Effects of Vehicle Speed on Vehicle-Induced Dynamic Behaviors of a Concrete Bridge with Smooth and Rough Road Surfaces

Round 1

Reviewer 1 Report

 

1. Overall the paper is easy to follow, with its main aim to answer an unsolved problem in the coupling of speed, roughness and road damage. The simulation seems right, though more details should be added for reader understanding.  

2 fig. 7, 10: the variable unit should be added.

3 Fig. 5 is not mentioned all through the paper, but is important to understand the correctness of simulation. In preparing the revision, the authors should note that the vehice-road coupling dynamics should be explained, e.g. how such model can be used for reasonable calculation.

4 The reason why 4th span's fundamental frequency (0.82) is different from that in simulation should be discussed.

5 The authors categorize the roughness into three levels, namely perfect, slightly rough, severely rough, which are further simulated. The detailed road elevations are given, too. However, in the field experiment, only Ref 8 is mentioned, 'severely rough'. I think 'severely rough' may be understood differently by different readers, including the authors in Ref. 8. Therefore, a certain quantative data/information on the real road roughness should be given.

6 In real vehicle experiments, how the vehicle  speed is controlled? Since the excitation and response are sensitive to all main forces on the bridge, if the vehicle speed is not well controlled, it may further complicate the results. For simulations, this can be well handled. For experiments, I suggest the vehicle speed variations (may be in statistics) or even the vehicle along the entire process should be given. 

language can be improved, e.g. to avoid long and difficult-to-understand sentences.

...taken account --> take into account...

marked/ -ly --> markable/-ly

Author Response

1 Overall the paper is easy to follow, with its main aim to answer an unsolved problem in the coupling of speed, roughness and road damage. The simulation seems right, though more details should be added for reader understanding.

Response: Thank you for the comment. More details of the numerical simulation have been added in the revised manuscript for readers to better understand related knowledge (see the part highlight in blue).

 

2 fig. 7, 10: the variable unit should be added.

Response: Thank you for pointing out our mistake. We have added the variable unit for Figs. 7, 10 and 14.

 

3 Fig. 5 is not mentioned all through the paper, but is important to understand the correctness of simulation. In preparing the revision, the authors should note that the vehice-road coupling dynamics should be explained, e.g. how such model can be used for reasonable calculation.

Response: Thank you for pointing out our mistake. Fig. 5 has been mentioned in the revised manuscript (see the part highlighted in italic in section 3). Besides, the rationality of the vehicle-road coupling model utilized is explained in the revised manuscript (see the part highlighted in red).

 

4 The reason why 4th span's fundamental frequency (0.82) is different from that in simulation should be discussed.

Response: In fact, the natural frequencies of the actual system measured should be independent of excitations and measurements, and the result measured at the mid-span of 4th main span in 20 km/h vehicle speed case should be close to results measured for other cases. However, on location physical tests suffer from inherent uncertainties and environmental interferences. Therefore, the field modal test results obtained for different cases might occasionally be different from each other. These technical discussions are added in the revised manuscript (see the part highlight in green).

 

5 The authors categorize the roughness into three levels, namely perfect, slightly rough, severely rough, which are further simulated. The detailed road elevations are given, too. However, in the field experiment, only Ref 8 is mentioned, 'severely rough'. I think 'severely rough' may be understood differently by different readers, including the authors in Ref. 8. Therefore, a certain quantative data/information on the real road roughness should be given.

Response: According to Ref. [8], the variation range of the road surface of the actual Renyihe Bridge roughly is [-0.025 m, 0.025 m], which is reported in the revised manuscript. Sorry that other quantitative information concerning the real road roughness is not provided by Ref. [8]. In fact, within the variation range, the realistic elevation of the bridge deck is random in nature, which is effectively simulated using the white noise sequence by the numerical analysis undertaken in this study. Therefore, the present numerical and physical results can be reasonably compared.

 

6 In real vehicle experiments, how the vehicle  speed is controlled? Since the excitation and response are sensitive to all main forces on the bridge, if the vehicle speed is not well controlled, it may further complicate the results. For simulations, this can be well handled. For experiments, I suggest the vehicle speed variations (may be in statistics) or even the vehicle along the entire process should be given.

