Dynamic Response Test Research Articles

Simulation and experimental analysis of traveling wave resonance of flexible spiral bevel gear system

Considering the traveling wave resonance (TWR) phenomenon of the spiral bevel gear system in the aero engine accessory casing, the flexible spiral bevel gear model is established by three-dimensional (3D) shell element and beam element. The dynamic model of flexible bevel gear system considering the change of meshing teeth pairs in the operating process is established by component mode synthesis (CMS) method and rotational modal projection method. The proposed model is verified by finite element (FE) solid model and experiment test results. On this basis, the TWR phenomenon of the bevel gear system is studied in combination with dynamic response and vibration stress experimental test. The results show that the bevel gear system has 3 nodal diameter resonance speeds within the actual operating speed range, which are one 1st nodal diameter resonance of pinion and two 1st nodal diameter resonance of gear. When the bevel gear system operates at TWR state, the amplitude corresponding to fm ± m·fr (fm is meshing frequency, m is nodal diameter number, fr is shaft rotational frequency) is larger than that corresponding to fm in the Fast Fourier transform (FFT) spectrum of the of the gear foundation vibration stress, and the vibration stress cloud map of the gear foundation shows the corresponding nodal diameter vibration shape. The research results provide a theoretical basis for feature recognition and influence law evaluation of TWR of bevel gear system.

Experimental study on the influence of radial internal clearances of the rolling bearings on dynamics of a flexible rotor system

To investigate the impact of radial internal clearance of rolling bearings on the dynamic response of a flexible rotor system in a turbo-shaft engine, a dynamic similarity model of the power turbine rotor was established. Experimental research was then conducted. Four rolling bearings supporting the rotor were examined, with dynamic response tests carried out under varying radial internal clearances. The influence of the radial internal clearance on the dynamic characteristics of the rotor system was studied using the controlled variable method. The amplitude, orbit, and asynchronous vibration were analyzed through time-domain signal comparison, waterfall diagrams, and spectral analysis. The experimental results demonstrate that: (1) Adjusting the radial internal clearance of the bearings can significantly reduce the dynamic response of the flexible rotor system, with a maximum observed displacement response reduction of 88%. (2) The efficiency of vibration reduction is closely related to the axial location of the bearing. (3) Optimal radial internal clearance is not necessarily achieved at the maximum or minimum values. (4) The "locked-up" frequency phenomenon, which increases the resonance opportunities of the rotor system, can be mitigated by adjusting the radial internal clearance of different bearings. This research is of great significance and engineering value for understanding, diagnosing, and preventing excessive vibration in flexible rotor systems.

Fast excitation structure for improving the transient time of magnetic controlled reactors

With the increasing proportion of renewable energy usage, the randomness and volatility of renewable energy have led to a corresponding increase in the demand for reactive power regulation in the power system. Magnetic controlled reactor (MCR) is one of the technical and economic means used to solve problems such as reactive power compensation and voltage regulation in the power system. However, the transient time of traditional MCR is relatively long compared to other reactive power compensation devices, which limits the further application of MCR. At present, most methods for optimizing the dynamic response time of MCR are to add additional circuits or change control strategies, which will increase the difficulty of MCR control and reduce stability. Therefore, without adding additional circuit structure and control difficulty, this paper proposes a three-phase MCR fast excitation structure that changes the winding connection method, which can improve the DC voltage in the control circuit and reduce the transient time of the MCR. A magnetic circuit model in the MCR core under the fast excitation structure is built and analyzed, based on which, the transient time of the MCR is mathematically calculated. A fast excitation MCR simulation model was constructed based on MATLAB/Simulink platform for dynamic response test simulation. Compared with typical MCR simulation results, the transient time was reduced from 400 ms to 37.1 ms. Dynamic response tests were conducted on a three-phase MCR prototype of 35 kV/18 Mvar, and drop test indicates that the fast excitation structure could reduce the transient time of the three-phase MCR prototype to 36.6 ms, which substantiate the precision of mathematical and simulation results and the efficacy of the fast excitation structure.

