Review of Wind-Induced Effects Estimation through Nonlinear Analysis of Tall Buildings, High-Rise Structures, Flexible Bridges and Transmission Lines

Round 1

Reviewer 1 Report

Point 1: The paper is well written, and concise and precise, my only comments on the abstract to be summarized or shorten, and must be straightforward and clear to the readers. The abstract should be improved. The abstract should contain the motivation and most important information of the study.

 

Point 2: Line 176 - F₁ and F₂ in Equation (1) should be explained more fully.

 

Point 3: Figure 5 - The manuscript only explains the three methods First-order inelastic analysis, Second-order elastic analysis and Second-order inelastic analysis. Why is there no explanation for the other methods mentioned in Figure 5, such as First-order elastic analysis.

 

Point 4: Figure 7 - The lines representing doubled-frequency and mixed-frequency in Figure 7 (b) should be indicated in a reasonable way to facilitate understanding.

Point 5: The authors should carefully address the details of the paper, e.g.: tense, and writing format. English can be improved.

Author Response

Response to Reviewers’ Comments

We appreciate the careful reading and valuable comments given by the reviewers. We have made changes in the manuscript (indicated there by a highlighter) by taking into account the reviewers’ comments and suggestions. The following summarizes the detailed responses to reviewer 1, reviewer 2 and reviewer 3.

 

Question 1 (from Reviewer 1):

The paper is well written, and concise and precise, my only comments on the abstract to be summarized or shorten, and must be straightforward and clear to the readers. The abstract should be improved. The abstract should be improved. The abstract should contain the motivation and most important information of the study.

Answer:

The nonlinear behavior of four common wind-sensitive structures, namely, tall buildings, high-rise structures, flexible bridges and transmission lines, is increasingly prominent under the action of wind loads. The purpose of this paper is to reveal the occurrence mechanism of the nonlinear effects of the above wind-sensitive structures by summarizing their geometric nonlinearities, material nonlinearities and aerodynamic nonlinearities. It provides cutting-edge research advances in theoretical studies, experimental methods and vibration-damping control, and points out the unsolved or insufficient key problems and challenges identified in the existing studies to shed light on future research directions. The first two sentences of the Abstract in the original manuscript have been revised to indicate the motivation for this paper, as follows: (see page 1 and lines 11-16 in the revised paper)

"The nonlinear effects exhibited by structures under the action of wind loads have gradually stepped into the vision of wind-resistant researchers. By summarizing the prominent wind-induced nonlinear problems of four types of wind-sensitive structures, namely, tall buildings, high-rise structures, flexible bridges and transmission lines, to reveal the occurrence mechanism of their nonlinear effects and to provide cutting-edge research progress in theoretical studies, experimental methods and vibration control."

Some important information is added in the Section of the Abstract. This added information involves methods for solving nonlinear vibration equations, modeling methods for analyzing local nodes GN and MN, nonlinear aerodynamic models of Bridges, existing shortcomings and some future challenges, as follows: (see page 1, lines 18-31 in the revised paper)

"The equivalent nonlinear equation method is used to solve nonlinear vibration equations with generalized van der Pol-type aerodynamic damping terms. The elastic-plastic finite element method and multi-scale modeling method are widely employed to analyze the effects of geometric nonlinearity (GN) and material nonlinearity (MN) at local nodes on the wind-induced response of latticed tall structures."

"Volterra series aerodynamic models are more suitable for nonlinear aerodynamic modeling of Bridges than polynomial models studied more in the past."

"The complex numerical calculations and nonlinear analyses involved in wind-induced nonlinear effects continue to consume significant computational resources and time, especially for complex wind field conditions and flexible and variable structural forms. It is necessary to further development of analytical, modeling and identification tools to facilitate the modeling of nonlinear features in the future."

To make the Abstract concise and straightforward, we have deleted part of the description of the phenomenon of structural nonlinear effects, but retained the more important conclusions of nonlinear problems. In addition, we have deleted some unnecessary expressions of "has become an important research hotspot in the field of bridge wind engineering" and "a common solution method". These revisions are as follows: (see page 1 and lines 23-24 in the revised paper).

"Volterra series aerodynamic models are more suitable for nonlinear aerodynamic modeling of Bridges than polynomial models studied more in the past."

 

Question 2 (from Reviewer 1):

Line 176 - F₁ and F₂ in Equation (1) should be explained more fully. Figure 5 - The manuscript only explains the three methods First-order inelastic analysis, Second-order elastic analysis and Second-order inelastic analysis. Why is there no explanation for the other methods mentioned in Figure 5, such as First-order elastic analysis. Figure 7 - The lines representing doubled-frequency and mixed-frequency in Figure 7 (b) should be indicated in a reasonable way to facilitate understanding.

Answer:

We have supplemented or modified the content according to the reviewer's suggestions as follows：

Equation (3) and Equation (4) are added to give a fuller explanation of F₁ and F₂, respectively. (see page 6 and lines 182 in the revised paper).

"	(3)"
"	(4)"

" and  are model parameters " is added to explain the parameters in Equation (3) and Equation (4). (see page 6 and lines 184 in the revised paper).

 

This part mainly introduces a range of structural wind-induced non-linear analysis methods, so the explanation of the First-order elastic analysis is omitted because it is a method within the elastic range. The description of this section is modified as follows:

"These methods are summarized in Figure 5:" is replaced by "Since the First-order elastic analysis in Figure 5 is a method within the elastic range, only the other three methods are summarized as follows:" (see page 8 and lines 290 in the revised paper).

 

The lines representing doubled-frequency and mixed-frequency in Figure 7 (b) have been modified for facilitate understanding as follows.

"As shown by the dashed line in Figure 7, by applying forced vibration with vertical frequency f_h and torsional frequency f_a to the main beam, Chen [110] find that there may be doubled-frequency (2f_h and 2f_a, etc.) and mixed-frequency (f_a - f_h and f_a + f_h, etc.) components in the self-excited lift amplitude spectrum S_sl and in the self-excited torque amplitude spectrum S_st." (see page 12 and lines 437 in the revised paper).

(a)	(b)

Figure 7. Higher-order components in the self-excited force: (a) Displacement input; (b) Self-excited force output [110].

 

Question 3 (from Reviewer 1):

The authors should carefully address the details of the paper, e.g.: tense, and writing format. English can be improved.

Answer:

A native English-speaker has reviewed and edited the original text to polish the language. Some revisions are as follows:

1. The expression "evolution" is replaced by "evolutionary";(see page 1 and lines 44 in the revised paper)

"This will allow for a deeper understanding of the nonlinear properties, mechanisms, and evolutionary laws associated with wind-induced phenomena."

2. The expression "nonlinearly vary" is replaced by "vary nonlinearly";(see page 4 and lines 143 in the revised paper)

"The vortex-locked wind speed region, occurring during vortex-induced resonance, causes the aerodynamic damping to vary nonlinearly with wind speed and amplitude, resulting in significant AN."

3. The expression "at a given wind speed" is replaced by "for a given wind speed";(see page 7 and lines 243 in the revised paper)

"To overcome the limitations of equivalent aerodynamic damping models, aerodynamic damping is further described as a function of time-variant displacement or velocity for a given wind speed."

4. The expression "amplifies" is replaced by "has amplified";(see page 12 and lines 446 in the revised paper)

"The obtuse body structure of the bridge, coupled with its mode-dense characteristics, has amplified the significance of aerodynamic higher-order effects."

5. The expression "can be highly sensitive" is replaced by "is highly sensitive";(see page 14 and lines 494 in the revised paper)

"However, the specific form of the polynomial aerodynamic model is highly sensitive to the profile of the bridge structure section."

6. The expression "on input amplitude" is replaced by "on the input amplitude";(see page 15 and lines 514 in the revised paper)

"The third-order Volterra series model can capture the dependence of the system transfer function on the input amplitude, such as the flutter derivative with amplitude."

7. The expression "so MN is" is replaced by "and thus MN is";(see page 15 and lines 537 in the revised paper)

"However, its elongation deformation is typically considered as a smaller range of linear elastic deformation, and thus MN is generally ignored."

8. The expression "does not effectively reduce" is replaced by "is not effective in reducing";(see page 16 and lines 564 in the revised paper)

"The results demonstrated that increasing mechanical damping is not effective in reducing the amplitude of wake-induced galloping in the leeward cylindrical wake when the windward cylinder is fixed."

9. The expression "overlooking GN resulting from " is replaced by "neglecting the GN induced by";(see page 16 and lines 575 in the revised paper)

"However, they used the mode superposition method to solve the galloping equations, neglecting the GN induced by large-amplitude motion "

10. The expression "a failure " is replaced by "fails";(see page 17 and lines 645 in the revised paper)

"They found that neglecting static swing leads to an overestimation of the along-wind dynamic displacement and fails to capture the dynamic cross-wind and longitudinal tensions."

 

Question 4 (from Reviewer 2):

It is stated that there are few researches on torsional wind-induced nonlinear effects in tall buildings. This is not true since the torsional of vibration of tall buildings are also investigated by several authors. As the reviewer understands, tall building is a type of high-rise building. The authors are suggested to revise the title of Section 2 and Section 3.

Answer:

We sincerely appreciate the valuable comments. We have checked the literature carefully and added some research progress on torsional wind-induced nonlinear effects of tall buildings in the revised manuscript. (see page 7 and lines 258-281 in the revised paper).