Response: According to Ref. [8], the vehicle drivers tried to keep the vehicles moving at the constant speeds. Although the statistics concerning the vehicle speed variations through the entire process are not measured, it is reported that vehicle speed is well controlled, and the effects of the vehicle speed variation on the excitation and the response are reduced to the minimum. These are explained in the revised manuscript (see the part highlighted in yellow).

Reviewer 2 Report

Manuscript Number: applsci-2541644-v1

Full Title: Effects of Vehicle Speed on Vehicle-induced Dynamic Behaviors of a Concrete Bridge with Smooth and Rough Road Surface

 

I – General Comments

The present manuscript numerically investigates the relation between increase in road surface roughness and the resonant response of a bridge.  In general, the latter has been significantly amplified for the low vehicle speed cases, which, probably explains the phenomenon related in the literature. The topic is hot, however, there are important comments addressed to authors, before to accept their manuscript as an Applied Science’s paper.

 

II - Specific Comments

(i) In “Abstract”, the main contribution of the present work into the specialized literature context must be better clarified aiming to justify the intended publication.

(ii) It is suggested to reduce the number of keywords.

(ii) The authors must improve/reorganize their “Introduction” by considering:  a) some more detailed information on the specific topic of the research into the Applied Science’s scope by introducing previous works (there is no citation of previous works published by other authors in Applied Sciences); b) a description of the exact question or hypothesis that the paper will address; and c) a summary of the adopted approach to solve the investigated problem. Therefore, it is necessary to present more technical discussions concerning these key points including examples of past models through a critical review. As consequence, the contributions of the manuscript can better explained and contextualized in this part of the paper.

(iii) The list of References is extremely poor only with 8 (eight) citations of previous works. Why?

(iv) The section 2 is weak, because the authors omitted the assumed hypothesis, governing equations and boundary conditions for the chosen problem.

(v) In section 3, it is necessary more details concerning the numerical approach. If the authors utilize a numerical method, it is important to include detailed information about the implementation of the present method algorithm.

(vi) How does the roughness effect behave over the years? A technical discussion is welcome.

(vii) Figures 10 and 14 need to be better presented and discussed.

(viii) In Figure 11, the legend must be improved and increased.

 

(viii) In section 6, it is necessary to include specific comments about the main contributions of present work by comparing with the present state of the art.

(ix) In closing, in section 6, a clear perspective for future investigation is welcome.

 

III - Recommendation for the Applied Sciences´ Editor

In my opinion, the present manuscript needs attend all topics above presented. Upon consideration of all points above, I think the paper could be considered for publication in Applied Sciences.

Moderate editing of English language required.

Author Response

Manuscript Number: applsci-2541644-v1

Full Title: Effects of Vehicle Speed on Vehicle-induced Dynamic Behaviors of a Concrete Bridge with Smooth and Rough Road Surface

 

I – General Comments

 

The present manuscript numerically investigates the relation between increase in road surface roughness and the resonant response of a bridge.  In general, the latter has been significantly amplified for the low vehicle speed cases, which, probably explains the phenomenon related in the literature. The topic is hot, however, there are important comments addressed to authors, before to accept their manuscript as an Applied Science’s paper.

Response: Thank you. All comments from the reviewer have been addressed. We hope the quality of the revised manuscript can reaches the standard of a publication in the present journal.

 

II - Specific Comments

 

(i) In “Abstract”, the main contribution of the present work into the specialized literature context must be better clarified aiming to justify the intended publication.

Response: After extensive review, it is found that existing literatures separately considered the effects of the road surface roughness [2-5] and the effects of the vehicle speed [9, 13-15] on the vehicle-bridge coupling dynamics. However, no study has well revealed the interactions between the vehicle speed and the road surface roughness in the context of vehicle-bridge coupling dynamics which is proven to be non-negligible. This scientific gap is filled in this article which justifies the main contribution of the present work. These explanations are reported in the revised manuscript (see the part highlighted in bold).

 

(ii) It is suggested to reduce the number of keywords.

Response: Thank you for the comment. The number of keywords has been reduced from 7 to 4.

 

(ii) The authors must improve/reorganize their “Introduction” by considering:  a) some more detailed information on the specific topic of the research into the Applied Science’s scope by introducing previous works (there is no citation of previous works published by other authors in Applied Sciences); b) a description of the exact question or hypothesis that the paper will address; and c) a summary of the adopted approach to solve the investigated problem. Therefore, it is necessary to present more technical discussions concerning these key points including examples of past models through a critical review. As consequence, the contributions of the manuscript can better explained and contextualized in this part of the paper.

