Critical Wind Speed Research Articles

Modal effects of span-layout types on coupled flutter of long-span suspension bridges

This study provides a theoretical explanation for a perplexing experimental phenomenon observed frequently in suspension bridge flutter testing, where the flutter critical wind speed (Ucr) predicted by two-dimensional (2D) section model testing is higher than that predicted by three-dimensional (3D) full aeroelastic model testing. Six long-span suspension bridges with either a single simply supported span or multiple continuously supported spans were taken as research examples, then the comparative studies on the flutter critical wind speeds, flutter frequencies, modal energy ratios and aerodynamic damping corresponding to 2D and 3D coupled flutter states were carried out to illustrate the flutter modal effects. The research findings indicate that the Ucr of 2D testing being higher than that of 3D testing is an inherent characteristic for single-span simply-supported suspension bridges, which can be attributed to the prominent aerodynamic negative damping associated with 2nd-order vertical bending mode. However, due to the aerodynamic positive damping associated with 3rd-order vertical bending mode, the Ucr of 2D testing is consistently lower than that of 3D testing in the cases of multi-spans continuously-supported suspension bridges. Additionally, to eliminate unsafe 2D evaluations, a reasonable modal matching principle is recommended for section model testing of single-span simply-supported suspension bridges.

Effects of wind-induced static angle of attack on flutter performance of long-span bridges using 2D bimodal and 3D multimodal analysis

Flutter performance of long span bridges is directly affected by winds featured with large angles of attack (AoAs) in typhon climates and mountainous areas. Flutter critical wind speed and flutter derivatives (FDs) of a streamlined closed-box girder under various initial AoAs are obtained by free and forced vibration wind tunnel tests of a section model, based on which the two-dimensional(2D) and three-dimensional (3D) flutter performance and evolution mechanisms are further investigated. The results indicate that FDs identified at small vibration amplitudes through different forced vibration control methods, i.e., fixing wind speed or vibration frequency, in wind axis or body axis are almost identical. The flutter performance of the closed-box girder is susceptible to the AoA. The flutter critical wind speed changes significantly with the initial AoA due to the nonlinear variation of some typical FDs. The sign of A2* shifts from negative to positive and the reduced wind speed associated with the sign change becomes lower as the initial AoA increases, which worsens the flutter performance. The flutter critical wind speed would significantly decrease because of the consideration of the static additional AoA in the range of positive initial AoA. In addition, the participation of multi modes and different longitudinal distribution of static additional AoA are taken into consideration in 3D numerical analysis, which have little influence on the flutter critical wind speed of long span bridges between the 2D and 3D numerical analysis.

Explicit solution framework and new insights of 3-DOF linear flutter considering various frequency relationships

Different engineering structures, e.g., long-span bridges, bundled conductors, and cable-supported photovoltaic modules, exhibit various frequency relationships among different degrees of freedom (DOFs). Despite extensive research, the initiation mechanisms of flutter remain somewhat ambiguous for a 3-DOF system considering heaving-lateral-torsional motions, especially when frequencies are close among different DOFs. This study introduced an explicit eigenvalue solution framework for tackling the 3-DOF linear flutter problem by utilizing matrix perturbation methods, enabling the extraction of modal damping and frequency solutions for all possible frequency scenarios. These solutions explicitly clarified the influence mechanism of all flutter derivatives (aerodynamic damping and stiffness), structural frequencies, and mechanical dampings. Important flutter derivatives, flutter risk level, and sensitivity level to mechanical damping and to frequency detuning were summarized in a table for all frequency scenarios, providing a panoramic perspective on flutter instability and the coupling mechanism. Numerical studies were conducted on a thin plate, the Akashi Kaikyo Bridge, and an eight-bundled conductor to examine the proposed explicit solutions. The results showed that approaching frequencies can amplify the coupling effect among different DOFs by half an order, but this does not necessarily mean the system is more prone to flutter. A system where the torsional frequency approximates the heaving/lateral frequency is expected to face a higher flutter risk if given significant torsional-related aerodynamic stiffness (H3*, P3*). Evidently, this high risk exhibits insensitivity to mechanical damping and small frequency-detuning. Though usually ignored in bridge flutter analysis, drag force and lateral motion could exert noticeable influence in a minority of cases, e.g., more than 10 m/s decrease of critical wind speed for the Akashi Kaikyo Bridge at large angles of attack. The proposed explicit solution framework provides a systematic view and new insights into the flutter initiation mechanism, serving as a reference in the design and studies of various engineering structures with different frequencies and coupling features.