"Wind-induced nonlinear torsional vibration in tall buildings is usually caused by the imbalance in the instantaneous wind pressure distributions on all building surfaces and the eccentricity between the elastic and mass centers [59,60]. For symmetric tall buildings with large stiffness, the asymmetric aerodynamic-induced torsion is usually small and generally negligible. However, for flexible tall buildings, rotating members can generate large shear forces and bending moments in the members, and the torque loads may have nonlinear coupling effects with downwind and lateral loads, resulting in a strong wind vibration response [61]. Especially slender tall buildings tend to suffer greater rotational damage under wind loads. Ref. [62] studied the torsional response for symmetric and asymmetric linear systems, where the relative distance between the center of mass (CM) and the center of stiffness (CS) varies with time during structural motions and an instantaneous load eccentricity occurs during horizontal motions of the CM in the plane, which may lead to additional torsional motions not considered in codes [11,12,63], naming this second-order nonlinear effect as the A-∆ effect. Some authors [64] solved the nonlinear differential equations considering the A-∆ second-order nonlinear effect by means of state-space model assembly, and showed that the A-∆ effect has a small effect on the wind-driven displacements and accelerations, but the correlation coefficients between the wind forces have the most important influence on the response, suggesting that the different correlation levels between the wind force and the torque must be taken into account in the evaluation of the wind-driven response. In addition, nonlinearities may cause the structure to become more flexible, thereby increasing the dynamic response of the structure [65], and therefore further analysis is required to assess the impact of the A-∆ effect on the wind response of high-rise buildings considering both structural geometric nonlinearities and material nonlinear behavior."

 

26. Australia/New Zealand Standard, Structural Design Actions. Part 2: Wind Actions; AS/NZS 1170.2; Standards Australia International Ltd.: Sydney, Australia; Standards New Zealand: Wellington, New Zealand, 2011.
27. Minimum Design Loads for Buildings and Other Structures; ASCE 7-10; American Society of Civil Engineers: Reston, VA, USA, 2013.
28. Li, Y. g.; Liu, P.; Li, Y.; Yan, J. h.; Quan, J. Wind loads characteristics of irregular shaped high-rise buildings. Struct. Eng. 2023, 26, 3-16.
29. Bhattacharya, S.; Dalui, S.K. Effect of tuned mass damper in wind-induced response of “v” plan-shaped tall building. Des. Tall Spec. 2022, 31, e1931.
30. Hou, F.; Jafari, M. Investigation approaches to quantify wind-induced load and response of tall buildings: A review. Cities Soc. 2020, 62, 102376.
31. Hong, H.P. Torsional responses under bidirectional seismic excitations: Effect of instantaneous load eccentricities. Struct. Eng. 2013, 139, 133-143.
32. Ministry of Construction of the People’s Republic of China. Load Code for the Design of Building Structures; GB 50009—2012; China Architecture and Building Press: Beijing, China, 2012.
33. López-Ibarra, A.; Pozos-Estrada, A.; Nava-González, R. Effect of partially correlated wind loading on the response of two-way asymmetric systems: The impact of torsional sensitivity and nonlinear effects. Sci. 2023, 13, 6421.
34. Man, X.; Bin, Z.; Hong, Q.; Qing, X.; Guo, W.W.; He, X. Nonlinear dynamic response analysis of wind-train-bridge coupling system of hu-su-tong bridge. Mech. 2021, 38, 83.

 

The main difference between tall buildings and high-rise structures mentioned in the manuscript is that the former usually refers to office buildings, shopping malls, and other buildings that need to consider personnel access and life, while the latter refers to structures that people cannot be used for production and life, such as transmission towers, cooling towers, TV towers, etc. The above explanation was added to the new content of section 1 (Introduction) of the manuscript. (see page 1 and lines 39-41 in the revised paper).

"(To distinguish from the tall buildings, high-rise structures here are those that people cannot use for production and living, such as transmission towers, cooling towers, TV towers, etc.)"

 

Question 5 (from Reviewer 2 and Reviewer 3):

Some figures are re-drawn from previous papers. References should be provided for those figures. The author needs to explain how the graphs in Figures 4, 7, and 8 are created or cite the reference for each one of them.

Answer:

As suggested by the reviewers, the corresponding references are cited for Figures 4,7, and 8. The references are annotated in the statement and name sections of these figures.

(see page 5 and lines 155, page 12 and lines 437, page 13 and lines 461 in the revised paper respectively).

 

Question 6 (from Reviewer 2):

The nonlinearity from additional dampers is another of nonlinearity that is drawn increasing attention in recent years, e.g., Vortex-induced vibration control of a flexible circular cylinder using a nonlinear energy sink, Effect of inerter locations on the vibration control performance of nonlinear energy sink inerter. It is suggested to comment a bit on this topic.

 

Answer:

We sincerely appreciate the valuable comments. Adding additional dampers to wind-sensitive structures is a practical and effective measure to reduce the harm caused by nonlinear dynamic wind loads on the structures. As you are concerned, the nonlinear problem of additional dampers is a particularly important research topic in recent years. Therefore, we have checked the manuscript content carefully and added some research progress on the nonlinearity from additional dampers in Section 5 (Transmission lines) of the revised manuscript. (see page 17 and lines 652-673 in the revised paper).

"In recent years, the topic of reducing the hazards caused by nonlinear dynamic wind loading effects on transmission lines is of particular importance. Inter-wire friction is a major source of energy dissipation [172]. Its application to vibration isolation systems is considered advantageous. The spiral wire rope isolator (WRI) is a typical nonlinear hysteretic damping device [173], which is also effective for wind-induced vibration control of transmission lines [174]. In addition, a newly developed nonlinear energy sink (NES) damper [175,176] is the current research hotspot of nonlinear dampers. The NES damper is more stable compared to the general damper, due to its frequency-energy dependence, which makes it able to act nonlinearly in a broadband frequency-energy manner and is more predictable and controllable in the theoretical analysis of parameter optimization. Some scholars have utilized the segmented linear recovery forcing function of the NES has by adding nonlinear dampers with NES to single-span tension cables for mitigating chirp vibration [177]. For the problem of nonlinear dynamic interactions between transmission lines, nonlinear dampers and wind, scholars have combined the nonlinearity of plane stretching in the conductor, the equivalent cubic stiffness of the Stockbridge damper and the pulsating lift modeled as a Vanderbilt oscillator in a single model in order to study nonlinear vortex-excited vibrations of transmission lines. The results show that the nonlinearity in the system disappears with increasing axial tension and stall parameters of the wake oscillator [178]. In addition, the application of the NES to wind-sensitive structures such as tall buildings, hagh-rise structures and flexible bridges has gradually become a topic of future research being interested by many scholars [179-180]."

172. Vanderveldt, H.H.; Chung, B.S.; Reader, W.T. Some dynamic properties of axially loaded wire ropes. Mech. 1973, 13, 24-30.
173. Ni, Y.Q.; Ko, J.M.; Wong, C.W.; Zhan, S. Modelling and identification of a wire-cable vibration isolator via a cyclic loading test. I. Mech. Eng. I-J Sys. 1999, 213, 163-172.
174. Tinker, M.L.; Cutchins, M.A. Damping phenomena in a wire rope vibration isolation system. Sound Vib. 1992, 157, 7-18.
175. Cao, Y.; Yao, H.; Li, Q.; Yang, P.; Wen, B. Vibration mitigation and dynamics of a rotor-blade system with an attached nonlinear energy sink. J. Non-Lin. Mech. 2020, 127, 103614.
176. Li, H.; Li, A.; Kong, X. Design criteria of bistable nonlinear energy sink in steady-state dynamics of beams and plates. Nonlinear Dyn. 2021, 103, 1475-1497.
177. Leroux, M.; Langlois, S.; Savadkoohi, A.T. Nonlinear passive control of galloping of overhead transmission lines: Design and numerical verifications. Sur, Vib. Shock Noise. 2023.
178. Gupta, S.K.; Malla, A.L.; Barry, O.R. Nonlinear vibration analysis of vortex-induced vibrations in overhead power lines with nonlinear vibration absorbers. Nonlinear Dyn. 2021, 103, 27-47.
179. Chen, D.; Gu, C.; Fang, K.; Yang, J.; Guo, D.; Marzocca, P. Vortex-induced vibration of a cylinder with nonlinear energy sink (NES) at low Reynolds number. Nonlinear Dyn. 2021, 104, 1937-1954.
180. Zuo, H.; Zhu, S. Development of novel track nonlinear energy sinks for seismic performance improvement of offshore wind turbine towers. Syst. Signal Pr. 2022, 172, 108975.

 

Question 7 (from Reviewer 3):

Are these methods applicable for wind-sensitive structures with active or passive vibration dissipation systems such as active/passive dampers or base isolation?

Answer:

The methods in this paper are considered for the wind-induced nonlinearities of four typical wind-sensitive structures. Additions to the substructure may have an influence on affecting the wind-induced response of the structure but are not relevant to the applicability of these methods. Adding active or passive dampers to the structure can be regarded as adding substructures to the main structure, and the addition of substructures does not affect the applicability of these methods. Therefore, these methods are applicable to the structures mentioned by the reviewer. For example, the forced vibration test method for identifying nonlinear aerodynamic damping in tall buildings is mentioned in Section 3 (Tall buildings). Attaching dampers to a tall building changes the wind-induced vibration nonlinear behavior of the original structure, but this does not affect the effectiveness of the forced vibration test in identifying wind-induced vibration nonlinear features. Another example is the Lindstedt-Poincare perturbation method for solving the nonlinear vibration equations mentioned in Section 5 (Transmission lines). For transmission lines with additional dampers, new nonlinear vibration equations need to be developed with respect to the dampers, but the idea of the Lindstedt-Poincare perturbation method remains the same in solving the nonlinear vibration equations.

 

Question 8 (from Reviewer 3)

The author needs to add a reference for general statements in the context. This happened multiple times in the manuscript such as line 81, 251, etc.

Answer:

We carefully recheck the general statement in the context. New references have been added to support these places where similar problems occur.

(see page 2 and lines 73, the page 2 and lines 79, the page 6 and lines 195, the page 8 and lines 283, the page 9 and lines 317 in the revised paper respectively).

 

Question 9 (from Reviewer 3):

The author needs to explain how the review paper was structured and what methods are used for obtaining the resources related to this topic. What aspects are not accounted for in the research?

