Wind-vehicle-bridge-vortex-induced vibration analysis method considering sudden wind load changes in the tower area

Abstract

The present invention relates to the field of bridge safety technology, and discloses a windmill-bridge-vortex-induced vibration analysis method that takes into account the sudden change of wind load in the tower area. The method disclosed by the present invention forms a windmill-bridge-vortex-induced vibration coupling system by taking into account the static wind load and vortex-induced vibration that take into account the sudden change effect of wind load in the tower area as external excitations. Compared with the known methods for evaluating the safety and comfort of trains running on bridges under vortex-induced vibration conditions, the present invention can more accurately evaluate the dynamic response of trains running on bridges, especially the safety and comfort when crossing tower areas. In addition, the present invention fully considers the coupling between the train and the bridge under the vortex-induced vibration state by directly adding the vortex-induced vibration to the bridge in the form of displacement, and can more carefully evaluate the impact of vortex-induced vibration on the dynamic response of the vehicle-bridge system.

Description

Technical Field

[0001] The present invention relates to the technical field of bridge safety, and in particular to a wind-vehicle-bridge-vortex-induced vibration analysis method taking into account sudden changes in wind loads in a tower area. Background Art

[0002] The contents in this section merely provide background information related to the present invention and may not constitute prior art.

[0003] With the breakthrough of bridge span, the main beam structure is becoming more and more complex and gradually developing towards low damping. This structure is sensitive to wind action and easily induces vortex vibration. For railway bridges, the periodic vibration of the bridge caused by vortex vibration will not only cause structural fatigue, but also affect the stability of the train running on the bridge. The deformation of the bridge deck caused by vertical vortex vibration will seriously deteriorate the dynamic performance of the train operation, reduce the train ride comfort, and even endanger the driving safety of the train in severe cases. Therefore, it is necessary to evaluate the safety and comfort of the train running on the bridge during the design stage of the bridge.

[0004] At present, it is common to add external excitations (such as static wind force and buffeting force acting on trains and bridges) to the wind-vehicle-bridge coupling system to solve the values ​​of the dynamic response evaluation indicators of trains and bridges, and evaluate the safety and comfort of trains when traveling on bridges. For example, the patent document with application number "CN202410907916.9" and titled "A wind-vehicle-bridge coupling calculation method considering bridge vortex vibration" discloses a method for evaluating train safety and comfort using the above-mentioned method. Summary of the invention

[0005] The inventor of the present invention has found that in a strong wind environment, when a train passes through the tower area of ​​a bridge, the aerodynamic force and dynamic response of the train will change dramatically due to the sudden change effect of the wind load in the tower area, and the risk of the train being blown over will increase. However, in the methods for evaluating the safety and comfort of trains disclosed in the patent documents listed above, the influence of the sudden change effect of the wind load in the tower area on the aerodynamic force and dynamic response of the train is not considered, so that the safety and comfort of the train when passing through the tower area cannot be accurately evaluated.

[0006] In view of this, the purpose of the present invention is to provide a wind-vehicle-bridge-vortex-induced vibration analysis method taking into account the sudden change of wind load in the tower area, so as to more accurately evaluate the safety and comfort of trains running on bridges, especially when passing through the bridge tower area.

[0007] The purpose of the present invention is achieved through the following technical solutions:

[0008] The present invention discloses a wind-vehicle-bridge-vortex-induced vibration analysis method considering the sudden change of wind load in the tower area, comprising the following steps:

[0009] Step S1. Establishing a vehicle-bridge numerical model for computational fluid dynamics numerical simulation;

[0010] Step S2. Calculate the vehicle-bridge numerical model established in step S1 to calculate the static wind load acting on the train and the bridge during the entire process of the train crossing the bridge and taking into account the sudden change effect of the wind load on the tower area;

[0011] Step S3. Establish a vehicle-bridge dynamic model; use the static wind load calculated in step S2 as one of the external excitations and add it to the vehicle-bridge dynamic model to form a wind-vehicle-bridge-vortex-induced vibration coupling system.

[0012] Furthermore, in step S1, the process of establishing the vehicle-bridge numerical model includes:

[0013] Step S11. Establishing a three-dimensional geometric model of the vehicle-bridge according to the structural parameters of the bridge and the train;

[0014] Step S12. Meshing the vehicle-bridge three-dimensional geometric model established in step S11, and using overlapping meshes to simulate the movement of the train;

[0015] Step S13. Importing the three-dimensional geometric model of the vehicle-bridge meshed in step S12 into computational fluid dynamics software, defining initial variables and boundary conditions, and performing iterative calculations by solving NS equations and turbulence equations to obtain a vehicle-bridge numerical model;

[0016] In the rectangular coordinate system, the NS equation is:

[0017]

[0018] In the above formula: is the fluid density; x , y , z They represent the coordinate axes in the rectangular coordinate system respectively; u 1. u 2. u 3 are the velocity of the fluid in the rectangular coordinate system x , y , z Three components below the axis; t For time; is the hydrostatic pressure; is the fluid dynamic viscosity coefficient;

[0019] The turbulence equation is:

[0020]

[0021] In the above two formulas: is the fluid density; is the turbulent kinetic energy coefficient; is the turbulence kinetic energy coefficient The empirical formula of is the dissipation rate of turbulent kinetic energy per unit mass of fluid; is the velocity component; t For time; , is the coordinate axis component; , Represent the turbulent kinetic energy coefficients The dissipation rate of turbulent kinetic energy per unit mass of fluid The effective diffusion term of , is a constant.