Determinants of Hospital Length of Stay in Respiratory Infections: Insights from Cheras, Malaysia

Respiratory virus infections pose a significant public health concern, contributing to increase morbidity and mortality rates. This study investigated the determinants of hospital length of stay (LOS) for patients with Influenza-like illness (ILI) and Severe Acute Respiratory Infection (SARI). A quantitative study was conducted in Cheras, Kuala Lumpur, Malaysia, from 1 September 2022 until 28 February 2023. Demographic data, viral infection status (influenza A, influenza B, and COVID-19), and environmental factors (temperature, humidity, wind speed, and particulate matter levels) were collected for 632 patients. The data were analysed using ordinal logistic regression in Statistical Package for Social Sciences (SPSS) version 22.0. The results revealed that older age and higher body mass index (BMI) were associated with longer hospital stays, highlighting their significance as risk factors during respiratory outbreaks. Unexpectedly, patients tested positive for the investigated viruses experienced shorter LOS, indicating potential comorbidities or co-infections. Environmental factors played a critical role, with temperature, humidity, and wind speed significantly influencing LOS. These findings provided valuable insights for healthcare resource allocation during epidemics and underscored the need for comprehensive diagnostic tools and further research to enhance prediction accuracy.

The wind tunnel test research on the aerodynamic stability of wind turbine airfoils

The issue of nonlinear aerodynamic stability of blades is a significant technological bottleneck in the development of large-scale wind turbines. In order to explore the influencing parameters and mechanisms of the nonlinear aerodynamic stability of large-scale wind turbine blades, the flexible blade was simplified into a two-dimensional rigid blade segment with elastic supports, which formed the pitch single-degree-of-freedom aeroelastic wind tunnel test system. Through wind tunnel vibration and pressure measurement synchronization tests, the torsional vibration characteristics and the flow field development mechanism of the airfoil under different wind speeds and attack angles were studied in detail. The wind tunnel tests revealed two distinct torsional aeroelastic behaviors: the static equilibrium state with negligible amplitude and high vibrational randomness, and the stall flutter state with larger amplitude, which was changed according to sinusoidal law substantially. The stall flutter state was confined within a specific wind speed range, and its stability boundary, which included the critical initiation wind speed and the critical cessation wind speed, all varied linearly with the installation attack angle. The growth rate of the critical cessation wind speed with the installation attack angle was significantly higher than that of the critical initiation wind speed, making the wind speed range for the occurrence of stall flutter also linearly larger. Additionally, the frequency of the stall flutter was significantly higher than the natural frequency of the model, and it exhibited a positive correlation with the critical initiation wind speed. The flow state around the airfoil during stall flutter was primarily distinguished from its static counterpart by the presence of leading-edge vortices. The formation and shedding of these leading-edge vortices would significantly influence the characteristics of stall flutter.

