-induced vibrations. Journal of Intelligent Material Systems and Structures, 25(14), 1861-1874.
Reply: We checked the coefficients of the ordinary differential equation (Eqs. (12)) obtained by the Galerkin method, and compared them with their counterparts in the existing literature. We did not found any errors in the coefficients. The reference recommended by you is an interesting paper that demonstrates the potential applications of vortex-induced vibrations in energy harvesting. This may provide a potential application scenario for vortex-induced vibration of suspension bridges. Therefore, we have added this paper to the revised draft (Ref. 21) and commented on it in lines 69-80.
Comments 7. It is suggested to make more specific conclusion linking to the problem of the statement.
Reply: We have already considered the wind speed, structural damping and excitation frequency in the present paper. We found that the vibrations of the suspension bridge are sensitive to structural damping and excitation frequency. We did not further consider the combination of different parameters to study their effects on the structures. The conclusions in the present paper can be obtained through Eq. (28). However, we did not give more conclusions because particular conclusions require further research. We will study details of combination parameters in another paper for vortex-induced vibrations of suspension bridges.
Comments 8. There are minor typos in the manuscript; checking the typos and grammatical odds thoroughly is suggested.
Reply: We thoroughly checked the writing of the paper and revised the problems found in grammar, spelling, etc.
Comments 9. Reference needs to be revised based on the journal guideline.
Reply: We checked reference and revised the questions.
Comments 9. Besides these minor issues, overall, the article seems relevant for scientific publication.
Reply: Thank you for your comments. These comments improved the quality of the manuscript.
Reviewer 2 Report
This study investigates the vertical vortex-induced vibrations of a suspension bridge considering the effect of static wind loads. The authors use a standard static wind load model and an old vortex-induced force model. These two models are combined to calculate the vibration response of a suspension bridge. The simulation is standard dynamic analysis while the novelty of this paper is not clear. The paper studies VIV while no lock-in range is reported throughout the paper. It is not clear whether the reported vibration responses are VIV or not. Based on these concerns, the paper cannot be recommended for publication in the present form.
English language should be improved.
Author Response
Comments: This study investigates the vertical vortex-induced vibrations of a suspension bridge considering the effect of static wind loads. The authors use a standard static wind load model and an old vortex-induced force model. These two models are combined to calculate the vibration response of a suspension bridge. The simulation is standard dynamic analysis while the novelty of this paper is not clear. The paper studies VIV while no lock-in range is reported throughout the paper. It is not clear whether the reported vibration responses are VIV or not. Based on these concerns, the paper cannot be recommended for publication in the present form.
Reply: Thank you for your comments. You point out some weaknesses in the manuscript. We have made changes in the revised draft in response to your comments.
Selection of vortex-induced load: Typically, the amplitude and frequency of vortex-induced loads are related to the wind speed, in which the load’s frequency is related to the Strouhal number. For different bridges, the amplitude and frequency of the loads have different relationships with respect to the wind speed. If we use specific parameters for a given bridge, the conclusions in the present study may lose their universality. Therefore, we took the amplitude and frequency of vortex-induced loads as variable parameters. This makes the conclusions in this paper can extend to a wider scope. Moreover, the distinctive feature of vortex induced vibrations is that the periodic shedding of the vortex produces periodic forced vibration. Harmonic loads with variable amplitude and frequency can describe this main characteristics. This also allows us to reveal the sensitivity of nonlinear vibration for suspension bridges to structural damping and stiffness. In fact, the aerodynamic parameters of suspension bridges may also change in use. For example, in 2019, the Humen Bridge in China appears abnormal vortex-induced vibrations because its overhaul induced the change of aerodynamic shape. That the vortex frequency and amplitude took as variable parameters, can qualitatively explain such phenomena in the Humen Bridge. We have provided additional clarification on this issue in lines 69-80 and 124-129.
In the present revised manuscript, we also added four references to extend some content related to this article (Refs. 9, 20, 21 and 22). Furthermore, we revised the manuscript according to the comments, and carefully proofread the manuscript to minimize typographical, grammatical, and bibliographical errors. Relevant changes are marked in red.
Reviewer 3 Report
In this article, the nonlinear partial differential-integral equation, which models the planar bending motion of suspension bridges, was discretized as a nonlinear ordinary differential equation by the Galerkin method. An ordinary differential equation was used to demonstrate the symmetric bending vibration of first-order suspension bridges under static wind loading and induced vortex loading. An approximate analytical solution of the ordinary differential equation was obtained by the method of multiple scales, and the results presented at the end of the paper were determined by the analytical solution. I agree with the conclusions. The post is clearly made and has good informative value. In my opinion, it can be published. I have a comment or a question: 1. define your scientific contribution. 2. Check the font size in mathematical relationships.
Author Response
Comments ： In this article, the nonlinear partial differential-integral equation, which models the planar bending motion of suspension bridges, was discretized as a nonlinear ordinary differential equation by the Galerkin method. An ordinary differential equation was used to demonstrate the symmetric bending vibration of first-order suspension bridges under static wind loading and induced vortex loading. An approximate analytical solution of the ordinary differential equation was obtained by the method of multiple scales, and the results presented at the end of the paper were determined by the analytical solution. I agree with the conclusions. The post is clearly made and has good informative value. In my opinion, it can be published. I have a comment or a question: 1. define your scientific contribution. 2. Check the font size in mathematical relationships.
Reply: Thank you for your comments. Your comments help us improve the quality of the manuscript. In the present revised manuscript, we added four papers to discuss content related to this article (Refs. 9, 20, 21 and 22). Furthermore, we revised the manuscript according to the comments, and carefully proofread the manuscript to minimize typographical, grammatical, and bibliographical errors. At the end of the fourth section, the conclusions of this paper are further discussed in order to clarify the significance of the present research for the wind-induced nonlinear vibration of suspension bridges.
We have added some content about the vortex-induced vibration in lines 38-44 and lines 69-80 in the revision. At the same time, a reference papers recommended by reviewers have been added to help readers understand the recent progress of vortex-induced vibration (Refs. 9). In addition, we have added a review of the vortex-induced vibrations that recently occurred at the Humen Bridge in China in the revised draft (lines 69-80). (Refs. 22). Significant changes have been marked in red font.