[0022] Furthermore, step S2 specifically includes:

[0023] Step S21. Calculate the train-bridge numerical model to obtain the time history of the three-force coefficients taking into account the sudden change effect of wind load in the tower area during the whole process of the train crossing the bridge;

[0024] Step S22. According to the three-force coefficient time history calculated in step S21, the static wind load acting on the train and the bridge during the whole process of the train crossing the bridge and taking into account the sudden change effect of the wind load on the tower area is calculated.

[0025] Furthermore, the step S3 also includes: taking the displacement caused by the vortex-induced vibration of the bridge as one of the external excitations and adding it to the nodes of the bridge main beam in the vehicle-bridge dynamics model.

[0026] Furthermore, in step S3, the process of establishing the vehicle-bridge dynamics model includes:

[0027] Step S31. Establishing a finite element model of a bridge, and assembling a mass matrix, a stiffness matrix, and a damping matrix of the bridge;

[0028] Step S32. Calculating the natural frequency and corresponding vibration mode of the bridge according to the finite element model of the bridge;

[0029] Step S33. Performing substructure analysis on the bridge finite element model to ultimately generate a flexible body input file of the bridge finite element model containing relevant information;

[0030] Step S34. Establishing a train dynamics model;

[0031] Step S35. Import the flexible body input file from the bridge finite element model and the train dynamics model into the multi-body dynamics software to form a vehicle-bridge dynamics model.

[0032] Furthermore, in step S33, the relevant information includes mass matrix, stiffness matrix, natural frequency and corresponding vibration mode, and geometric characteristics.

[0033] Furthermore, in step S3, the external excitation also includes buffeting force acting on the bridge and track unevenness.

[0034] Furthermore, the wind-vehicle-bridge-vortex-induced vibration analysis method considering the sudden change of wind load in the tower area also includes:

[0035] Step S4. Calculate the dynamic responses of the train and the bridge in the wind-vehicle-bridge-vortex-induced vibration coupling system to obtain the safety and comfort evaluation index of the train based on the dynamic response calculation of the train and the bridge.

[0036] The technical solution of the embodiment of the present invention has at least the following advantages and beneficial effects:

[0037] 1. The method disclosed in the present invention takes the static wind load and vortex-induced vibration that take into account the sudden change effect of wind load in the tower area as external excitations to form a wind-vehicle-bridge-vortex-induced vibration coupling system. Compared with the known methods for evaluating the safety and comfort of a train running on a bridge under a vortex-induced vibration state, the present invention can more accurately evaluate the dynamic response of a train running on a bridge, especially the safety and comfort when crossing a tower area.

[0038] 2. The present invention directly adds vortex-induced vibration to the bridge in the form of displacement, fully considering the coupling between the train and the bridge under the vortex-induced vibration state, and can more carefully evaluate the impact of vortex-induced vibration on the dynamic response of the vehicle-bridge system. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 A flow chart of a wind-vehicle-bridge-vortex-induced vibration analysis method considering sudden changes in wind loads in the tower area provided by an embodiment of the present invention;

[0040] Figure 2 A schematic diagram of an overlapping grid provided for an embodiment of the present invention;

[0041] Figure 3 This is the calculation domain layout diagram of the vehicle-bridge numerical model;

[0042] Figure 4 It is a curve diagram showing the change of the three-force coefficient with the distance traveled by the train during the whole process of the train crossing the bridge;

[0043] Figure 5It is a curve diagram showing the static wind load acting on the train changing with time during the whole process of the train crossing the bridge;

[0044] Figure 6 This is a graph showing the variation of the vertical displacement at the mid-span of the bridge with time. DETAILED DESCRIPTION

[0045] In order to make the purpose, technical solution and advantages of the present invention clearer, the technical solution of the present invention will be clearly and completely described in conjunction with specific implementation methods below. The same figure marks in the accompanying drawings represent the same components. It should be noted that the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the described embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0046] Compared to the embodiments shown in the drawings, feasible embodiments within the scope of the present invention may have fewer components, other components not shown in the drawings, different components, differently arranged components, or differently connected components, etc. In addition, two or more components in the drawings may be implemented in a single component, or a single component shown in the drawings may be implemented as multiple separate components.