The bonding performance of desert sand self-compacting concrete overlay on normal strength concrete substrate: Macro, micro, and ultrasonic testing

This study investigates the performance of concrete containing desert sand (desert sand concrete and desert sand self-compacting concrete) as overlay concrete to bond with normal-strength concrete substrate, with different bonding interfaces being considered. The impermeability of the bonding interface is determined by the electrical resistance test. Static bonding strength is tested by conventional mechanical tests. The dynamic properties of bonded specimens are also studied by dynamic response tests. Non-linear parameters, low-frequency energy parameters and ultrasonic velocity are included in the bonding interface ultrasound detection. The microstructural and chemical compositional of the overlay transition zone (OTZ) are analysed to reveal the mechanisms of bonding behaviour. The results indicate that the interface electrical resistance is positively related to bonding strength. Using concrete containing desert sand as the overlay concrete improves bonding interface adhesion for 30 % at most. Bonding performance can be affected by the interface pattern and volume density in both static and dynamic conditions. The bonding strength and damping ratio with properly treated interfaces can be increased by over 300 % and 38 % than those of untreated groups, respectively. The dynamic response of the bonded specimens can effectively reflect the bonding performance. The non-linear ultrasound method and the ultrasound energy method are more accurate and sensitive than traditional way (ultrasonic velocities) in detecting the bonding interface. The incorporation of desert sand in the concrete or lowering W/B considerably contributes to a series of benefits to the microstructure of the bonding interface. The bonding gap width is reduced by 17 % and 72 % for DS incorporation and lower W/B, respectively. Characterized by Ca/Si, the OTZ width is reduced by 10 % and 31 % for DS incorporation and lower W/B, respectively. Characterized by micro-hardness, the OTZ width is reduced by 21 % and 24 % for DS incorporation and lower W/B, respectively, which provides an important reference for the engineering application of desert sand self-compacting concrete.

摆式主被动悬架喷雾机喷杆稳定性试验研究

When a sprayer is operating in the field, the uneven ground excitation causes the spray boom to move irregularly, significantly affecting the spray distribution uniformity and reducing the effectiveness of pesticide application. Installing a suspension between the vehicle and the boom is a crucial method to improve the boom stability. In this paper, experimental research on the stability of a boom with an active and passive pendulum suspension was carried out. The results of the transient response test of the passive suspension demonstrate that an increase in the suspension rotation damping coefficient reduces the overshoot of the system but slows down the response speed. Conversely, an increase in the suspension rotation stiffness coefficient speeds up the response speed. The results of the dynamic response test of the active suspension indicate that a smaller adjustment threshold of the control system for the boom inclination angle results in higher control accuracy. However, when the threshold is less than 1cm, the boom becomes challenging to balance. The results of the combination experiments based on the response surface method reveal that the rotation stiffness coefficient, rotation damping coefficient, unit forward speed, and their interactions significantly impact the adjustment time of the boom and the variation coefficient of the boom inclination angle. Through contribution rate analysis, the influence order of each factor on the adjustment time and variation coefficient was obtained. Additionally, the analysis of variance results show that the established regression model fits the actual situation well, and has reference significance for the design and application of the suspension.

The research on flow-induced vibration of compact curved tube bundles subjected to liquid cross flow

This paper presents a series of dynamic tests and analyses on single and compactly bundled straight and curved tubes subjected to liquid cross flow. The purpose of this research is to study the flow-induced vibration behavior of compact curved tube bundles, with particular interest in their differences to those of the straight tubes. Both modal and dynamic response tests are performed with tube structures of different bending radius and pitch-diameter ratios. Based on the test results, the vortex shedding phenomenon and Strouhal numbers of single straight tube and single curved tube are analyzed in this paper, and so are the fluid-elastic instability phenomenon and Connors constant of straight tube bundles and curved tube bundles. The test results and analysis conclusions provide valuable assessment tool for the design of helically coiled tube bundles commonly used in steam generators or heat exchangers.

Seismic performance of soft rock tunnel under composite support conditions

In order to effectively improve the seismic and impact resistance performance of soft rock tunnels, a composite support method was proposed and validated in the paper. The UDEC (Universal Distinct Element Code) model of soft rock layers was established, and the movement and subsidence characteristics of the roof and floor of the rock layers under impact loads was simulated and calculated. As a result, a composite support scheme with good cushioning performance was proposed. The top and sides of the tunnel were supported by a combination of anchor rods of different lengths and metal mesh, reinforced by steel beams and vibration absorbing filler around. The anchor rod was designed as a segmented loading structure, and can be set to different preloading forces based on the internal deformation of the rock layer. The dynamic response testing scheme was designed, and the results indicate that the segmented loading anchor rod has a significant buffering effect on the response to impact load, and can provide reasonable tension feedback at different stages. Research has found that when the water cement ratio is 0.5-1.5, the curing efficiency and strength are both higher. In order to compare the seismic performance of composite support and traditional constant resistance anchor rod support, local blasting experiments were conducted. Based on a blasting vibration tester, a data detection and transmission system were designed to obtain the vibration speed of the tunnel roof during the vibration process. The research results show that composite support can reduce the maximum vibration by more than 40 %, stabilize the fragmentation coefficient at 1.38, and have a very significant vibration reduction effect.