Response: Thank you for your good suggestions. First, some related articles published in the present journal in 2023 have been cited and discussed [18-20]. Second, after extensive review, it is found that existing literatures separately considered the effects of the road surface roughness [2-5] and the effects of the vehicle speed [9, 13-15] on the vehicle-bridge coupling dynamics. However, no study has well revealed the interactions between the vehicle speed and the road surface roughness in the context of vehicle-bridge coupling dynamics which is proven to be non-negligible. The present manuscript mainly deals with this scientific issue which has been explained in the revised manuscript. Third, the adopted approaches to solve the investigated problem are the numerical simulation and the physical test, which have been emphasized in the introduction part of the revised manuscript. Through these revisions, we suppose the contributions of the manuscript are better explained and contextualized in the introduction part.

 

(iii) The list of References is extremely poor only with 8 (eight) citations of previous works. Why?

Response: Yes, the number of references is extremely small before revision. We have increased the references to 20 after this round of revision.

 

(iv) The section 2 is weak, because the authors omitted the assumed hypothesis, governing equations and boundary conditions for the chosen problem.

Response: Thank you for the suggestion. As suggested, we have strengthened section 2 by reporting more details of the numerical model established, including the assumed hypothesis, governing equations and boundary conditions (see the part highlight in blue).

 

(v) In section 3, it is necessary more details concerning the numerical approach. If the authors utilize a numerical method, it is important to include detailed information about the implementation of the present method algorithm.

Response: Thank you for the comment. As suggested, the detailed information concerning the implementation of the present numerical algorithm has been included in the revised manuscript (see the part highlighted with underline).

 

(vi) How does the roughness effect behave over the years? A technical discussion is welcome.

Response: Based on the basic rule of physics, the road surface roughness will increase over the years, which has been explained in the revised manuscript (see the part highlighted in purple).

 

(vii) Figures 10 and 14 need to be better presented and discussed.

Response: As suggested, Figs. 10 and 14 have been revised with a higher definition, and further discussed.

 

(viii) In Figure 11, the legend must be improved and increased.

Response: As suggested, the legend of Fig. 11 has been increased.

 

(viii) In section 6, it is necessary to include specific comments about the main contributions of present work by comparing with the present state of the art.

Response: Thank you. Specific comment about the main contribution of present work by comparing with the present state of the art is added in the revised manuscript (point three in the conclusion part).

 

(ix) In closing, in section 6, a clear perspective for future investigation is welcome.

Response: Thank you for the comment. The perspective for future investigations is added (see the part highlighted in orange).

Reviewer 3 Report

The historical literature on bridges has shown that bridges designed for lower-speed vehicles are more prone to damage than those designed for higher-speed vehicles. However, this theory doesn't hold true for bridges with a smooth road surface. For the Renyihe Bridge, a concrete highway bridge with a rigid-frame and continuous spans of 80m+4x145m+80m, numerical simulations have revealed that rougher road surfaces can significantly amplify the bridge's resonant responses for low-speed vehicles. This finding provides a possible explanation for the damage observed in previous literature. The field experiments on the Renyihe Bridge have confirmed this mechanism, showing that as road roughness increases, the frequency of vehicle excitation can get closer to the bridge's natural frequencies, leading to significantly amplified resonant responses for low-speed vehicles. The authors propose that these crucial findings be appropriately considered in the design and maintenance of bridges to ensure the safety of all vehicles that use them.

 

This is a fairly well-written paper, the results have been presented vividly, and it can be considered for publication after the following major issues are appropriately responded to by the authors:

 

1.         What are the specific effects of road surface roughness on the vehicle-bridge dynamic interaction? Are there other factors besides road surface roughness that could contribute to the different degrees of dynamic amplification on concrete bridges? What are the practical implications of the findings on concrete bridge maintenance and monitoring?

 

2.         What are the practical implications of the findings for concrete bridge maintenance and monitoring? Could the authors provide some theoretical formulations, accounting for the roughness of the bridge surface and vehicle speed, to show the influence of the moving vehicle on the lateral vibration of the bridge?