Answer:

Tall buildings, high-rise structures, flexible bridges and transmission lines are not only important urban infrastructures, but also their unique structural behavior makes them more sensitive to wind loading effects. The problem of wind-induced nonlinear effects affecting their structural stability and safety has become increasingly prominent. The authors and the author's team have been engaged in research related to the wind-resistant design of wind-sensitive structures such as transmission towers and large-span flexible bridges for many years, and have sufficient background knowledge and understanding of wind-induced nonlinear analysis, including structural engineering, wind mechanics, nonlinear analysis methods, and other related fields. In constructing this review, extensive and systematic literature research on the more prominent wind nonlinear problems of four common wind-sensitive structures, namely, high-rise buildings, towering structures, flexible bridges, and transmission lines, is conducted to cover the major research progress and results in the related fields, such as the identification of cross-wind nonlinear aerodynamic damping in tall buildings, the geometric and material nonlinear effects at the local nodes of high-rise structures, the wind-induced nonlinear flutter behavior of bridges and strong geometric nonlinear characteristics of ice-covered transmission lines under the action of wind loads. Combined with the previous research experience on wind-induced nonlinear vibration theory and experimental methods, this literature is comprehensively analyzed and summarized, and the different research results are compared, generalized, and summarized to equip the written review paper with accurate arguments and proper citations.

This review paper focuses on the mainstream research on wind-induced nonlinear problems for four types of wind-sensitive structures, but the summary may be insufficient in some emerging or more specialized research areas, for example, for nonlinear problems under complex wind fields in coastal and mountainous areas, there is a lack of field measurement related research to be further supplemented and summarized in a unified model, especially for transient and non-Gaussian wind fields. The more advanced analysis, modeling and identification tools involved in wind tunnel tests are yet to be fully considered. In addition, the development of new predictive analysis tools in conjunction with artificial intelligence information technology is a new area of current research. Advanced nonlinear vibration control methods, such as aerodynamic optimization methods adapted to different Archimedean Optimization Algorithms (AOAs) and nonlinear damper control measures.

 

Question 10 (from Reviewer 3):

The author needs to explore the application of mentioned methods for all four wind-sensitive structures in well-known international codes and standards.

Answer:

We feel great thanks for your professional review work on our article. Based on your nice suggestions, we have added the following modifications regarding the application of the wind-induced nonlinear analysis methods for the four wind-sensitive structures mentioned above in well-known international codes and standards.

"However, the method uses a linearized solution that assumes a quasi-linear relationship between the building surface wind pressure and the incoming wind speed in the time domain with simultaneous pulsations. For example, the gust load factor widely used in codes and standards [11,12] is based on a Gaussian framework, so the term containing the velocity fluctuation squared is removed from the equation." (see page 3 and lines 85-89 in the revised paper).

11. Australia/New Zealand Standard, Structural Design Actions. Part 2: Wind Actions; AS/NZS 1170.2; Standards Australia International Ltd.: Sydney, Australia; Standards New Zealand: Wellington, New Zealand, 2011.
12. Minimum Design Loads for Buildings and Other Structures; ASCE 7-10; American Society of Civil Engineers: Reston, VA, USA, 2013.

 

"Vickery and Basu [31] developed a theoretical basis for aerodynamic damping modeling, and the aerodynamic damping model proposed by Vickery and Basu has been adopted by several codes and standards [32-34] in addition to being used for solving the cross-wind response in the framework of stochastic vibrations [35]. However, it has been shown that the response calculated using this aerodynamic damping model does not agree with the response measured in wind tunnel tests and may significantly overestimate the side wind response in most cases, especially for cylinders with small Scruton numbers [36,37]." (see page 5 and lines 173-180 in the revised paper).

31. Vickery, B.J.; Basu, R.I. Across-wind vibrations of structures of circular cross section. Part I: development of a mathematical model for two-dimensional conditions. Wind Eng. Ind. Aerod. 1983, 12, 49–73.
32. The American Society of Mechanical Engineers; ASME STS-1-2006; American Society of Mechanical Engineers: New York, USA, 2006.
33. CICIND Model Code for Steel Chimneys; CICIND 2010; International Committee for Industrial Construction: Ratingen, Germany, 2010.
34. Eurocode 1: Actions on structures; EN 1991; European Commission: Brussels, Belgium, 2010.
35. Vickery, B.J.; Clark, A.W. Lift of across-wind response of tapered stacks. Proceedings American Society of Civil Engineering. Struct. Div. 1972, 1, 1– 19.
36. Verboom, G.K.; Koten, H. Vortex excitation: three design rules tested on 13 industrial chimneys. Wind Eng. Ind. Aerod. 2010, 98, 145– 154.
37. Lupi, F.; Niemann, H.J.; Hoffer, R. A novel spectral method for cross-wind vibrations: application to 27 full-scale chimneys. Wind Eng. Ind. Aerod. 2017, 171, 353–365.

 

Question 11 (from Reviewer 3):

The conclusion part needs to be improved. The conclusion of this review paper not only needs to critically compare and identify the required parameters for each wind-sensitive structure but also identify the important challenges and gaps in the literature and enough insight for future research.

Answer:

This review article shows that developments in blunt-body aerodynamics and aeroelasticity over the past few decades have enhanced our ability to better understand and capture the effects of wind-induced nonlinearities on wind-sensitive structures, while at the same time progressively recognizing that, due to the emergence of new materials and new structural forms, as well as more comprehensive and accurate observations of extremes such as tornadoes and downburst storms, previously smooth, Gaussian, and linear characteristics of the implicit assumptions have departed from the actual structural wind vibration response. In order to study the mechanism of wind nonlinearities and to mitigate the hazards of wind nonlinear vibration, further theoretical studies or experimental methods related to wind nonlinearities are needed. Based on the reviewers' suggestions, we re-summarize the key findings discussed in this review article and the outlook for future research as follows: (see page 19 and lines 735-750 in the revised paper).

"(5) Existing instruments for free or forced vibration tests are not accurate enough to identify wind load parameters in the nonlinear region, and there is no uniformly recognized computational model for cross-wind nonlinear aerodynamic damping of tall buildings and nonlinear self-excited aerodynamic forces of flexible bridges, which still need to be explored. In addition, the complex numerical calculations and nonlinear analyses involved in wind-induced nonlinear effects still consume a lot of computational resources and time, especially for complex wind field conditions or flexible and variable structural forms. There is still a lack of sufficient in situ measurements to support the study of complex wind fields in coastal and mountainous regions, and uniform models need to be further supplemented and summarized, especially for transient and non-Gaussian wind fields. Some of the major challenges ahead include further development of analytical, modeling and identification tools to facilitate modeling of nonlinear features. The development of new predictive analysis tools in conjunction with artificial intelligence information technology is also a challenging area of research. Advanced suppression methods, such as aerodynamic optimization methods adapted to different Archimedean optimization algorithms (AOAs), and nonlinear damper control measures, are promising."

Author Response File: Author Response.docx

Reviewer 2 Report

This paper presents a systematic review of the wind-induced nonlinear analysis of flexible structures. The following issues are suggested before the paper can be recommend for acceptance.

1. It is stated that there are few researches on torsional wind-induced nonlinear effects in tall buildings. This is not true since the torsional of vibration of tall buildings are also investigated by several authors.

2. As the reviewer understands, tall building is a type of high-rise building. The authors are suggested to revise the title of Section 2 and Section 3.

3. Some figures are re-drawn from previous papers. References should be provided for those figures.

4. The nonlinearity from additional dampers is another of nonlinearity that is drawn increasing attention in recent years, e.g., Vortex-induced vibration control of a flexible circular cylinder using a nonlinear energy sink, Effect of inerter locations on the vibration control performance of nonlinear energy sink inerter. It is suggested to comment a bit on this topic.

Moderate editing of English language required

Author Response

Response to Reviewers’ Comments

We appreciate the careful reading and valuable comments given by the reviewers. We have made changes in the manuscript (indicated there by a highlighter) by taking into account the reviewers’ comments and suggestions. The following summarizes the detailed responses to reviewer 1, reviewer 2 and reviewer 3.

 

Question 1 (from Reviewer 1):

The paper is well written, and concise and precise, my only comments on the abstract to be summarized or shorten, and must be straightforward and clear to the readers. The abstract should be improved. The abstract should be improved. The abstract should contain the motivation and most important information of the study.

Answer:

The nonlinear behavior of four common wind-sensitive structures, namely, tall buildings, high-rise structures, flexible bridges and transmission lines, is increasingly prominent under the action of wind loads. The purpose of this paper is to reveal the occurrence mechanism of the nonlinear effects of the above wind-sensitive structures by summarizing their geometric nonlinearities, material nonlinearities and aerodynamic nonlinearities. It provides cutting-edge research advances in theoretical studies, experimental methods and vibration-damping control, and points out the unsolved or insufficient key problems and challenges identified in the existing studies to shed light on future research directions. The first two sentences of the Abstract in the original manuscript have been revised to indicate the motivation for this paper, as follows: (see page 1 and lines 11-16 in the revised paper)

"The nonlinear effects exhibited by structures under the action of wind loads have gradually stepped into the vision of wind-resistant researchers. By summarizing the prominent wind-induced nonlinear problems of four types of wind-sensitive structures, namely, tall buildings, high-rise structures, flexible bridges and transmission lines, to reveal the occurrence mechanism of their nonlinear effects and to provide cutting-edge research progress in theoretical studies, experimental methods and vibration control."

Some important information is added in the Section of the Abstract. This added information involves methods for solving nonlinear vibration equations, modeling methods for analyzing local nodes GN and MN, nonlinear aerodynamic models of Bridges, existing shortcomings and some future challenges, as follows: (see page 1, lines 18-31 in the revised paper)

"The equivalent nonlinear equation method is used to solve nonlinear vibration equations with generalized van der Pol-type aerodynamic damping terms. The elastic-plastic finite element method and multi-scale modeling method are widely employed to analyze the effects of geometric nonlinearity (GN) and material nonlinearity (MN) at local nodes on the wind-induced response of latticed tall structures."

"Volterra series aerodynamic models are more suitable for nonlinear aerodynamic modeling of Bridges than polynomial models studied more in the past."

"The complex numerical calculations and nonlinear analyses involved in wind-induced nonlinear effects continue to consume significant computational resources and time, especially for complex wind field conditions and flexible and variable structural forms. It is necessary to further development of analytical, modeling and identification tools to facilitate the modeling of nonlinear features in the future."