Instantaneous Power Balance Algorithm for Flutter Critical Wind Speed Prediction of Bridge Girders

Instantaneous Power Balance Algorithm for Flutter Critical Wind Speed Prediction of Bridge Girders

Wind Resistance Performance Assessment of Long-Span Cable-Supported Bridges Based on Time-Varying Reliability Theory

Long-span cable-supported bridges constitute the most common type of bridge with a span of more than 400 m. They are generally designed as a double-tower long-span structure with good spanning capacity and economic performance. Wind resistance safety performance is the main index used to control the long-span cable-supported bridge structure. During the life of a long-span cable-supported bridge structure, because the service life of the cables is far shorter than the design life of the structure, the wind resistance performance of the structure will inevitably deteriorate significantly, which will seriously affect the structural service performance of symmetric cable-supported bridges. Under strong wind loads, the static wind stability and flutter stability of cable-stayed bridge structures are components of the limit state of bearing capacity, which directly affects the safety performance of the structure. We take the flutter and static wind stability of a long-span cable-supported bridge structure as the main design control index, use inverse reliability theory to calculate the reliability index of a symmetric cable-supported bridge structure, use inverse reliability theory to calculate the safety factor of a symmetric cable-supported bridge structure, and evaluate the time-varying wind resistance performance of a long-span cable-supported bridge structure by comprehensively considering the reliability index and safety factor. Taking a practical project concerning a long-span cable-supported bridge as a specific case, the time-varying wind resistance reliability of the bridge throughout its operation for more than 30 years is analyzed along with the parameter sensitivity. The results show that the wind resistance performance of the cable-supported bridge structure is obviously affected by its cables, and the degradation of cable performance will have a significant impact on the time-varying wind resistance performance of the structure, especially the critical wind speed of the structure, which has obvious time-varying characteristics. The safety factor and reliability index can be used to objectively evaluate the time-varying wind resistance performance of long-span cable-supported bridge structures.

Flutter control optimization for a 5000 m suspension bridge with active aerodynamic flaps: a CFD-enabled strategy

The theoretical model of self-excited aerodynamic force with four active flaps attached to the deck is proposed in this study for a 5000 m bridge with a broad slotted section. The feedback control method is introduced with details, and the phase lag and gain coefficient of the flaps according to the vertical and torsional motions of the deck are used as key control parameters. And the assumption of linear superposition of the aerodynamic forces of the deck and flaps is verified by computational fluid dynamics (CFD) simulations. On this basis, considering the angle of attack (AoA) effect, the flutter derivative of the deck-flap system is identified utilizing forced vibration technology in different states, and the flutter analysis is carried out by the two-dimensional two-degree-of-freedom method. The results indicate that the feedback control based on the vertical and torsional motions can effectively increase the critical wind speed of flutter of the system, and the effective control range of each flap is revealed. Besides, it is found that there is almost no stable phase lag which can make the critical state of the system be improved at all AoAs, the AoA has a great influence on the control parameters. Finally, the control effects using the double flaps are compared, and using the flaps on the outside of the deck gives a better flutter improvement than that using the flaps on the inside of the deck. Flutter performance of deck-flaps system can be improved even more by using more flaps. When the four flaps are activated, the flutter performance of the system can be improved by 45.13% under the unity gain coefficient.

Critical Wind Speed Analysis of Large-section Steel Box Girder Lifting in Urban Areas Based on Lifting Offset

This study takes the lifting of steel box girders for interchanging traffic in a certain area as the research background, and considers the limitation of lifting by the surrounding buildings during the lifting process. Combined with the topographic environment and climatic conditions where the project is located, based on the key technology of large-section steel box girder lifting construction, the displacement change of large-section steel box girder lifting under different wind speeds is explored. To this end, a method for calculating the lifting offset is proposed, aiming to provide guidance for the safe construction of large-section steel box girder lifting in urban areas. Meanwhile, the concept of critical wind speed is introduced in this study to determine the critical conditions in the lifting process, i.e., the lifting process may be unsafe when the wind speed reaches the critical wind speed. The results show that the average displacement of the most unfavourable member increases from 0.024m to 1.541m when the wind speed increases from 3m/s to 27m/s; under the same wind speed, different area to mass ratios have a greater effect on the member displacement; considering the safety of the lifting construction, it is recommended that the value of the critical wind speed should be taken as 17m/s, and it is recommended to stop the lifting of the member or to strengthen the safety measures when the wind speed is greater than the critical wind speed during the lifting process. By analysing the change of lifting displacement and critical wind speed, this study provides an important reference and decision-making basis for the construction safety of large-section steel box girder lifting in urban areas.