 

3.         Include more data and evidence: The article relies heavily on Ref. [1] and lacks additional evidence to support its argument. More data and evidence could be included to strengthen the article's case. For example, the article could include more field tests and simulations beyond those conducted on Renyihe Bridge.

 

4.         Clarify the argument and streamline the text: The article presents a partially different argument from Ref. [1] regarding the degree of damage to bridge beams on different lanes with different vehicle speeds. However, the text is convoluted and difficult to follow. The argument could be clarified by streamlining the text and presenting a clearer thesis statement at the beginning of the article.

 

5.         Address other factors that could impact bridge health: The article suggests that road surface roughness could be a factor in the different degrees of dynamic actions on bridge beams. However, other factors such as weather conditions, traffic volume, and construction quality could also impact bridge health. The article could benefit from addressing other potential factors that could impact bridge health and how they might interact with vehicle speed and road surface roughness. Please explain them based on the existing models as well as other experimental studies, opening a new way to develop an inclusive math model for examining bridge health.

 

6.         The frequency analysis of the Renyihe bridge was performed by using MIDAS (version 6.71) software; however, no convergence study has been given to show the effectiveness of the established numerical model. In addition, it is not clear that the columns under the bridge have been fully in contact with the bridge decks through the vibration process since in some demonstrated vibrational modes, they have been shown in separate manner. Please clarify.

 

7.         Are the below columns of the bridge considered rigid or flexible? How the axial stiffness of these crucial elements could influence the overall dynamic response (maximum deflection and bending moment) of the beam-like bridge under moving vehicles? Please explain that with more detail in appropriate places within the paper.

 

8.         The paper suffers from the theoretical background and studies established in former years by experts on the vibrational analysis of multi-span beams subjected to moving loads and masses. In this regard, the authors are highly encouraged to display the following reference works in the paper:

(*) Zhu XQ, Law SS. Moving load identification on multi-span continuous bridges with elastic bearings. Mechanical Systems and Signal Processing. 2006 Oct 1;20(7):1759-82.

(*) Kiani K, Nikkhoo A, Mehri B. Assessing dynamic response of multispan viscoelastic thin beams under a moving mass via generalized moving least square method. Acta Mechanica Sinica. 2010 Oct;26:721-33.

(*) Kiani K, Nikkhoo A, Mehri B. Assessing dynamic response of multispan viscoelastic thin beams under a moving mass via generalized moving least square method. Acta Mechanica Sinica. 2010 Oct;26:721-33.

(*) Johansson C, Pacoste C, Karoumi R. Closed-form solution for the mode superposition analysis of the vibration in multi-span beam bridges caused by concentrated moving loads. Computers & Structures. 2013 Apr 1;119:85-94.

(*) Szyłko-Bigus O, Śniady P, Zakęś F. Application of Volterra integral equations in the dynamics of a multi-span Rayleigh beam subjected to a moving load. Mechanical Systems and Signal Processing. 2019 Apr 15;121:777-90.

Or even examining the dynamic response of bridge-like structures subjected to moving loads at a small scale:

(*) Kiani K, Roshan M. Nonlocal dynamic response of double-nanotube-systems for delivery of lagged-inertial-nanoparticles. International Journal of Mechanical Sciences. 2019 Mar 1;152:576-95.

(*) Yu G, Kiani K, Roshan M. Dynamic analysis of multiple-nanobeam-systems acted upon by multiple moving nanoparticles accounting for nonlocality, lag, and lateral inertia. Applied Mathematical Modelling. 2022 Aug 1;108:326-54.

(*) Abdelrahman AA, Esen I, Ozarpa C, Shaltout R, Eltaher MA, Assie AE. Dynamics of perforated higher order nanobeams subject to moving load using the nonlocal strain gradient theory. Smart Struct. Syst. 2021 Oct 1;28(4):515-33.

(*) Hosseini SA, Rahmani O, Bayat S. Thermal effect on forced vibration analysis of FG nanobeam subjected to moving load by Laplace transform method. Mechanics Based Design of Structures and Machines. 2023 Jul 3;51(7):3803-22.