To make the Abstract concise and straightforward, we have deleted part of the description of the phenomenon of structural nonlinear effects, but retained the more important conclusions of nonlinear problems. In addition, we have deleted some unnecessary expressions of "has become an important research hotspot in the field of bridge wind engineering" and "a common solution method". These revisions are as follows: (see page 1 and lines 23-24 in the revised paper).

"Volterra series aerodynamic models are more suitable for nonlinear aerodynamic modeling of Bridges than polynomial models studied more in the past."

 

Question 2 (from Reviewer 1):

Line 176 - F₁ and F₂ in Equation (1) should be explained more fully. Figure 5 - The manuscript only explains the three methods First-order inelastic analysis, Second-order elastic analysis and Second-order inelastic analysis. Why is there no explanation for the other methods mentioned in Figure 5, such as First-order elastic analysis. Figure 7 - The lines representing doubled-frequency and mixed-frequency in Figure 7 (b) should be indicated in a reasonable way to facilitate understanding.

Answer:

We have supplemented or modified the content according to the reviewer's suggestions as follows：

Equation (3) and Equation (4) are added to give a fuller explanation of F₁ and F₂, respectively. (see page 6 and lines 182 in the revised paper).

"	(3)"
"	(4)"

" and  are model parameters " is added to explain the parameters in Equation (3) and Equation (4). (see page 6 and lines 184 in the revised paper).

 

This part mainly introduces a range of structural wind-induced non-linear analysis methods, so the explanation of the First-order elastic analysis is omitted because it is a method within the elastic range. The description of this section is modified as follows:

"These methods are summarized in Figure 5:" is replaced by "Since the First-order elastic analysis in Figure 5 is a method within the elastic range, only the other three methods are summarized as follows:" (see page 8 and lines 290 in the revised paper).

 

The lines representing doubled-frequency and mixed-frequency in Figure 7 (b) have been modified for facilitate understanding as follows.

"As shown by the dashed line in Figure 7, by applying forced vibration with vertical frequency f_h and torsional frequency f_a to the main beam, Chen [110] find that there may be doubled-frequency (2f_h and 2f_a, etc.) and mixed-frequency (f_a - f_h and f_a + f_h, etc.) components in the self-excited lift amplitude spectrum S_sl and in the self-excited torque amplitude spectrum S_st." (see page 12 and lines 437 in the revised paper).

(a)	(b)

Figure 7. Higher-order components in the self-excited force: (a) Displacement input; (b) Self-excited force output [110].

 

Question 3 (from Reviewer 1):

The authors should carefully address the details of the paper, e.g.: tense, and writing format. English can be improved.

Answer:

A native English-speaker has reviewed and edited the original text to polish the language. Some revisions are as follows:

1. The expression "evolution" is replaced by "evolutionary";(see page 1 and lines 44 in the revised paper)

"This will allow for a deeper understanding of the nonlinear properties, mechanisms, and evolutionary laws associated with wind-induced phenomena."

2. The expression "nonlinearly vary" is replaced by "vary nonlinearly";(see page 4 and lines 143 in the revised paper)

"The vortex-locked wind speed region, occurring during vortex-induced resonance, causes the aerodynamic damping to vary nonlinearly with wind speed and amplitude, resulting in significant AN."

3. The expression "at a given wind speed" is replaced by "for a given wind speed";(see page 7 and lines 243 in the revised paper)

"To overcome the limitations of equivalent aerodynamic damping models, aerodynamic damping is further described as a function of time-variant displacement or velocity for a given wind speed."

4. The expression "amplifies" is replaced by "has amplified";(see page 12 and lines 446 in the revised paper)

"The obtuse body structure of the bridge, coupled with its mode-dense characteristics, has amplified the significance of aerodynamic higher-order effects."

5. The expression "can be highly sensitive" is replaced by "is highly sensitive";(see page 14 and lines 494 in the revised paper)

"However, the specific form of the polynomial aerodynamic model is highly sensitive to the profile of the bridge structure section."

6. The expression "on input amplitude" is replaced by "on the input amplitude";(see page 15 and lines 514 in the revised paper)

"The third-order Volterra series model can capture the dependence of the system transfer function on the input amplitude, such as the flutter derivative with amplitude."

7. The expression "so MN is" is replaced by "and thus MN is";(see page 15 and lines 537 in the revised paper)

"However, its elongation deformation is typically considered as a smaller range of linear elastic deformation, and thus MN is generally ignored."

8. The expression "does not effectively reduce" is replaced by "is not effective in reducing";(see page 16 and lines 564 in the revised paper)

"The results demonstrated that increasing mechanical damping is not effective in reducing the amplitude of wake-induced galloping in the leeward cylindrical wake when the windward cylinder is fixed."

9. The expression "overlooking GN resulting from " is replaced by "neglecting the GN induced by";(see page 16 and lines 575 in the revised paper)

"However, they used the mode superposition method to solve the galloping equations, neglecting the GN induced by large-amplitude motion "

10. The expression "a failure " is replaced by "fails";(see page 17 and lines 645 in the revised paper)

"They found that neglecting static swing leads to an overestimation of the along-wind dynamic displacement and fails to capture the dynamic cross-wind and longitudinal tensions."

 

Question 4 (from Reviewer 2):

It is stated that there are few researches on torsional wind-induced nonlinear effects in tall buildings. This is not true since the torsional of vibration of tall buildings are also investigated by several authors. As the reviewer understands, tall building is a type of high-rise building. The authors are suggested to revise the title of Section 2 and Section 3.

Answer:

We sincerely appreciate the valuable comments. We have checked the literature carefully and added some research progress on torsional wind-induced nonlinear effects of tall buildings in the revised manuscript. (see page 7 and lines 258-281 in the revised paper).

"Wind-induced nonlinear torsional vibration in tall buildings is usually caused by the imbalance in the instantaneous wind pressure distributions on all building surfaces and the eccentricity between the elastic and mass centers [59,60]. For symmetric tall buildings with large stiffness, the asymmetric aerodynamic-induced torsion is usually small and generally negligible. However, for flexible tall buildings, rotating members can generate large shear forces and bending moments in the members, and the torque loads may have nonlinear coupling effects with downwind and lateral loads, resulting in a strong wind vibration response [61]. Especially slender tall buildings tend to suffer greater rotational damage under wind loads. Ref. [62] studied the torsional response for symmetric and asymmetric linear systems, where the relative distance between the center of mass (CM) and the center of stiffness (CS) varies with time during structural motions and an instantaneous load eccentricity occurs during horizontal motions of the CM in the plane, which may lead to additional torsional motions not considered in codes [11,12,63], naming this second-order nonlinear effect as the A-∆ effect. Some authors [64] solved the nonlinear differential equations considering the A-∆ second-order nonlinear effect by means of state-space model assembly, and showed that the A-∆ effect has a small effect on the wind-driven displacements and accelerations, but the correlation coefficients between the wind forces have the most important influence on the response, suggesting that the different correlation levels between the wind force and the torque must be taken into account in the evaluation of the wind-driven response. In addition, nonlinearities may cause the structure to become more flexible, thereby increasing the dynamic response of the structure [65], and therefore further analysis is required to assess the impact of the A-∆ effect on the wind response of high-rise buildings considering both structural geometric nonlinearities and material nonlinear behavior."

 

26. Australia/New Zealand Standard, Structural Design Actions. Part 2: Wind Actions; AS/NZS 1170.2; Standards Australia International Ltd.: Sydney, Australia; Standards New Zealand: Wellington, New Zealand, 2011.
27. Minimum Design Loads for Buildings and Other Structures; ASCE 7-10; American Society of Civil Engineers: Reston, VA, USA, 2013.
28. Li, Y. g.; Liu, P.; Li, Y.; Yan, J. h.; Quan, J. Wind loads characteristics of irregular shaped high-rise buildings. Struct. Eng. 2023, 26, 3-16.
29. Bhattacharya, S.; Dalui, S.K. Effect of tuned mass damper in wind-induced response of “v” plan-shaped tall building. Des. Tall Spec. 2022, 31, e1931.
30. Hou, F.; Jafari, M. Investigation approaches to quantify wind-induced load and response of tall buildings: A review. Cities Soc. 2020, 62, 102376.
31. Hong, H.P. Torsional responses under bidirectional seismic excitations: Effect of instantaneous load eccentricities. Struct. Eng. 2013, 139, 133-143.
32. Ministry of Construction of the People’s Republic of China. Load Code for the Design of Building Structures; GB 50009—2012; China Architecture and Building Press: Beijing, China, 2012.
33. López-Ibarra, A.; Pozos-Estrada, A.; Nava-González, R. Effect of partially correlated wind loading on the response of two-way asymmetric systems: The impact of torsional sensitivity and nonlinear effects. Sci. 2023, 13, 6421.
34. Man, X.; Bin, Z.; Hong, Q.; Qing, X.; Guo, W.W.; He, X. Nonlinear dynamic response analysis of wind-train-bridge coupling system of hu-su-tong bridge. Mech. 2021, 38, 83.

 

The main difference between tall buildings and high-rise structures mentioned in the manuscript is that the former usually refers to office buildings, shopping malls, and other buildings that need to consider personnel access and life, while the latter refers to structures that people cannot be used for production and life, such as transmission towers, cooling towers, TV towers, etc. The above explanation was added to the new content of section 1 (Introduction) of the manuscript. (see page 1 and lines 39-41 in the revised paper).

"(To distinguish from the tall buildings, high-rise structures here are those that people cannot use for production and living, such as transmission towers, cooling towers, TV towers, etc.)"

 

Question 5 (from Reviewer 2 and Reviewer 3):

Some figures are re-drawn from previous papers. References should be provided for those figures. The author needs to explain how the graphs in Figures 4, 7, and 8 are created or cite the reference for each one of them.

Answer:

As suggested by the reviewers, the corresponding references are cited for Figures 4,7, and 8. The references are annotated in the statement and name sections of these figures.

(see page 5 and lines 155, page 12 and lines 437, page 13 and lines 461 in the revised paper respectively).