Formation and movement of multiple fire whirls

This paper presents an experimental study on the formation and movement characteristics of multiple fire whirls on the line fire under different slope angles (θ). Experiments were performed in a rotating screen facility with independently controlled heat release rate per unit length (Q˙l) and shear wind speed (us). The evolution of the line fire under different shear wind speeds and slope angles involved six regimes, including free line fire, interacting line fire, moving fire whirls, stationary fire whirls, stationary unstable fire whirls, and moving unstable fire whirls. The critical us for the formation and movement of fire whirls decreased roughly with increasing θ. The moving fire whirl would become stationary when us reached the critical value, which may be explained by the balance between the buoyancy-induced velocity and us. A correlation was proposed for predicting the critical shear wind speed of the stationary fire whirl on the sloped surface. The spacing between adjacent fire whirls increased steadily with us under various θ, and the dimensionless spacing depended on the dimensionless us by the 0.5 power law for all θ. The formation frequency of the moving fire whirl increased steadily with θ, and was inversely proportional to us. The variation of the average moving speed of the fire whirls with us differed among different θ. The average moving speed decreased steadily with us for the relatively low slope angles (θ ≤ 15°), and increased first and then decreased with us for the relatively large slope angles (θ ≥ 20°). The steady decrease of the flame height with the large us was associated with the apparent bulge structure at the flame tip, and the critical us for the occurrence of the bulge structure decreased at the relatively large slope angles (θ ≥ 20°).

Integrating wind disturbances into forest planning: a stochastic programming approach

Forest disturbances challenge our ability to carefully plan for sustainable use of forest resources. As forest disturbances are stochastic, we cannot plan for the disturbance at any specific time or location. However, we can prepare for the possibility of a disturbance by integrating its potential intensity range and frequency when developing forest management plans. This study uses stochastic programming to integrate wind intensity (wind speed) and wind event frequency (number of occurrences) into the forest planning process on a small coastal Finnish forest landscape. We used a mechanistic model to quantify the critical wind speed for tree felling, with a Monte Carlo approach to include wind damage and salvage logging into forest management alternatives. We apply a stochastic programming model to explore two objectives: maximizing the expected forest net present value or maximizing the even-flow of income. To assess the effects of improper wind risk assumptions in planning, we compare the results when optimizing for correct versus incorrect wind intensity and frequency assumptions. When maximizing for net present value, the impacts of misidentifying wind intensity and frequency are minor, likely due to harvests planned immediately as trees reach maturity. For the case when maximizing even-flow of income, incorrectly identifying wind intensity and frequency severely impacts the ability to meet the required harvest targets and reduces the expected net present value. The specific utility of risk mitigation therefore depends on the planning problem. Overall, we show that incorporating wind disturbances into forest planning can inform forest owners about how they can manage wind risk based on their specific risk preferences.

Flutter Suppression Effects of Movable Vertical Stabilizers on Suspension Bridges With Steel Box Girders

