Optimal Design of Nonlinear Negative-Stiffness Damper with Flexible Support for Mitigating Cable Vibration

Round 1

Reviewer 1 Report

This paper studies the optimal design of nonlinear negative stiffness damper with flexible support for mitigating cable vibration. The paper contains valuable information that is worthy to be published. The following issues are suggested before the paper can be recommended for acceptance.

1. It is suggested to disuse practical issues concerning design nonlinear negative stiffness damper for a prototype cable. For example, the size the springs, the effect of weight should be discussed.

2. The quality of figure 3 should be improved.

3. It is suggested to explain the process of energy transferring from low-order modes to high-order modes.

4. It is suggested to enrich the literature review with recent studies on vibration control using passive device, e.g., A programmable pseudo negative stiffness control device and its role in stay cable vibration control, Tuned mass damper for self-excited vibration control: Optimization involving nonlinear aeroelastic effect.

Minor editing of English language required

Author Response

Thanks a lot for the reviewer’s careful reading and constructive comments which will surely improve and clarify the manuscript. We highly appreciate the opportunity to clarify our research objectives and results. Responses to each item can be found in the attached word. Please see the attachment.

Author Response File: Author Response.docx

Reviewer 2 Report

This paper presents

Negative stiffness damper is a promising device to mitigate cable vibrations effectively. In contrast to traditional rigid supports, recent study has found that flexible supports are actually beneficial for enhancing the performance of negative stiffness dampers. This study investigates the optimization of negative stiffness dampers with flexible supports. Both linear and nonlinear damping conditions are taken into account. First, taking damping nonlinearity into account, a unified model is established for the negative stiffness damper with flexible support. Theoretical equivalent negative stiffness and damping are obtained for linear case, followed by numerical verification. Thereafter, equivalent parameters under friction case are presented. Experiments are conducted to validate the analytical derivation. Then, problem formulation is developed for the controlled cable. Optimization process is proposed to determine the required negative stiffness damper and support for multimode cable vibration. A series of numerical simulations are performed to demonstrate the design process. Moreover, nonlinear examples are presented to show the potential for improving control performance. As indicated by the research results, a flexible support is capable of amplifying the equivalent negative stiffness and damping under linear and nonlinear conditions. For multimode cable vibration, it is sufficient to determine the optimized negative stiffness and support by only considering the highest mode. Nonlinear negative stiffness dampers exhibit superior performance due to the leakage of vibration energy towards high-order modes.

1.     Main novelty of this work? Explain in detail.

2.     Comparison of your results with the literature to prove your novelty and improvement.

3.     Comparison for point 2 is needed in the form of a table with references cited and comparison must prove your contribution or addition to existing literature.

4.     Your abstract, results, and comparison table with the conclusion must be aligned to verify your claim.

5.     Revise your paper with technical writing by making long sentences short and concise.

6.     References must be updated, and old ones need to be replaced by new ones within the last 5-10 years duration.

7.     Some figures' quality needs improvement please ensure 300 dpi at least.

 

 

Minor editing needed

Author Response

Thanks a lot for the reviewer’s careful reading and constructive comments which will surely improve and clarify the manuscript. We highly appreciate the opportunity to clarify our research objectives and results. Responses to each item can be found in the attached word. Please see the attachment.

Author Response File: Author Response.docx

Reviewer 3 Report

The manuscript focuses on a simulation study of negative stiffness damper supported on a flexible element for reduce cable vibrations. Some experimental results at lab scale are also introduced.

The topic is relevant and, in general, the information presented is enough for this kind of studies. Before to be accepted for publications, some corrections and modifications in the manuscript organization are suggested. 

The methods should be presented in a single section to help the reader to clearly identify the theoretical and the practical work.

First line next figure 1. It is required to explain the considerations to obtain the simplificated mechanical model. In addition, please, include in Figure 1 the symbols (Fd, vd, etc.) which will be used as equivalences in the simplified model.

Figure 2. The angle of the support wrt the deck is not represented in the simplified model, how is it justified? Briefly explain.

Equation 1. As for the other elements, please provide a physical interpretation of velocity index.

Equation 3. Please provide a  physical interpretation of the assumption of velocity as sinusoidal form; this displacement form corresponds to a situation in reality?  

Figure 3. Please, indicate somewhere in the manuscript the software and the version used for the simulations. 

Four lines after figure 3. Mention how the values for  the parameters where selected.

In general, results requiere to be compared, at leat qualitatively, with other reports.

Figure 4. Blue lines are not visible, please find a way to show it clearly. On the other side, what is the difference between theoretical and numerical?

Figure 6. Please, clearly indicate how the prototype was used, what experiments were performed and why some others are only made in simulation.

First line after figure 8. Wat is the shape of figure 5 which is compared with figure 8?

Table 2. Briefly explain which are the real implications of each design scheme; i mean, what is required to implement each design in a real application? The protoype presented before is useful to perform these evaluations?

Three lines before Figure 11. Which is the uncontrolled case?

 

Author Response

Thanks a lot for the reviewer’s careful reading and constructive comments which will surely improve and clarify the manuscript. We highly appreciate the opportunity to clarify our research objectives and results. Responses to each item can be found in the attached word. Please see the attachment.

Author Response File: Author Response.docx

Round 2

Reviewer 2 Report

Table 2 needs to be revised again by adding your analysis parameters and results for the literature and the present study. The current table does not give an idea of contribution just helps in similar work done in literature only.

Author Response

Thanks a lot for the reviewer’s careful reading and earnest comment.  We have carefully considered the comment and have made  necessary revision as suggested. Please see the attachment.

Author Response File: Author Response.docx