 

Question 6 (from Reviewer 2):

The nonlinearity from additional dampers is another of nonlinearity that is drawn increasing attention in recent years, e.g., Vortex-induced vibration control of a flexible circular cylinder using a nonlinear energy sink, Effect of inerter locations on the vibration control performance of nonlinear energy sink inerter. It is suggested to comment a bit on this topic.

 

Answer:

We sincerely appreciate the valuable comments. Adding additional dampers to wind-sensitive structures is a practical and effective measure to reduce the harm caused by nonlinear dynamic wind loads on the structures. As you are concerned, the nonlinear problem of additional dampers is a particularly important research topic in recent years. Therefore, we have checked the manuscript content carefully and added some research progress on the nonlinearity from additional dampers in Section 5 (Transmission lines) of the revised manuscript. (see page 17 and lines 652-673 in the revised paper).

"In recent years, the topic of reducing the hazards caused by nonlinear dynamic wind loading effects on transmission lines is of particular importance. Inter-wire friction is a major source of energy dissipation [172]. Its application to vibration isolation systems is considered advantageous. The spiral wire rope isolator (WRI) is a typical nonlinear hysteretic damping device [173], which is also effective for wind-induced vibration control of transmission lines [174]. In addition, a newly developed nonlinear energy sink (NES) damper [175,176] is the current research hotspot of nonlinear dampers. The NES damper is more stable compared to the general damper, due to its frequency-energy dependence, which makes it able to act nonlinearly in a broadband frequency-energy manner and is more predictable and controllable in the theoretical analysis of parameter optimization. Some scholars have utilized the segmented linear recovery forcing function of the NES has by adding nonlinear dampers with NES to single-span tension cables for mitigating chirp vibration [177]. For the problem of nonlinear dynamic interactions between transmission lines, nonlinear dampers and wind, scholars have combined the nonlinearity of plane stretching in the conductor, the equivalent cubic stiffness of the Stockbridge damper and the pulsating lift modeled as a Vanderbilt oscillator in a single model in order to study nonlinear vortex-excited vibrations of transmission lines. The results show that the nonlinearity in the system disappears with increasing axial tension and stall parameters of the wake oscillator [178]. In addition, the application of the NES to wind-sensitive structures such as tall buildings, hagh-rise structures and flexible bridges has gradually become a topic of future research being interested by many scholars [179-180]."

172. Vanderveldt, H.H.; Chung, B.S.; Reader, W.T. Some dynamic properties of axially loaded wire ropes. Mech. 1973, 13, 24-30.
173. Ni, Y.Q.; Ko, J.M.; Wong, C.W.; Zhan, S. Modelling and identification of a wire-cable vibration isolator via a cyclic loading test. I. Mech. Eng. I-J Sys. 1999, 213, 163-172.
174. Tinker, M.L.; Cutchins, M.A. Damping phenomena in a wire rope vibration isolation system. Sound Vib. 1992, 157, 7-18.
175. Cao, Y.; Yao, H.; Li, Q.; Yang, P.; Wen, B. Vibration mitigation and dynamics of a rotor-blade system with an attached nonlinear energy sink. J. Non-Lin. Mech. 2020, 127, 103614.
176. Li, H.; Li, A.; Kong, X. Design criteria of bistable nonlinear energy sink in steady-state dynamics of beams and plates. Nonlinear Dyn. 2021, 103, 1475-1497.
177. Leroux, M.; Langlois, S.; Savadkoohi, A.T. Nonlinear passive control of galloping of overhead transmission lines: Design and numerical verifications. Sur, Vib. Shock Noise. 2023.
178. Gupta, S.K.; Malla, A.L.; Barry, O.R. Nonlinear vibration analysis of vortex-induced vibrations in overhead power lines with nonlinear vibration absorbers. Nonlinear Dyn. 2021, 103, 27-47.
179. Chen, D.; Gu, C.; Fang, K.; Yang, J.; Guo, D.; Marzocca, P. Vortex-induced vibration of a cylinder with nonlinear energy sink (NES) at low Reynolds number. Nonlinear Dyn. 2021, 104, 1937-1954.
180. Zuo, H.; Zhu, S. Development of novel track nonlinear energy sinks for seismic performance improvement of offshore wind turbine towers. Syst. Signal Pr. 2022, 172, 108975.

 

Question 7 (from Reviewer 3):

Are these methods applicable for wind-sensitive structures with active or passive vibration dissipation systems such as active/passive dampers or base isolation?

Answer:

The methods in this paper are considered for the wind-induced nonlinearities of four typical wind-sensitive structures. Additions to the substructure may have an influence on affecting the wind-induced response of the structure but are not relevant to the applicability of these methods. Adding active or passive dampers to the structure can be regarded as adding substructures to the main structure, and the addition of substructures does not affect the applicability of these methods. Therefore, these methods are applicable to the structures mentioned by the reviewer. For example, the forced vibration test method for identifying nonlinear aerodynamic damping in tall buildings is mentioned in Section 3 (Tall buildings). Attaching dampers to a tall building changes the wind-induced vibration nonlinear behavior of the original structure, but this does not affect the effectiveness of the forced vibration test in identifying wind-induced vibration nonlinear features. Another example is the Lindstedt-Poincare perturbation method for solving the nonlinear vibration equations mentioned in Section 5 (Transmission lines). For transmission lines with additional dampers, new nonlinear vibration equations need to be developed with respect to the dampers, but the idea of the Lindstedt-Poincare perturbation method remains the same in solving the nonlinear vibration equations.

 

Question 8 (from Reviewer 3)

The author needs to add a reference for general statements in the context. This happened multiple times in the manuscript such as line 81, 251, etc.

Answer:

We carefully recheck the general statement in the context. New references have been added to support these places where similar problems occur.

(see page 2 and lines 73, the page 2 and lines 79, the page 6 and lines 195, the page 8 and lines 283, the page 9 and lines 317 in the revised paper respectively).

 

Question 9 (from Reviewer 3):

The author needs to explain how the review paper was structured and what methods are used for obtaining the resources related to this topic. What aspects are not accounted for in the research?

Answer:

Tall buildings, high-rise structures, flexible bridges and transmission lines are not only important urban infrastructures, but also their unique structural behavior makes them more sensitive to wind loading effects. The problem of wind-induced nonlinear effects affecting their structural stability and safety has become increasingly prominent. The authors and the author's team have been engaged in research related to the wind-resistant design of wind-sensitive structures such as transmission towers and large-span flexible bridges for many years, and have sufficient background knowledge and understanding of wind-induced nonlinear analysis, including structural engineering, wind mechanics, nonlinear analysis methods, and other related fields. In constructing this review, extensive and systematic literature research on the more prominent wind nonlinear problems of four common wind-sensitive structures, namely, high-rise buildings, towering structures, flexible bridges, and transmission lines, is conducted to cover the major research progress and results in the related fields, such as the identification of cross-wind nonlinear aerodynamic damping in tall buildings, the geometric and material nonlinear effects at the local nodes of high-rise structures, the wind-induced nonlinear flutter behavior of bridges and strong geometric nonlinear characteristics of ice-covered transmission lines under the action of wind loads. Combined with the previous research experience on wind-induced nonlinear vibration theory and experimental methods, this literature is comprehensively analyzed and summarized, and the different research results are compared, generalized, and summarized to equip the written review paper with accurate arguments and proper citations.

This review paper focuses on the mainstream research on wind-induced nonlinear problems for four types of wind-sensitive structures, but the summary may be insufficient in some emerging or more specialized research areas, for example, for nonlinear problems under complex wind fields in coastal and mountainous areas, there is a lack of field measurement related research to be further supplemented and summarized in a unified model, especially for transient and non-Gaussian wind fields. The more advanced analysis, modeling and identification tools involved in wind tunnel tests are yet to be fully considered. In addition, the development of new predictive analysis tools in conjunction with artificial intelligence information technology is a new area of current research. Advanced nonlinear vibration control methods, such as aerodynamic optimization methods adapted to different Archimedean Optimization Algorithms (AOAs) and nonlinear damper control measures.

 

Question 10 (from Reviewer 3):

The author needs to explore the application of mentioned methods for all four wind-sensitive structures in well-known international codes and standards.

Answer:

We feel great thanks for your professional review work on our article. Based on your nice suggestions, we have added the following modifications regarding the application of the wind-induced nonlinear analysis methods for the four wind-sensitive structures mentioned above in well-known international codes and standards.

"However, the method uses a linearized solution that assumes a quasi-linear relationship between the building surface wind pressure and the incoming wind speed in the time domain with simultaneous pulsations. For example, the gust load factor widely used in codes and standards [11,12] is based on a Gaussian framework, so the term containing the velocity fluctuation squared is removed from the equation." (see page 3 and lines 85-89 in the revised paper).

11. Australia/New Zealand Standard, Structural Design Actions. Part 2: Wind Actions; AS/NZS 1170.2; Standards Australia International Ltd.: Sydney, Australia; Standards New Zealand: Wellington, New Zealand, 2011.
12. Minimum Design Loads for Buildings and Other Structures; ASCE 7-10; American Society of Civil Engineers: Reston, VA, USA, 2013.

 

"Vickery and Basu [31] developed a theoretical basis for aerodynamic damping modeling, and the aerodynamic damping model proposed by Vickery and Basu has been adopted by several codes and standards [32-34] in addition to being used for solving the cross-wind response in the framework of stochastic vibrations [35]. However, it has been shown that the response calculated using this aerodynamic damping model does not agree with the response measured in wind tunnel tests and may significantly overestimate the side wind response in most cases, especially for cylinders with small Scruton numbers [36,37]." (see page 5 and lines 173-180 in the revised paper).