As the combination of springs and vertical stabilizers, the movable downward vertical central stabilizer (MDVCS) is proposed to further control the nonlinear flutter of super long‐span suspension bridges in this paper. A series of flutter suppression tests of closed‐box girders and twin‐box steel girders with various MDVCSs are conducted. Based on the coupled flutter theoretical method, the sensitivity analysis of two important parameters including the height and stiffness of MDVCS are carried out to compare their nonlinear flutter control mechanism. The results show that the flutter critical wind speed (Ucr) of the closed‐box girder continued to increase with the decrease of the height of the DVCS and the increase of spring stiffness, whereas the Ucr of the twin‐box girder increased at first and then decreased. The cubic polynomial function and quadratic Holliday function are suitable to modify the correction coefficients of Ucr for the closed‐box girder with various stiffnesses and heights of MDVCS, while the Lorentz peak‐value function and cubic polynomial function are suitable to modify the Ucr of the twin‐box girder. Furthermore, the MDVCS significantly changes the rules of two positive and negative aerodynamic damping ratios for the closed‐box girder and two negative aerodynamic damping ratios for the twin‐box girder. Besides, the peak vertical displacement amplitudes of the box girder are about half of the MDVCS, since both the height and stiffness of MDVCS alter the elliptical radius of vertical phase planes to affect the limit cycle oscillation of soft flutter, especially for the leeward MDVCS for the twin‐box girder.

Study on the effect of width and slope of large cross-section tunnel on critical velocity of fire

When a tunnel fire occurs, due to the difference of tunnel width and slope, both smoke countercurrent length distribution law and critical velocity will become different, and these two are very important parameters in tunnel longitudinal ventilation design. Therefore, for the design of smoke control and longitudinal ventilation of the tunnel, based on actual highway tunnel size, this paper established and ran a series of numerical simulations through FDS simulation software to study tunnel width and slope?s effect on smoke countercurrent length and critical velocity. The results of this paper show that smoke countercurrent length decreases with tunnel slope?s increase and increases with tunnel width?s increase. Through dimensionless analysis, the prediction formulas of smoke countercurrent length and critical wind speed of large cross-section tunnel about tunnel width, slope and height are modified and established. The research conclusions can provide a theoretical basis for the longitudinal ventilation design, smoke prevention and exhaust measures and personnel evacuation in large cross-section tunnel fires.

Variation of Local Wind Fields under the Background of Climate Change and Its Impact on Algal Blooms in Lake Taihu, China

Global climate change can greatly promote the continuing expansion of algal blooms in eutrophic inland lakes. Wind fields, an important climate factor, provide an external driving force for the movement of algal blooms. Based on algal bloom satellite imageries and wind observation data from 2003 to 2022, this study explored a quantitative assessment of the variations in surface wind fields and their impacts on the algal blooms in Lake Taihu, China. The results indicate that the mean wind speed at different time scales in the Lake Taihu area presents a continuous descending tendency in recent decades, which is the probable cause for the increasing frequency and severity of algal blooms in the lake. Wind fields affect the formation, location, and severity of algal blooms in diverse and complex ways. The area and frequency of algal blooms in Lake Taihu increase with the decrease in wind speed. The 6 h mean wind speed before 12:00 LT (Local Time) on the day of the algal bloom occurrence generally follows a Gaussian distribution, with a wind speed range of (0.6 m/s, 3.4 m/s) at the 95.5% confidence level. Accordingly, the wind speeds of 0.6 m/s and 3.4 m/s are identified to be the lower and upper critical wind speed indicators suitable for the formation of algal blooms, respectively. Another meaningful finding is that the outbreak of large-scale algal blooms requires stricter wind speed conditions, with a significantly lower wind speed threshold of around 2 m/s. Our study also demonstrates that the dominant wind direction of southeast in the region may be an important cause of the continuous water-quality decline and the high frequency and severity of algal blooms in the northwest waters of the lake. These findings will contribute to further studies on the dynamic mechanism of algal blooms and provide support for water environment management and algal bloom prevention and control.