 

9.         For the time-history plots given in Figures 17 and 18 for various speeds of the vehicles (i.e., 20, 30, 40, and 50 km/hr), these are reported based on the accelerometer attached to the midspan point of 3rd and 4th spans. It should be noticed that these are not only related to the bridge structure alone but also bridge + moving vehicles, indicating that the role of the velocity and mass weight of the vehicles should be appropriately removed from these plots to arrive at the near-to-exact natural frequencies of the bridge structure. How this critical issue has been considered by the authors and what is the role of moving vehicles in the whole dynamic response? Please clarify this within your manuscript, where the above-introduced reference works can also help you in handling this.

 

10.       The writing can be improved by addressing potential counterarguments or alternative explanations for the observed phenomenon. This will make the argument more robust and demonstrate a thorough consideration of different perspectives. In addition, there exist some grammatical errors that should be carefully revised in the next version of the paper.

 

Please see the review comment

Author Response

The historical literature on bridges has shown that bridges designed for lower-speed vehicles are more prone to damage than those designed for higher-speed vehicles. However, this theory doesn't hold true for bridges with a smooth road surface. For the Renyihe Bridge, a concrete highway bridge with a rigid-frame and continuous spans of 80m+4x145m+80m, numerical simulations have revealed that rougher road surfaces can significantly amplify the bridge's resonant responses for low-speed vehicles. This finding provides a possible explanation for the damage observed in previous literature. The field experiments on the Renyihe Bridge have confirmed this mechanism, showing that as road roughness increases, the frequency of vehicle excitation can get closer to the bridge's natural frequencies, leading to significantly amplified resonant responses for low-speed vehicles. The authors propose that these crucial findings be appropriately considered in the design and maintenance of bridges to ensure the safety of all vehicles that use them.

 

This is a fairly well-written paper, the results have been presented vividly, and it can be considered for publication after the following major issues are appropriately responded to by the authors:

 

1. What are the specific effects of road surface roughness on the vehicle-bridge dynamic interaction? Are there other factors besides road surface roughness that could contribute to the different degrees of dynamic amplification on concrete bridges? What are the practical implications of the findings on concrete bridge maintenance and monitoring?

Response: Thank you for the comment. According to the present study, with the increase in the road surface roughness, the stronger structural response is supposed to be induced by the passing vehicle, especially for low vehicle speed cases. This indicates stronger vehicle-bridge interaction should be induced for high road surface roughness cases. Besides the road surface roughness, the vehicle weight, the vehicle speed and the vehicle location could contribute to the different degrees of dynamic amplification on concrete bridges [17]. The practical implication of the present findings on concrete bridge maintenance and monitoring is that for bridges with the smooth road surface (newly built bridges), maintenance and monitoring should focus on those undertaking high speed vehicles; while for bridges with sufficiently rough road surfaces (bridges in operation for years), maintenance and monitoring should focus on those undertaking low speed vehicles.

 

2. What are the practical implications of the findings for concrete bridge maintenance and monitoring? Could the authors provide some theoretical formulations, accounting for the roughness of the bridge surface and vehicle speed, to show the influence of the moving vehicle on the lateral vibration of the bridge?

Response: The practical implication of the present findings on concrete bridge maintenance and monitoring is that for bridges with the smooth road surface (newly built bridges), maintenance and monitoring should focus on those undertaking high speed vehicles; while for bridges with sufficiently rough road surfaces (bridges in operation for years), maintenance and monitoring should focus on those undertaking low speed vehicles. Since only nine cases have been considered for the present numerical simulations assuming a 30 ton vehicle running through Renyihe Bridge at 3 vehicle speeds (20 km/h, 50 km/h, 90 km/h) with 3 road surface roughness levels (smooth, slightly rough, severely rough), mathematical models accounting for the roughness of the bridge surface and the vehicle speed effects can hardly be established at present due to the sample scarcity. However, after more cases have been studied on Renyihe Bridge or other bridges, we can formulate useful empirical formulae to quantitatively guide concrete bridge maintenance and monitoring. We beg the reviewer’s permission for us to undertake this work in the near future. Thank you for your good comment.

 

3. Include more data and evidence: The article relies heavily on Ref. [1] and lacks additional evidence to support its argument. More data and evidence could be included to strengthen the article's case. For example, the article could include more field tests and simulations beyond those conducted on Renyihe Bridge.

Response: After extensive literature review, it is found that not many studies deal with similar scientific issues (the coupled road surface roughness and vehicle speed effects on the vehicle-bridge dynamics) besides Ref. [1]. However, we have cited another related article to be published in a prestigious journal [17] to strengthen the article's case with more data and evidence.