Vibration feature extraction and fault detection method for transmission towers

AbstractThis paper presents a novel bolt looseness detection method for power transmission towers based on vibration signal analysis. The proposed method utilizes pulse excitation to extract the vibration signal of the tower, which is then adaptively decomposed using the Variational Mode Decomposition of Spider Wasp optimizer (SWVMD). This overcomes limitations of traditional Variational Mode Decomposition methods by leveraging bio‐inspired optimization to improve signal decomposition. Simulated signals processed with different optimization methods verify the superiority of the SWO approach. Field tests on a 110‐kV transmission tower further demonstrate the effectiveness of the proposed SWVMD technique for analyzing on‐site vibration data. A new improved intrinsic multiscale sample entropy feature is also introduced for bolt state characterization. A Spider Wasp Support Vector Machine classifier is developed to realize accurate bolt loosening monitoring using the extracted features. Dynamic response tests under varying bolt conditions show that the method can identify early loosening and reduce tower damage risks compared to conventional techniques. This novel vibration‐based detection framework presents an innovative application of nature‐inspired computing for power infrastructure health monitoring.

Research on online monitoring technology for transmission tower bolt looseness

Minor damages such as tower bolt looseness are difficult to detect through manual inspections. Operational modal analysis plays an important role in the online monitoring of transmission tower structure safety. However, the traditional analysis methods select feature parameters manually, and the deviation generated will directly affect the estimation accuracy of structural modal parameters. This article proposes a method for diagnosing tower bolt looseness without human intervention. This method can reduce the influence of background noise greatly through data cleaning and data fusion. Besides, the intelligent feature recognition of vibration acceleration time-domain signals based on an improved 1DCNN algorithm can improve the monitoring accuracy and speed significantly. The effectiveness of the method has been validated by conducting dynamic response tests on a 110KV transmission tower under different bolt loosening conditions. In the end, an online monitoring technology for transmission towers bolt looseness has been developed and successfully applied to the Guangdong power grid. The results show that this method has high identification accuracy and provides a new approach for online monitoring of tower bolt looseness.

Generalized, Complete and Accurate Modeling of Non-Ideal Push–Pull Converters for Power System Analysis and Control

Power converters are a basic element for the control and design of any power electronic system. Among the many available topologies, the push–pull converter is widely used due to its versatility, safety and efficiency. For its correct analysis, sizing, simulation and control, models that meet the characteristics of generality, accuracy and simplicity are required, especially if its control is to be optimized by means of some analytical technique. This requires models that consider the practical non-idealities intrinsic to the converter, as well as being intuitive and easy to handle analytically in a control loop. In general, the models reviewed in the scientific literature adopt simplifications in their definition that are detrimental to their accuracy. In response to the posed problem, this work presents a generalized, complete, accurate and versatile model of real (non-ideal) push–pull converters, ideal for the analysis, simulation, and control of power systems. Following the premise of general and complete converters, the proposed model includes all the practical non-idealities of the converter elements, and it is accurate because it faithfully reflects its dynamics. Furthermore, the model is versatile, as its state space formulation allows for its easy adaptability to the converter operating conditions (voltage, current and temperature) for each sampling time. Also, the model is excellent for use in model-based control techniques, as well as for making very accurate simulators. The behavior of the developed model has been contrasted with a real push–pull converter, as well as with reference models present in the scientific literature for both dynamic and steady-state response tests. The results show excellent performance in all the studied cases, with behavior faithful to the real converter and with relative errors that are much lower than those obtained for the reference models. It follows that the model behaves like a digital twin of a real push–pull converter.