Research on online monitoring and anti-dance technology of transmission line dance based on wide-area information transmission

Abstract This paper diagnoses the transmission line dancing situation based on the wide-area traveling wave information transmission and dancing mechanism. The characteristics of the wide-area initial traveling wave propagation are analyzed, and the traveling wave information of transmission line dancing is analyzed using wavelet transform. Measure the voltage traveling wave energy distribution for online monitoring and diagnosis of transmission lines. To study the dancing amplitude of transmission lines, a finite element analysis model is created. The detuned pendulum anti-dancing device is designed, the detuned pendulum dynamics equation is constructed, and the critical wind speed leading to transmission line dancing is investigated by the theoretical equation method and the stability theory method. Through the empirical analysis method, the transmission line dance monitoring and the anti-dance effect are analyzed. The experiments show that when the transmission line dances at a slower speed, the online monitoring method based on wide-area information monitors the motion of the target spacer bar between two neighboring frames between [1,3], and the processing speed is 138.2 frames per second faster than the other techniques, which is successful in tracking the dancing target of the transmission line. In the anti-dance test, before the anti-dancer was added, the transmission line amplitude reached 12,12m/s from the beginning at a wind speed of 18m/s and 14m/s to provoke dance. After the installation of the anti-dancer, the amplitude is maintained between [0,1] in most cases, and the anti-dancer has a good anti-dance effect.

Predicting the risk of tree fall onto railway lines

Tree fall onto railway lines puts passengers at risk and causes large economic losses due to disruption of train services and damage to infrastructure. Railway lines in Germany are vulnerable to tree fall because of the large number of trackside trees that exist in that country with approximately 70% of all railway lines being tree-lined. In this paper we first tested whether a hybrid-mechanistic tree wind damage model, ForestGALES, could identify the sections of the railway network affected by tree fall in two federal states of Germany, Northrhine-Westphalia (NRW) and Thuringia (TH). We secondly tested whether the model, in combination with meteorological forecast models, could predict where tree fall occurred during a damaging windstorm. We used information on tree characteristics derived from LiDAR and aerial photography along the railway line network in NRW and TH to calculate the critical wind speed (CWS) at which damage is expected to happen for every individual tree as a function of its size and species, and the underlying soil. The railway network was then divided into 500 m sections and the statistics of the CWS, tree height, and species composition (broadleaf/conifer mix) within each section were calculated. Analysis of past tree fall events recorded by Deutsche Bahn AG (DB) showed that there was a significantly lower minimum CWS and significantly greater maximum tree height in sections that had recorded damage. In a second step we compared the calculated CWS values for all trees against downscaled wind speed assessments across the two federal states during Storm Friederike (named Storm David internationally) on 18 January 2018 and tested the ability of the model to discriminate sections with recorded damage during the storm. Excellent model discrimination was found with an AUC value of 0.82 and an overall model accuracy of 74.2%. The first test showed that the ForestGALES model with precise individual tree information can identify the sections of a railway network most vulnerable to tree fall. The second analysis showed, for the one storm tested, that the ForestGALES model when combined with predicted storm wind speeds can identify the most probable sections of the railway network to experience tree fall during an approaching damaging storm. Such information could be of value in firstly planning remedial work along railway lines, and secondly preparing the railway network ahead of a major storm.

Study on the Influence of Coil Arrangement on the Output Characteristics of Electromagnetic Galloping Energy Harvester.

The arrangement of the induction coil influences the electromagnetic damping force and output characteristics of electromagnetic energy harvesters. Based on the aforementioned information, this paper presents a proposal for a multiple off-center coil electromagnetic galloping energy harvester (MEGEH). This study establishes both a theoretical model and a physical model to research the influence of the position and quantity of the induction coils on the output characteristics of an energy harvester. Additionally, it conducts wind tunnel tests and analyzes the obtained results. With the increase in the number of induction coils, there is a significant improvement in the duty cycle and output power of the MEGEH, resulting in an amplified energy conversion efficiency. At a wind speed of 9 m/s, the duty ratios of a single set of coils (SC), two sets of coils (TC), and multiple sets of coils (MC) are 30%, 51%, and 100%, respectively. The total output powers are 0.4 mW, 0.62 mW, and 0.72 mW. However, the rate of output growth has decreased from 55% to 16%. The position of the coils affects the initial electromagnetic damping of the energy harvester. Changing the position can reduce the initial electromagnetic damping, thereby decreasing the critical wind speed. The critical wind speed of the MEGEH decreases as the induction coil is positioned further away from the vibration center. When the distance is sufficiently large, the electromagnetic damping force becomes negligible. When the induction coil is positioned centrally, the MEGEH demonstrates its maximum critical wind speed, which has been measured at 4.01 m/s. When the initial distance between the induction coil and the vibrating component is increased to 10 mm, the critical wind speed reaches its minimum value of 2.23 m/s. Therefore, it is necessary to optimize the arrangement of the coils. The coils of the MEGEH should be arranged with the MC and a 10 mm offset from the center.