 

4. Clarify the argument and streamline the text: The article presents a partially different argument from Ref. [1] regarding the degree of damage to bridge beams on different lanes with different vehicle speeds. However, the text is convoluted and difficult to follow. The argument could be clarified by streamlining the text and presenting a clearer thesis statement at the beginning of the article.

Response: Thank you for the comment. Yes, the sentence is convoluted and difficult to follow. We have changed the expression to ‘the present article holds a viewpoint different from Ref. [1]’ in the revised manuscript. We suppose our argument is clarified. Thank you again for the good suggestion.

 

5. Address other factors that could impact bridge health: The article suggests that road surface roughness could be a factor in the different degrees of dynamic actions on bridge beams. However, other factors such as weather conditions, traffic volume, and construction quality could also impact bridge health. The article could benefit from addressing other potential factors that could impact bridge health and how they might interact with vehicle speed and road surface roughness. Please explain them based on the existing models as well as other experimental studies, opening a new way to develop an inclusive math model for examining bridge health.

Response: Thank you for the comment. Yes, other factors such as weather conditions, traffic volume, and construction quality could also impact bridge health and interact with vehicle speed and road surface roughness. Related researches can help open a new way to develop an inclusive math model for examining bridge health. However, these topics are not the focus of the present study. Due to the limited article length, we beg your permission for us to undertake these researches in another article.

 

6. The frequency analysis of the Renyihe bridge was performed by using MIDAS (version 6.71) software; however, no convergence study has been given to show the effectiveness of the established numerical model. In addition, it is not clear that the columns under the bridge have been fully in contact with the bridge decks through the vibration process since in some demonstrated vibrational modes, they have been shown in separate manner. Please clarify.

Response: Commercial FE platforms, such as MIDAS, are like black boxes. Namely, after the numerical model is established, and the required analysis is set, the program will automatically undertake calculations and generate analysis results without providing detailed information reflecting the calculation process, e.g., the convergence property. Anyway, thank you for your good comment. Besides, for modes in which the dynamics of the girder and the piers are not coupled, the columns and the deck are not separated. In these cases, it is shown that the columns do not vibrate, and the bridge deck vibrates alone.

 

7. Are the below columns of the bridge considered rigid or flexible? How the axial stiffness of these crucial elements could influence the overall dynamic response (maximum deflection and bending moment) of the beam-like bridge under moving vehicles? Please explain that with more detail in appropriate places within the paper.

Response: The axial stiffness of columns depends on the length of the columns and the tensile/compressive stiffness of the columns. The shorter the length of the columns and the greater the tensile/compressive stiffness of the columns, the higher the axial stiffness of columns is. For the case of Renyihe Bridge, although the length of the columns is comparatively long, the tensile/compressive stiffness of the columns is sufficiently large. Therefore, the axial stiffness of the piers of Renyihe Bridge is still very large, and they can be simply considered rigid. These are explained in the revised manuscript (see the part highlighted in pink).

 

8. The paper suffers from the theoretical background and studies established in former years by experts on the vibrational analysis of multi-span beams subjected to moving loads and masses. In this regard, the authors are highly encouraged to display the following reference works in the paper:

 

(*) Zhu XQ, Law SS. Moving load identification on multi-span continuous bridges with elastic bearings. Mechanical Systems and Signal Processing. 2006 Oct 1;20(7):1759-82.

 

(*) Kiani K, Nikkhoo A, Mehri B. Assessing dynamic response of multispan viscoelastic thin beams under a moving mass via generalized moving least square method. Acta Mechanica Sinica. 2010 Oct;26:721-33.

 

(*) Kiani K, Nikkhoo A, Mehri B. Assessing dynamic response of multispan viscoelastic thin beams under a moving mass via generalized moving least square method. Acta Mechanica Sinica. 2010 Oct;26:721-33.

 

(*) Johansson C, Pacoste C, Karoumi R. Closed-form solution for the mode superposition analysis of the vibration in multi-span beam bridges caused by concentrated moving loads. Computers & Structures. 2013 Apr 1;119:85-94.

 

(*) Szyłko-Bigus O, Śniady P, Zakęś F. Application of Volterra integral equations in the dynamics of a multi-span Rayleigh beam subjected to a moving load. Mechanical Systems and Signal Processing. 2019 Apr 15;121:777-90.