Simulation and Experimental Study on Harmonic Optimization of Magnetically Controlled Reactor Based on Multistage Saturated Magnetic Valve Structure

The magnetically controlled reactor adjusts its output capacity based on the principle of magnetic saturation. Due to the iron core working in the saturated region, higher harmonics will be generated in the working current. A large number of harmonics will affect the power quality and safety of the power system. This study derives the expression for the harmonic content of a magnetically controlled reactor with a multistage saturated magnetic valve core structure. The magnetization curves of different iron core structures can be obtained through expressions. This study used different magnetization curves for simulations of magnetically controlled reactors. The suppression effect of the multilevel magnetic valve structure on harmonics was analyzed through simulation results. A prototype of a magnetically controlled reactor with a two-stage magnetic valve structure was manufactured, and dynamic response tests were conducted. The experimental results show that the harmonic content in the working current of the magnetically controlled reactor with a two-stage magnetic valve structure is less than 2%, which is much smaller than the harmonic content of ordinary magnetically controlled reactors in the past. This article verifies the suppression effect of the improved magnetic valve structure on harmonics through experiments.

Motor Current Model for Detecting Localized Defects in Planet Rolling Bearings

A motor current model for the diagnosis of localized defects in planet rolling bearings (PRBs) is proposed in this study. A dynamic analysis of the motor-driven planetary gearbox system is conducted, and a translational-torsional vibration model of the system is developed. Both the additional time-varying impact caused by localized defects and the influence of the Hertzian contact and radial clearance on the translational support forces of PRBs are considered in the model. Based on the magnetic equivalent circuit network model, vibrational-electromagnetic coupling analysis is performed with the aid of the air-gap permeance and electromagnetic torque. By iteratively solving the nonlinear algebraic differential equations describing the dynamic characteristics of the coupling system, the motor current variation curve with localized defects in the PRB is obtained. Taking a typical motor-driven planetary gearbox system as the object, electromagnetic finite element calculations and dynamic response tests are performed to verify the proposed motor current model. The results show that the characteristic motor current frequencies are a combination of the fault passing frequency and power supply frequency when the inner race of the PRB has a localized spall fault. When the outer race (or roller) has a localized spall fault, the combination of current characteristic frequencies, which generally consists of the fault passing frequency, power supply frequency, and PRB outer-race rotational frequency (outer-race spall) or cage revolution frequency (roller spall), become complex. By discussing the effect of the spall width on the motor current spectra in detail, the characteristic frequencies sensitive to defects are extracted, providing a theoretical basis for the quantitative diagnosis of PRB-localized defects.

Non-contact type dynamic responses test of wind turbines

The performance analysis of wind turbine systems should be considered when calculating the wind speed relative to the wind turbine structure, and is essential for wind turbine design. Since the conditions are precarious in transient state and the operating environments are challenging, the wind turbine is a complex, multivariate, nonlinear system. This paper presents a novel dynamic response test method for wind turbines based on three-dimensional digital speckle measurement. This method use a real-time speckle image collection of objects in various stages using binocular stereo vision to perform stereo matching of deformation points on object surface. A digital image correlation algorithm is used to rebuild three-dimensional space coordinates of matching points so as to achieve wind turbine dynamic response. A laboratory-scale experimental platform is constructed to test the dynamic response of the wind turbine system. In order to verify the accuracy of the proposed method, a three-dimensional model of a wind turbine is built. With dynamic structure response process adopted to carry out dynamic analysis and compare theoretical results with test results, the results vary by less than 10 %, indicating that the test method presented in the paper is feasible and effective.

Design of a Teat Cup Attachment Robot for Automatic Milking Systems

Automatic milking systems (AMSs) for medium and large dairy farms in China require manual assistance to attach the teat cup, which greatly affects the milking efficiency and labor costs. In this regard, it is necessary to realize the automatic completion of cow teat attachment work. To address this issue, the authors developed a teat cup attachment robot for an AMS based on the theory of the solution of inventive problems (TRIZ). Specifically, we developed an enhanced algorithm for teat detection and designed a six-degree-of-freedom manipulator with integrated drive control. The design parameters were simulated and analyzed to validate their efficacy, while the rationality of the manipulator’s movement during teat cup attachment was verified. The maximum displacement and angle error of the cup was 1.625 mm and 1.216 mm, respectively, as verified by the teat cup attachment error test. A dynamic response test showed that the manipulator could follow the teat of the cow in real time. The attachment time for teat cups was 21 s per cow, with a success rate of 98%. The performance of the teat cup attachment robot was capable of meeting the automatic attachment teat cup needs for medium and large dairy farms during milking.