Effect of taper ratio on 2-D mechanical wind sensors

In this paper, the effect of sensing-structure taper ratio on two-dimensional (2-D) mechanical wind sensors is demonstrated for the first time. The mechanical wind sensor consists of a sensing structure vertically arranged in the center of a cross cantilever. It detects the wind speed and direction by measuring the airflow-induced cantilever deformation with eight strain gauges attached to the beam surface. Five forms of sensing structures with different taper ratios are designed and manufactured to investigate their effects on the performance of 2-D mechanical wind sensors. A series of experiments are conducted and the results reveal that the taper ratio of the sensing structure can affect the measurement range and the sensitivity of the 2-D mechanical wind sensor. A lower taper ratio results in a higher critical wind speed, which makes the mechanical wind sensor a wider measurement range. Moreover, the results also show that a wider measurement range usually means a lower sensitivity for a single device, and hence the measurement range and the sensitivity of the mechanical wind sensor are a contradiction. The effect rule of the taper ratio presented in this paper can provide a valuable reference for the design and manufacture of 2-D mechanical wind sensors.

Analysis of a Dust Storm Profile: A Case Study in Iraq

In recent years, many academics have investigated various aspects of dust storms as one of the environmental challenges. In this study, a Battelle laser photometer coupled to a portable computer was used to monitor, analyze, and correlate the particle size distribution to wind speed across a 24-hour period that included the dust storm from January 18–19, 2020. These were connected with wind speed data obtained from an automated weather station (F.A. 511, Wilh Lambrecht). They also examined how the ratio of fibers to particles varied when the wind speed changed during a dust storm within the same period as the aforementioned. The results show that, during storms, a rise in the number of particles occurs as a consequence of high wind speeds, local near-ground turbulence, and strong wind, which work together to effectively lift up heavier particles. Also, it demonstrates a perfect relationship between the profiles of dust particles and fibers with a time lag in relation to wind speed, and an inversion in the order of the individual particle size profiles corresponding to a critical wind speed was noticed. A time lag of around five hours relative to the wind speed profile is also observed. Despite the similar shapes and the trend of the profiles, the ratio of fiber to particle is not constant.

Nonlinear vortex-induced vibration of wind turbine towers: Theory and experimental validation

Vortex-induced vibration (VIV) of wind turbine tower is a common occurrence in practical engineering, significantly impacting the safety and reliability of structure. An effective method is developed to investigate the VIV characteristics of a wind turbine tower with an elastic foundation and a lumped mass. To simulate the fluid–structure interaction, the van der Pol equation is utilized. The equations of motion of wind turbine tower, accounting for aerodynamic force, are established using Hamilton’s principle and the assumed mode method, and they are solved by the method of multiple scales. Modal functions of the wind turbine tower are obtained through the finite element method (FEM). The analysis further explores the influences of various parameters on the VIV characteristics of wind turbine tower. The results show that the VIV occurs within the frequency lock-in and multi-value ranges, and the critical wind speeds are mainly determined by the diameters of the segments near the tower top. Moreover, as the lumped mass increases or the foundation stiffness decreases, the occurrence of VIV shifts to lower wind speeds. A wind tunnel experiment of a scaled wind turbine tower model validates the frequency lock-in range of the VIV analysis results.