 

Or even examining the dynamic response of bridge-like structures subjected to moving loads at a small scale:

 

(*) Kiani K, Roshan M. Nonlocal dynamic response of double-nanotube-systems for delivery of lagged-inertial-nanoparticles. International Journal of Mechanical Sciences. 2019 Mar 1;152:576-95.

 

(*) Yu G, Kiani K, Roshan M. Dynamic analysis of multiple-nanobeam-systems acted upon by multiple moving nanoparticles accounting for nonlocality, lag, and lateral inertia. Applied Mathematical Modelling. 2022 Aug 1;108:326-54.

 

(*) Abdelrahman AA, Esen I, Ozarpa C, Shaltout R, Eltaher MA, Assie AE. Dynamics of perforated higher order nanobeams subject to moving load using the nonlocal strain gradient theory. Smart Struct. Syst. 2021 Oct 1;28(4):515-33.

 

(*) Hosseini SA, Rahmani O, Bayat S. Thermal effect on forced vibration analysis of FG nanobeam subjected to moving load by Laplace transform method. Mechanics Based Design of Structures and Machines. 2023 Jul 3;51(7):3803-22.

Response: Thank you for providing us with these significant publications. We have read and cited all of them [9-16] which greatly help to strengthen the literature review of the present manuscript.

 

9. For the time-history plots given in Figures 17 and 18 for various speeds of the vehicles (i.e., 20, 30, 40, and 50 km/hr), these are reported based on the accelerometer attached to the midspan point of 3rd and 4th spans. It should be noticed that these are not only related to the bridge structure alone but also bridge + moving vehicles, indicating that the role of the velocity and mass weight of the vehicles should be appropriately removed from these plots to arrive at the near-to-exact natural frequencies of the bridge structure. How this critical issue has been considered by the authors and what is the role of moving vehicles in the whole dynamic response? Please clarify this within your manuscript, where the above-introduced reference works can also help you in handling this.

Response: Yes, according to Ref. [17], the natural frequencies of the bridge structure measured are influenced by the velocity and mass weight of the vehicles, as the weight and location of the vehicle become part of some new system. Ref. [17] formulated an approach relying on dynamic FE model updating to compensate for the deviation of the results of the modal experiment using vehicle excitations due to the adverse effects of running vehicles. In details, the measurement change in the 1st modal frequency caused by the running vehicles has been captured by on location modal experiments using both ambient and vehicle excitations, and the equivalent vehicle weight is thereby identified via dynamic FE model updating. Using the updated numerical model, the measurement change of the high order modal frequency due to the added equivalent vehicle weight is calculated, and the high order modal frequency measured on location is then compensated for use. However, according to Table 3, most fundamental frequencies identified for Renyihe Bridge in different cases are at around 0.77 Hz, suggesting the effects of the velocity and mass weight of the vehicles on natural frequencies of the bridge are similar for most vehicle speed cases. The focus of the present research is the variation of the frequency difference between the fundamental natural frequency and the frequency of the forced vehicle excitation among different vehicle speed cases, which is not significantly influenced by the velocity and mass weight of the vehicles based on the above. Therefore, the role of the velocity and mass weight of the vehicles does not have to be removed from plots given in Figs. 17 and 18 to arrive at the near-to-exact natural frequencies of the bridge structure for the required study to take place. We have added these explanations in the revised manuscript (see the part highlighted in brown).

 

10. The writing can be improved by addressing potential counterarguments or alternative explanations for the observed phenomenon. This will make the argument more robust and demonstrate a thorough consideration of different perspectives. In addition, there exist some grammatical errors that should be carefully revised in the next version of the paper.

Response: Thank you for the comment. As suggested, the writing has been improved by addressing potential counterarguments or alternative explanations for the observed phenomenon, and some typos and grammatical errors have been observed and revised.

Round 2

Reviewer 2 Report

Manuscript Number: applsci-2541644-v2

Full Title: Effects of Vehicle Speed on Vehicle-induced Dynamic Behaviors of a Concrete Bridge with Smooth and Rough Road Surface

 

The original text of the manuscript has been satisfactorily revised. In my opinion, the manuscript can be published as an Applied Science’s paper.

 Minor editing of English language required.

Reviewer 3 Report

It can be accepted

It can be improved more