Development of flexible glove sensors for virtual reality (VR) applications

Virtual reality (VR) technology has catalyzed the development of flexible sensors to interact with objects in a virtual environment. Current solutions for smart glove sensors are limited by rigid factors. In this article, a novel smart glove is developed that utilizes a flexible sensor made from a polyethylene-carbon composite (Velostat) to manipulate a hand model in a 3-dimensional (3D) virtual reality (VR) environment. The sensors are specifically designed to measure the angle of finger joint flexion, and an interface circuit has been developed to process the joint angle data. The strain sensors attached to the smart glove show a high sensitivity of 59.8 % rad−1, with a response time of 15.8 ms when the joint angle increases from 0° to 30° under the dynamic response test. The fabricated smart glove successfully controls a 3D hand in a VR environment. This proof-of-concept experiment explores the potential application of the smart glove for VR telerehabilitation.

Reliability Analysis of Deep-Water Explosion Test Vessel Based on Fuzzy Interval

The safety of such a high-security structure as a deep-water explosion test vessel in service is still in the exploration stage. The reliability of the vessel needs to be analyzed in order to prevent the underwater explosion shock wave and other explosion products on the test equipment causing great damage to the experimental personnel. The safety of such a high-security structure as a deep-water explosion test vessel in service has gradually attracted the attention of scholars. The reliability of the vessel needs to be analyzed in order to prevent the shock wave of underwater explosion and other explosion products on the test equipment causing great damage to the experimental personnel. In this paper, the dynamic response test data of a deepwater explosion test vessel in service under different conditions and the Elman neural network are used to establish the dynamic response prediction model of the deepwater explosion test vessel, and using the established model to make dynamic response prediction in the next experiment; the vessel yield strength and modulus of elasticity are taken as random variables, and the container dynamic strain prediction interval is the interval variable, the random-interval reliability model is established by using the interval variable and random variable. The random variables of the model are transformed into interval variables, and the interval variables are fuzzified using the affiliation function to calculate the reliability index. Since the interval variable obtained from the model will change with the change of the container dynamic test data, the interval reliability index calculated by the stochastic-interval reliability analysis model can quantify the reliability of the container and can be used as a reference for the subsequent use of the container by reducing the reliability index to calculate the service life and drug filling amount.

Dynamic Analysis of the Lifting Arm System in the Integrated Offshore Platform Decommissioning Equipment in Complicated Sea States

With the further exploitation of offshore resources, there are more and more offshore oil and gas fields which cannot meet the production capacity requirements. So, it becomes extremely urgent to pay attention to the decommissioning of the exploitation equipment in abandoned offshore fields. A new decommissioning solution is offered by the double-ship integrated offshore platform decommissioning equipment comes. However, as the equipment will inevitably bear the combined actions of various dynamic and static loads during operation, the strength and stability of the overall unit and the connections between different modules will be greatly challenged by the complex ocean. Firstly, the dynamic characteristics of the integrated decommissioning system are analyzed in this paper. Mathematical modeling of the lifting arm system is established based on the unit characteristics matrix, and a dynamic equation of the flexible lifting arm unit and system is developed based on Lagrange’s equation and solved through numerical calculation. Secondly, modal analysis and transient analysis of the lifting arm in specific working conditions are performed according to the prototype parameters of the designed decommissioning system. Finally, according to the principle of similitude, a hydrodynamic experiment method is proposed with an integrated decommissioning multi-dimensional vibration test bench. The decommissioning system model test bench is designed and built to perform the dynamic response test, and this paper compares the test results and the simulation results for verification. The comparison verifies that the theoretical analysis and the tests prove each other valid and the results are accurate, meaning this work provides a powerful theoretical reference and offers effective research methods for future studies on super-large-scale integrated decommissioning equipment.