31. Vickery, B.J.; Basu, R.I. Across-wind vibrations of structures of circular cross section. Part I: development of a mathematical model for two-dimensional conditions. Wind Eng. Ind. Aerod. 1983, 12, 49–73.
32. The American Society of Mechanical Engineers; ASME STS-1-2006; American Society of Mechanical Engineers: New York, USA, 2006.
33. CICIND Model Code for Steel Chimneys; CICIND 2010; International Committee for Industrial Construction: Ratingen, Germany, 2010.
34. Eurocode 1: Actions on structures; EN 1991; European Commission: Brussels, Belgium, 2010.
35. Vickery, B.J.; Clark, A.W. Lift of across-wind response of tapered stacks. Proceedings American Society of Civil Engineering. Struct. Div. 1972, 1, 1– 19.
36. Verboom, G.K.; Koten, H. Vortex excitation: three design rules tested on 13 industrial chimneys. Wind Eng. Ind. Aerod. 2010, 98, 145– 154.
37. Lupi, F.; Niemann, H.J.; Hoffer, R. A novel spectral method for cross-wind vibrations: application to 27 full-scale chimneys. Wind Eng. Ind. Aerod. 2017, 171, 353–365.

 

Question 11 (from Reviewer 3):

The conclusion part needs to be improved. The conclusion of this review paper not only needs to critically compare and identify the required parameters for each wind-sensitive structure but also identify the important challenges and gaps in the literature and enough insight for future research.

Answer:

This review article shows that developments in blunt-body aerodynamics and aeroelasticity over the past few decades have enhanced our ability to better understand and capture the effects of wind-induced nonlinearities on wind-sensitive structures, while at the same time progressively recognizing that, due to the emergence of new materials and new structural forms, as well as more comprehensive and accurate observations of extremes such as tornadoes and downburst storms, previously smooth, Gaussian, and linear characteristics of the implicit assumptions have departed from the actual structural wind vibration response. In order to study the mechanism of wind nonlinearities and to mitigate the hazards of wind nonlinear vibration, further theoretical studies or experimental methods related to wind nonlinearities are needed. Based on the reviewers' suggestions, we re-summarize the key findings discussed in this review article and the outlook for future research as follows: (see page 19 and lines 735-750 in the revised paper).

"(5) Existing instruments for free or forced vibration tests are not accurate enough to identify wind load parameters in the nonlinear region, and there is no uniformly recognized computational model for cross-wind nonlinear aerodynamic damping of tall buildings and nonlinear self-excited aerodynamic forces of flexible bridges, which still need to be explored. In addition, the complex numerical calculations and nonlinear analyses involved in wind-induced nonlinear effects still consume a lot of computational resources and time, especially for complex wind field conditions or flexible and variable structural forms. There is still a lack of sufficient in situ measurements to support the study of complex wind fields in coastal and mountainous regions, and uniform models need to be further supplemented and summarized, especially for transient and non-Gaussian wind fields. Some of the major challenges ahead include further development of analytical, modeling and identification tools to facilitate modeling of nonlinear features. The development of new predictive analysis tools in conjunction with artificial intelligence information technology is also a challenging area of research. Advanced suppression methods, such as aerodynamic optimization methods adapted to different Archimedean optimization algorithms (AOAs), and nonlinear damper control measures, are promising."

Author Response File: Author Response.docx

Reviewer 3 Report

1-     The author needs to explain how the review paper was structured and what methods are used for obtaining the resources related to this topic. What aspects are not accounted for in the research?

  

2-     The author needs to explore the application of mentioned methods for all four wind-sensitive structures in well-known international codes and standards.

 

3-      Are these methods applicable for wind-sensitive structures with active or passive vibration dissipation systems such as active/passive dampers or base isolation?

 

4-     The author needs to explain how the graphs in Figures 4, 7, and 8 are created or cite the reference for each one of them.

 

5-     The author needs to add a reference for general statements in the context. This happened multiple times in the manuscript such as line 81, 251, etc.

 

 

6-     The conclusion part needs to be improved. The conclusion of this review paper not only needs to critically compare and identify the required parameters for each wind-sensitive structure but also identify the important challenges and gaps in the literature and enough insight for future research.

Minor editing required for the fluency of the manuscript.  

Author Response

Response to Reviewers’ Comments

We appreciate the careful reading and valuable comments given by the reviewers. We have made changes in the manuscript (indicated there by a highlighter) by taking into account the reviewers’ comments and suggestions. The following summarizes the detailed responses to reviewer 1, reviewer 2 and reviewer 3.

 

Question 1 (from Reviewer 1):

The paper is well written, and concise and precise, my only comments on the abstract to be summarized or shorten, and must be straightforward and clear to the readers. The abstract should be improved. The abstract should be improved. The abstract should contain the motivation and most important information of the study.

Answer:

The nonlinear behavior of four common wind-sensitive structures, namely, tall buildings, high-rise structures, flexible bridges and transmission lines, is increasingly prominent under the action of wind loads. The purpose of this paper is to reveal the occurrence mechanism of the nonlinear effects of the above wind-sensitive structures by summarizing their geometric nonlinearities, material nonlinearities and aerodynamic nonlinearities. It provides cutting-edge research advances in theoretical studies, experimental methods and vibration-damping control, and points out the unsolved or insufficient key problems and challenges identified in the existing studies to shed light on future research directions. The first two sentences of the Abstract in the original manuscript have been revised to indicate the motivation for this paper, as follows: (see page 1 and lines 11-16 in the revised paper)

"The nonlinear effects exhibited by structures under the action of wind loads have gradually stepped into the vision of wind-resistant researchers. By summarizing the prominent wind-induced nonlinear problems of four types of wind-sensitive structures, namely, tall buildings, high-rise structures, flexible bridges and transmission lines, to reveal the occurrence mechanism of their nonlinear effects and to provide cutting-edge research progress in theoretical studies, experimental methods and vibration control."

Some important information is added in the Section of the Abstract. This added information involves methods for solving nonlinear vibration equations, modeling methods for analyzing local nodes GN and MN, nonlinear aerodynamic models of Bridges, existing shortcomings and some future challenges, as follows: (see page 1, lines 18-31 in the revised paper)

"The equivalent nonlinear equation method is used to solve nonlinear vibration equations with generalized van der Pol-type aerodynamic damping terms. The elastic-plastic finite element method and multi-scale modeling method are widely employed to analyze the effects of geometric nonlinearity (GN) and material nonlinearity (MN) at local nodes on the wind-induced response of latticed tall structures."

"Volterra series aerodynamic models are more suitable for nonlinear aerodynamic modeling of Bridges than polynomial models studied more in the past."

"The complex numerical calculations and nonlinear analyses involved in wind-induced nonlinear effects continue to consume significant computational resources and time, especially for complex wind field conditions and flexible and variable structural forms. It is necessary to further development of analytical, modeling and identification tools to facilitate the modeling of nonlinear features in the future."

To make the Abstract concise and straightforward, we have deleted part of the description of the phenomenon of structural nonlinear effects, but retained the more important conclusions of nonlinear problems. In addition, we have deleted some unnecessary expressions of "has become an important research hotspot in the field of bridge wind engineering" and "a common solution method". These revisions are as follows: (see page 1 and lines 23-24 in the revised paper).

"Volterra series aerodynamic models are more suitable for nonlinear aerodynamic modeling of Bridges than polynomial models studied more in the past."

 

Question 2 (from Reviewer 1):

Line 176 - F₁ and F₂ in Equation (1) should be explained more fully. Figure 5 - The manuscript only explains the three methods First-order inelastic analysis, Second-order elastic analysis and Second-order inelastic analysis. Why is there no explanation for the other methods mentioned in Figure 5, such as First-order elastic analysis. Figure 7 - The lines representing doubled-frequency and mixed-frequency in Figure 7 (b) should be indicated in a reasonable way to facilitate understanding.

Answer:

We have supplemented or modified the content according to the reviewer's suggestions as follows：

Equation (3) and Equation (4) are added to give a fuller explanation of F₁ and F₂, respectively. (see page 6 and lines 182 in the revised paper).

"	(3)"
"	(4)"

" and  are model parameters " is added to explain the parameters in Equation (3) and Equation (4). (see page 6 and lines 184 in the revised paper).

 

This part mainly introduces a range of structural wind-induced non-linear analysis methods, so the explanation of the First-order elastic analysis is omitted because it is a method within the elastic range. The description of this section is modified as follows:

"These methods are summarized in Figure 5:" is replaced by "Since the First-order elastic analysis in Figure 5 is a method within the elastic range, only the other three methods are summarized as follows:" (see page 8 and lines 290 in the revised paper).

 

The lines representing doubled-frequency and mixed-frequency in Figure 7 (b) have been modified for facilitate understanding as follows.

"As shown by the dashed line in Figure 7, by applying forced vibration with vertical frequency f_h and torsional frequency f_a to the main beam, Chen [110] find that there may be doubled-frequency (2f_h and 2f_a, etc.) and mixed-frequency (f_a - f_h and f_a + f_h, etc.) components in the self-excited lift amplitude spectrum S_sl and in the self-excited torque amplitude spectrum S_st." (see page 12 and lines 437 in the revised paper).

(a)	(b)

Figure 7. Higher-order components in the self-excited force: (a) Displacement input; (b) Self-excited force output [110].

 

Question 3 (from Reviewer 1):

The authors should carefully address the details of the paper, e.g.: tense, and writing format. English can be improved.

Answer:

A native English-speaker has reviewed and edited the original text to polish the language. Some revisions are as follows:

1. The expression "evolution" is replaced by "evolutionary";(see page 1 and lines 44 in the revised paper)

"This will allow for a deeper understanding of the nonlinear properties, mechanisms, and evolutionary laws associated with wind-induced phenomena."

2. The expression "nonlinearly vary" is replaced by "vary nonlinearly";(see page 4 and lines 143 in the revised paper)

"The vortex-locked wind speed region, occurring during vortex-induced resonance, causes the aerodynamic damping to vary nonlinearly with wind speed and amplitude, resulting in significant AN."

3. The expression "at a given wind speed" is replaced by "for a given wind speed";(see page 7 and lines 243 in the revised paper)

"To overcome the limitations of equivalent aerodynamic damping models, aerodynamic damping is further described as a function of time-variant displacement or velocity for a given wind speed."

4. The expression "amplifies" is replaced by "has amplified";(see page 12 and lines 446 in the revised paper)

"The obtuse body structure of the bridge, coupled with its mode-dense characteristics, has amplified the significance of aerodynamic higher-order effects."