Dynamic characteristics of large permanent magnet direct‐drive generators considering electromagnetic–structural coupling effects

AbstractDynamic characteristics of large permanent magnet direct‐drive generators (PMDGs) considering electromagnetic–structural coupling effects are analyzed in this study. Using the conformal mapping method, the scalar magnetic potential of the air gap magnetic field considering the slot effect is calculated. On the basis of the discrete current element and magnetic equivalent circuit model, the local magnetic saturation effect of the stator and rotor is quantitatively simulated and the air gap magnetic field intensity distribution is obtained via numerical simulation. A series of uniformly distributed equivalent electromagnetic springs are introduced to develop an electromagnetic–structural coupling finite element PMDG model. The proposed air gap field analysis method is verified by the finite element analysis results. On the basis of the test platform for the Goldwind 1.5 MW PMDG, both modal and dynamic response tests for the stator/rotor coupling system are conducted, and the results are compared with the natural frequencies, mode shapes, and vibration responses obtained using the numerical model. The effects of the air gap length and rotor speed on the natural frequencies of the coupling system are analyzed. The proposed model has the potential to accurately evaluate the PMDG vibration energy, avoiding resonance points, and maintaining stable operations of the unit.

Test of Broken Suspender Specimen and Equivalent Static Calculation Method for Half-Through and Through Concrete-Filled Steel Tubular Arch Bridges

In response to the frequent collapse of main girders caused by the breakage of suspenders on half-through and through arch bridges, a test specimen has been designed and fabricated with a through concrete-filled steel tube (CFST) arch bridge as the engineering background. A new electromagnetic disconnect trigger is employed to realize the rapid suspender breakage in the test specimen. Dynamic response tests of the residual structure of the arch bridge after suspender failures employing the test specimen have been carried out. A finite element model accounting for the suspender breakage dynamic process has been constructed by implementing ANSYS/LS-DYNA, and the results of the test and finite element analysis are compared. In order to simplify the dynamic response calculation process of the residual structure after hanger failures, the dynamic coefficient is introduced, and an equivalent static calculation method (ESCM) considering the dynamic effect of the suspender fracture is presented. Eleven kinds of CFST standard arch bridges with different spans are constructed, the static and dynamic effects of the standard arch bridge with various dynamic coefficients are compared, and then their corresponding dynamic coefficients for various suspender fractures are determined. The obtained results reveal that the proposed electromagnetic suspender breakage trigger can realize the hanger fracturing within 0.1 s, which accurately simulates the fracture process of an actual bridge suspender, and the influence on the value of the dynamic coefficient can be ignored when the duration for suspender fracture is less than or equal to 0.15 s. The influence of suspender fracture on the displacement and stress of the longitudinal beam is more notable than those of the arch rib. In particular, the long suspender breakage has the highest influence on the displacement and stress of the longitudinal beam and arch rib. The fracture of the second short suspender has a remarkable impact on the suspender force of the adjacent hanger. When the ESCM is utilized to assess the mechanical behavior of the half-through and through CFST arch bridge, the dynamic coefficients of the longitudinal beam (suspender) were evaluated to be, conservatively, 1.8 (1.8) and 1.8 (1.7), respectively.

Aerodynamic stability of typical sea-crossing bridge with streamlined box girder under wave-interfered complex wind fields

Tropical cyclones landing on the coast are usually associated with both strong winds and waves, posing a major threat to sea-crossing bridges. Strong waves riding on the elevated storm surge squeeze the narrow gap between the sea surface and bottom of the bridge deck, thus complicating the wind field and leading to different bridge nonlinear flutter responses as compared with the steady flow field. In this study, to evaluate the bridge safety under such circumstances, wind tunnel test was carried out for a typical sea-crossing bridge with streamlined box girder based on a developed dynamic response test system for simulating the coupling effect of wind, wave, and current on bridges, where the clearance, underneath the bridge deck, and wave speed can be systematically adjusted to investigate the wind field characteristics and bridge nonlinear flutter response. Numerical simulation with the LES (large eddy simulation) scheme was employed to successfully visualize the wind field around the bridge and the mechanism of the nonlinear flutter response was analyzed in detail. The results of this preliminary investigation show that: (a) In the wind tunnel tests, when the wave crest passes under the bridge, the acceleration effect due to the narrow gap can lead to an increase for the nonlinear flutter amplitude of the bridge, which threatens the structural safety; (b) The measured wind speed at the bridge site exhibits strong turbulence intensity and non-Gaussian distribution tendency; and (c) Based on the numerical simulation, the airflow between the wave crest and the main structure features a large vertical velocity component, leading to a large AOA (angle of attack) value of the incoming flow. Meanwhile, the air pressure around the girder is unevenly distributed, thus unavoidably weakening the aerodynamic stability of the bridge.