5. The expression "can be highly sensitive" is replaced by "is highly sensitive";(see page 14 and lines 494 in the revised paper)

"However, the specific form of the polynomial aerodynamic model is highly sensitive to the profile of the bridge structure section."

6. The expression "on input amplitude" is replaced by "on the input amplitude";(see page 15 and lines 514 in the revised paper)

"The third-order Volterra series model can capture the dependence of the system transfer function on the input amplitude, such as the flutter derivative with amplitude."

7. The expression "so MN is" is replaced by "and thus MN is";(see page 15 and lines 537 in the revised paper)

"However, its elongation deformation is typically considered as a smaller range of linear elastic deformation, and thus MN is generally ignored."

8. The expression "does not effectively reduce" is replaced by "is not effective in reducing";(see page 16 and lines 564 in the revised paper)

"The results demonstrated that increasing mechanical damping is not effective in reducing the amplitude of wake-induced galloping in the leeward cylindrical wake when the windward cylinder is fixed."

9. The expression "overlooking GN resulting from " is replaced by "neglecting the GN induced by";(see page 16 and lines 575 in the revised paper)

"However, they used the mode superposition method to solve the galloping equations, neglecting the GN induced by large-amplitude motion "

10. The expression "a failure " is replaced by "fails";(see page 17 and lines 645 in the revised paper)

"They found that neglecting static swing leads to an overestimation of the along-wind dynamic displacement and fails to capture the dynamic cross-wind and longitudinal tensions."

 

Question 4 (from Reviewer 2):

It is stated that there are few researches on torsional wind-induced nonlinear effects in tall buildings. This is not true since the torsional of vibration of tall buildings are also investigated by several authors. As the reviewer understands, tall building is a type of high-rise building. The authors are suggested to revise the title of Section 2 and Section 3.

Answer:

We sincerely appreciate the valuable comments. We have checked the literature carefully and added some research progress on torsional wind-induced nonlinear effects of tall buildings in the revised manuscript. (see page 7 and lines 258-281 in the revised paper).

"Wind-induced nonlinear torsional vibration in tall buildings is usually caused by the imbalance in the instantaneous wind pressure distributions on all building surfaces and the eccentricity between the elastic and mass centers [59,60]. For symmetric tall buildings with large stiffness, the asymmetric aerodynamic-induced torsion is usually small and generally negligible. However, for flexible tall buildings, rotating members can generate large shear forces and bending moments in the members, and the torque loads may have nonlinear coupling effects with downwind and lateral loads, resulting in a strong wind vibration response [61]. Especially slender tall buildings tend to suffer greater rotational damage under wind loads. Ref. [62] studied the torsional response for symmetric and asymmetric linear systems, where the relative distance between the center of mass (CM) and the center of stiffness (CS) varies with time during structural motions and an instantaneous load eccentricity occurs during horizontal motions of the CM in the plane, which may lead to additional torsional motions not considered in codes [11,12,63], naming this second-order nonlinear effect as the A-∆ effect. Some authors [64] solved the nonlinear differential equations considering the A-∆ second-order nonlinear effect by means of state-space model assembly, and showed that the A-∆ effect has a small effect on the wind-driven displacements and accelerations, but the correlation coefficients between the wind forces have the most important influence on the response, suggesting that the different correlation levels between the wind force and the torque must be taken into account in the evaluation of the wind-driven response. In addition, nonlinearities may cause the structure to become more flexible, thereby increasing the dynamic response of the structure [65], and therefore further analysis is required to assess the impact of the A-∆ effect on the wind response of high-rise buildings considering both structural geometric nonlinearities and material nonlinear behavior."

 

26. Australia/New Zealand Standard, Structural Design Actions. Part 2: Wind Actions; AS/NZS 1170.2; Standards Australia International Ltd.: Sydney, Australia; Standards New Zealand: Wellington, New Zealand, 2011.
27. Minimum Design Loads for Buildings and Other Structures; ASCE 7-10; American Society of Civil Engineers: Reston, VA, USA, 2013.
28. Li, Y. g.; Liu, P.; Li, Y.; Yan, J. h.; Quan, J. Wind loads characteristics of irregular shaped high-rise buildings. Struct. Eng. 2023, 26, 3-16.
29. Bhattacharya, S.; Dalui, S.K. Effect of tuned mass damper in wind-induced response of “v” plan-shaped tall building. Des. Tall Spec. 2022, 31, e1931.
30. Hou, F.; Jafari, M. Investigation approaches to quantify wind-induced load and response of tall buildings: A review. Cities Soc. 2020, 62, 102376.
31. Hong, H.P. Torsional responses under bidirectional seismic excitations: Effect of instantaneous load eccentricities. Struct. Eng. 2013, 139, 133-143.
32. Ministry of Construction of the People’s Republic of China. Load Code for the Design of Building Structures; GB 50009—2012; China Architecture and Building Press: Beijing, China, 2012.
33. López-Ibarra, A.; Pozos-Estrada, A.; Nava-González, R. Effect of partially correlated wind loading on the response of two-way asymmetric systems: The impact of torsional sensitivity and nonlinear effects. Sci. 2023, 13, 6421.
34. Man, X.; Bin, Z.; Hong, Q.; Qing, X.; Guo, W.W.; He, X. Nonlinear dynamic response analysis of wind-train-bridge coupling system of hu-su-tong bridge. Mech. 2021, 38, 83.

 

The main difference between tall buildings and high-rise structures mentioned in the manuscript is that the former usually refers to office buildings, shopping malls, and other buildings that need to consider personnel access and life, while the latter refers to structures that people cannot be used for production and life, such as transmission towers, cooling towers, TV towers, etc. The above explanation was added to the new content of section 1 (Introduction) of the manuscript. (see page 1 and lines 39-41 in the revised paper).

"(To distinguish from the tall buildings, high-rise structures here are those that people cannot use for production and living, such as transmission towers, cooling towers, TV towers, etc.)"

 

Question 5 (from Reviewer 2 and Reviewer 3):

Some figures are re-drawn from previous papers. References should be provided for those figures. The author needs to explain how the graphs in Figures 4, 7, and 8 are created or cite the reference for each one of them.

Answer:

As suggested by the reviewers, the corresponding references are cited for Figures 4,7, and 8. The references are annotated in the statement and name sections of these figures.

(see page 5 and lines 155, page 12 and lines 437, page 13 and lines 461 in the revised paper respectively).

 

Question 6 (from Reviewer 2):

The nonlinearity from additional dampers is another of nonlinearity that is drawn increasing attention in recent years, e.g., Vortex-induced vibration control of a flexible circular cylinder using a nonlinear energy sink, Effect of inerter locations on the vibration control performance of nonlinear energy sink inerter. It is suggested to comment a bit on this topic.

 

Answer:

We sincerely appreciate the valuable comments. Adding additional dampers to wind-sensitive structures is a practical and effective measure to reduce the harm caused by nonlinear dynamic wind loads on the structures. As you are concerned, the nonlinear problem of additional dampers is a particularly important research topic in recent years. Therefore, we have checked the manuscript content carefully and added some research progress on the nonlinearity from additional dampers in Section 5 (Transmission lines) of the revised manuscript. (see page 17 and lines 652-673 in the revised paper).

"In recent years, the topic of reducing the hazards caused by nonlinear dynamic wind loading effects on transmission lines is of particular importance. Inter-wire friction is a major source of energy dissipation [172]. Its application to vibration isolation systems is considered advantageous. The spiral wire rope isolator (WRI) is a typical nonlinear hysteretic damping device [173], which is also effective for wind-induced vibration control of transmission lines [174]. In addition, a newly developed nonlinear energy sink (NES) damper [175,176] is the current research hotspot of nonlinear dampers. The NES damper is more stable compared to the general damper, due to its frequency-energy dependence, which makes it able to act nonlinearly in a broadband frequency-energy manner and is more predictable and controllable in the theoretical analysis of parameter optimization. Some scholars have utilized the segmented linear recovery forcing function of the NES has by adding nonlinear dampers with NES to single-span tension cables for mitigating chirp vibration [177]. For the problem of nonlinear dynamic interactions between transmission lines, nonlinear dampers and wind, scholars have combined the nonlinearity of plane stretching in the conductor, the equivalent cubic stiffness of the Stockbridge damper and the pulsating lift modeled as a Vanderbilt oscillator in a single model in order to study nonlinear vortex-excited vibrations of transmission lines. The results show that the nonlinearity in the system disappears with increasing axial tension and stall parameters of the wake oscillator [178]. In addition, the application of the NES to wind-sensitive structures such as tall buildings, hagh-rise structures and flexible bridges has gradually become a topic of future research being interested by many scholars [179-180]."

172. Vanderveldt, H.H.; Chung, B.S.; Reader, W.T. Some dynamic properties of axially loaded wire ropes. Mech. 1973, 13, 24-30.
173. Ni, Y.Q.; Ko, J.M.; Wong, C.W.; Zhan, S. Modelling and identification of a wire-cable vibration isolator via a cyclic loading test. I. Mech. Eng. I-J Sys. 1999, 213, 163-172.
174. Tinker, M.L.; Cutchins, M.A. Damping phenomena in a wire rope vibration isolation system. Sound Vib. 1992, 157, 7-18.
175. Cao, Y.; Yao, H.; Li, Q.; Yang, P.; Wen, B. Vibration mitigation and dynamics of a rotor-blade system with an attached nonlinear energy sink. J. Non-Lin. Mech. 2020, 127, 103614.
176. Li, H.; Li, A.; Kong, X. Design criteria of bistable nonlinear energy sink in steady-state dynamics of beams and plates. Nonlinear Dyn. 2021, 103, 1475-1497.
177. Leroux, M.; Langlois, S.; Savadkoohi, A.T. Nonlinear passive control of galloping of overhead transmission lines: Design and numerical verifications. Sur, Vib. Shock Noise. 2023.
178. Gupta, S.K.; Malla, A.L.; Barry, O.R. Nonlinear vibration analysis of vortex-induced vibrations in overhead power lines with nonlinear vibration absorbers. Nonlinear Dyn. 2021, 103, 27-47.
179. Chen, D.; Gu, C.; Fang, K.; Yang, J.; Guo, D.; Marzocca, P. Vortex-induced vibration of a cylinder with nonlinear energy sink (NES) at low Reynolds number. Nonlinear Dyn. 2021, 104, 1937-1954.
180. Zuo, H.; Zhu, S. Development of novel track nonlinear energy sinks for seismic performance improvement of offshore wind turbine towers. Syst. Signal Pr. 2022, 172, 108975.

 

Question 7 (from Reviewer 3):

Are these methods applicable for wind-sensitive structures with active or passive vibration dissipation systems such as active/passive dampers or base isolation?

Answer:

The methods in this paper are considered for the wind-induced nonlinearities of four typical wind-sensitive structures. Additions to the substructure may have an influence on affecting the wind-induced response of the structure but are not relevant to the applicability of these methods. Adding active or passive dampers to the structure can be regarded as adding substructures to the main structure, and the addition of substructures does not affect the applicability of these methods. Therefore, these methods are applicable to the structures mentioned by the reviewer. For example, the forced vibration test method for identifying nonlinear aerodynamic damping in tall buildings is mentioned in Section 3 (Tall buildings). Attaching dampers to a tall building changes the wind-induced vibration nonlinear behavior of the original structure, but this does not affect the effectiveness of the forced vibration test in identifying wind-induced vibration nonlinear features. Another example is the Lindstedt-Poincare perturbation method for solving the nonlinear vibration equations mentioned in Section 5 (Transmission lines). For transmission lines with additional dampers, new nonlinear vibration equations need to be developed with respect to the dampers, but the idea of the Lindstedt-Poincare perturbation method remains the same in solving the nonlinear vibration equations.

 

Question 8 (from Reviewer 3)

The author needs to add a reference for general statements in the context. This happened multiple times in the manuscript such as line 81, 251, etc.

Answer:

We carefully recheck the general statement in the context. New references have been added to support these places where similar problems occur.

(see page 2 and lines 73, the page 2 and lines 79, the page 6 and lines 195, the page 8 and lines 283, the page 9 and lines 317 in the revised paper respectively).

 

Question 9 (from Reviewer 3):

The author needs to explain how the review paper was structured and what methods are used for obtaining the resources related to this topic. What aspects are not accounted for in the research?

Answer:

Tall buildings, high-rise structures, flexible bridges and transmission lines are not only important urban infrastructures, but also their unique structural behavior makes them more sensitive to wind loading effects. The problem of wind-induced nonlinear effects affecting their structural stability and safety has become increasingly prominent. The authors and the author's team have been engaged in research related to the wind-resistant design of wind-sensitive structures such as transmission towers and large-span flexible bridges for many years, and have sufficient background knowledge and understanding of wind-induced nonlinear analysis, including structural engineering, wind mechanics, nonlinear analysis methods, and other related fields. In constructing this review, extensive and systematic literature research on the more prominent wind nonlinear problems of four common wind-sensitive structures, namely, high-rise buildings, towering structures, flexible bridges, and transmission lines, is conducted to cover the major research progress and results in the related fields, such as the identification of cross-wind nonlinear aerodynamic damping in tall buildings, the geometric and material nonlinear effects at the local nodes of high-rise structures, the wind-induced nonlinear flutter behavior of bridges and strong geometric nonlinear characteristics of ice-covered transmission lines under the action of wind loads. Combined with the previous research experience on wind-induced nonlinear vibration theory and experimental methods, this literature is comprehensively analyzed and summarized, and the different research results are compared, generalized, and summarized to equip the written review paper with accurate arguments and proper citations.

This review paper focuses on the mainstream research on wind-induced nonlinear problems for four types of wind-sensitive structures, but the summary may be insufficient in some emerging or more specialized research areas, for example, for nonlinear problems under complex wind fields in coastal and mountainous areas, there is a lack of field measurement related research to be further supplemented and summarized in a unified model, especially for transient and non-Gaussian wind fields. The more advanced analysis, modeling and identification tools involved in wind tunnel tests are yet to be fully considered. In addition, the development of new predictive analysis tools in conjunction with artificial intelligence information technology is a new area of current research. Advanced nonlinear vibration control methods, such as aerodynamic optimization methods adapted to different Archimedean Optimization Algorithms (AOAs) and nonlinear damper control measures.

 

Question 10 (from Reviewer 3):

The author needs to explore the application of mentioned methods for all four wind-sensitive structures in well-known international codes and standards.

Answer:

We feel great thanks for your professional review work on our article. Based on your nice suggestions, we have added the following modifications regarding the application of the wind-induced nonlinear analysis methods for the four wind-sensitive structures mentioned above in well-known international codes and standards.

"However, the method uses a linearized solution that assumes a quasi-linear relationship between the building surface wind pressure and the incoming wind speed in the time domain with simultaneous pulsations. For example, the gust load factor widely used in codes and standards [11,12] is based on a Gaussian framework, so the term containing the velocity fluctuation squared is removed from the equation." (see page 3 and lines 85-89 in the revised paper).

11. Australia/New Zealand Standard, Structural Design Actions. Part 2: Wind Actions; AS/NZS 1170.2; Standards Australia International Ltd.: Sydney, Australia; Standards New Zealand: Wellington, New Zealand, 2011.
12. Minimum Design Loads for Buildings and Other Structures; ASCE 7-10; American Society of Civil Engineers: Reston, VA, USA, 2013.

 

"Vickery and Basu [31] developed a theoretical basis for aerodynamic damping modeling, and the aerodynamic damping model proposed by Vickery and Basu has been adopted by several codes and standards [32-34] in addition to being used for solving the cross-wind response in the framework of stochastic vibrations [35]. However, it has been shown that the response calculated using this aerodynamic damping model does not agree with the response measured in wind tunnel tests and may significantly overestimate the side wind response in most cases, especially for cylinders with small Scruton numbers [36,37]." (see page 5 and lines 173-180 in the revised paper).

31. Vickery, B.J.; Basu, R.I. Across-wind vibrations of structures of circular cross section. Part I: development of a mathematical model for two-dimensional conditions. Wind Eng. Ind. Aerod. 1983, 12, 49–73.
32. The American Society of Mechanical Engineers; ASME STS-1-2006; American Society of Mechanical Engineers: New York, USA, 2006.
33. CICIND Model Code for Steel Chimneys; CICIND 2010; International Committee for Industrial Construction: Ratingen, Germany, 2010.
34. Eurocode 1: Actions on structures; EN 1991; European Commission: Brussels, Belgium, 2010.
35. Vickery, B.J.; Clark, A.W. Lift of across-wind response of tapered stacks. Proceedings American Society of Civil Engineering. Struct. Div. 1972, 1, 1– 19.
36. Verboom, G.K.; Koten, H. Vortex excitation: three design rules tested on 13 industrial chimneys. Wind Eng. Ind. Aerod. 2010, 98, 145– 154.
37. Lupi, F.; Niemann, H.J.; Hoffer, R. A novel spectral method for cross-wind vibrations: application to 27 full-scale chimneys. Wind Eng. Ind. Aerod. 2017, 171, 353–365.

 

Question 11 (from Reviewer 3):

The conclusion part needs to be improved. The conclusion of this review paper not only needs to critically compare and identify the required parameters for each wind-sensitive structure but also identify the important challenges and gaps in the literature and enough insight for future research.

Answer:

This review article shows that developments in blunt-body aerodynamics and aeroelasticity over the past few decades have enhanced our ability to better understand and capture the effects of wind-induced nonlinearities on wind-sensitive structures, while at the same time progressively recognizing that, due to the emergence of new materials and new structural forms, as well as more comprehensive and accurate observations of extremes such as tornadoes and downburst storms, previously smooth, Gaussian, and linear characteristics of the implicit assumptions have departed from the actual structural wind vibration response. In order to study the mechanism of wind nonlinearities and to mitigate the hazards of wind nonlinear vibration, further theoretical studies or experimental methods related to wind nonlinearities are needed. Based on the reviewers' suggestions, we re-summarize the key findings discussed in this review article and the outlook for future research as follows: (see page 19 and lines 735-750 in the revised paper).

"(5) Existing instruments for free or forced vibration tests are not accurate enough to identify wind load parameters in the nonlinear region, and there is no uniformly recognized computational model for cross-wind nonlinear aerodynamic damping of tall buildings and nonlinear self-excited aerodynamic forces of flexible bridges, which still need to be explored. In addition, the complex numerical calculations and nonlinear analyses involved in wind-induced nonlinear effects still consume a lot of computational resources and time, especially for complex wind field conditions or flexible and variable structural forms. There is still a lack of sufficient in situ measurements to support the study of complex wind fields in coastal and mountainous regions, and uniform models need to be further supplemented and summarized, especially for transient and non-Gaussian wind fields. Some of the major challenges ahead include further development of analytical, modeling and identification tools to facilitate modeling of nonlinear features. The development of new predictive analysis tools in conjunction with artificial intelligence information technology is also a challenging area of research. Advanced suppression methods, such as aerodynamic optimization methods adapted to different Archimedean optimization algorithms (AOAs), and nonlinear damper control measures, are promising."

Author Response File: Author Response.docx

Round 2

Reviewer 2 Report

The paper can be accepted in the present form

Author Response

Response to Reviewers’ Comments

 

We appreciate the careful reading and valuable comments given by the reviewers. We have made changes in the manuscript (indicated there by yellow highlighter) by taking into account the reviewers’ comments and suggestions. The following summarizes the detailed responses to reviewer

 

Point 1(from Reviewer 2): The title seems not correct Review for wind-induced nonlinear analysis of tall buildings, high-rise structures, flexible bridges and transmission lines. I suggest Review for wind-induced effects estimation through nonlinear analysis of tall buildings, high-rise structures, flexible bridges and transmission lines.

Answer:

We sincerely appreciate the valuable comments. We have revised the title in the revised manuscript as follows. (See page 1 and lines 2-4 of the revised document)

"Review for wind-induced effects estimation through nonlinear analysis of tall buildings, high-rise structures, flexible bridges and transmission lines"

Author Response File: Author Response.docx