[0047] In combination with the foregoing description of the present invention, it can be seen that in the known method of adding external excitation to the wind-vehicle-bridge coupling system to evaluate the safety and comfort of a train traveling on a bridge, the influence of the sudden change effect of wind load in the tower area on the aerodynamic and dynamic response of the train is not taken into account, so that the safety and comfort of the train when passing through the bridge tower area cannot be accurately evaluated.

[0048] The so-called tower area wind load mutation effect is simply a phenomenon in which the wind generates complex flows when flowing through the bridge tower area, resulting in a sudden change in the static wind load acting on the bridge and the train. For ease of explanation, in this embodiment, the bridge tower area is referred to as the "tower area", and the non-tower area of ​​the bridge is referred to as the "non-tower area".

[0049] To this end, an embodiment of the present invention discloses a wind-vehicle-bridge-vortex-induced vibration analysis method that takes into account sudden changes in wind loads in the tower area, in the hope of more accurately evaluating the safety and comfort of trains running on bridges, especially when crossing the tower area.

[0050] Figure 1 FIG. 2 shows a flow chart of the wind-vehicle-bridge-vortex-induced vibration analysis method disclosed in this embodiment considering the sudden change of wind load in the tower area. Figure 1 As shown, the vibration analysis method disclosed in this embodiment may include the following steps:

[0051] Step S1. Establish a vehicle-bridge numerical model for computational fluid dynamics numerical simulation in computational fluid dynamics simulation software such as Fluent.

[0052] It can be understood that fluid mechanics simulation is a technology that uses computers to solve various conservation control partial differential equations of fluid flow to simulate the actual fluid flow. Its basic principle is to numerically solve the differential equations that control fluid flow and obtain the discrete distribution of the flow field of fluid flow in a continuous area, thereby approximately simulating the fluid flow.

[0053] Specifically, in step S1, the process of establishing a vehicle-bridge numerical model for computational fluid dynamics numerical simulation includes:

[0054] Step S11. Establish a three-dimensional geometric model of the vehicle-bridge according to the structural parameters of the bridge and the train. Among them, the structural parameters of the bridge may include the structural parameters of the main components such as the bridge section, bridge deck pavement, bridge deck anti-collision railing, bridge tower, etc. Further, the bridge section should meet the requirements of fully expressing the geometric characteristics of the main beam, which include length, width, height, angle, spatial position of the rod, etc.; the structural parameters of the bridge deck pavement include thickness, length and height, etc.; the structural parameters of the bridge deck anti-collision railing include component size, spatial position and connection method, etc.; the bridge tower should meet the requirements of fully expressing the geometric characteristics of the bridge tower, which include length, width, height, angle, etc.

[0055] Step S12: Mesh the three-dimensional geometric model of the vehicle-bridge established in step S11, and use overlapping meshes to simulate the movement of the train.

[0056] The core of overlapping grid is to divide the computational domain into multiple sub-regions, each of which generates a separate grid, and there is a mutual overlap between these sub-regions. The flow field information is realized by interpolating at the overlapping boundaries to ensure the exchange of flow field data between the main region and the subsidiary region.

[0057] In this embodiment, if Figure 2 As shown in the figure, the computational domain of the entire vehicle-bridge 3D geometric model is divided into the main area (i.e. Figure 2 The main grid in the Figure 2 The main area includes the bridge and the external area, and the auxiliary area includes the moving train. During the train movement, the overlapping boundaries are continuously updated with the movement of the train to ensure continuity with the main area, so that the aerodynamic force when the train passes through the tower area can be calculated for subsequent export to the computational fluid dynamics simulation software.

[0058] Step S13. The vehicle-bridge three-dimensional geometric model meshed in step S12 is imported into the computational fluid dynamics simulation software, and combined with Figure 3 As shown, initial variables and boundary conditions are defined in the computational fluid dynamics simulation software, and iterative calculations are performed by solving the NS equations and turbulence equations to obtain a vehicle-bridge numerical model for computational fluid dynamics numerical simulation.

[0059] Specifically, in the rectangular coordinate system, the NS equation is:

[0060]

[0061] In the above formula: is the fluid density; x , y , z They represent the coordinate axes in the rectangular coordinate system respectively; u 1. u 2. u 3 are the velocity of the fluid in the rectangular coordinate system x , y , z Three components below the axis; t For time; is the hydrostatic pressure; is the dynamic viscosity coefficient of the fluid.

[0062] The turbulence equation is:

[0063]

[0064] In the above two formulas: is the fluid density; is the turbulent kinetic energy coefficient; is the turbulence kinetic energy coefficient The empirical formula of is the dissipation rate of turbulent kinetic energy per unit mass of fluid; is the velocity component; t For time; , is the coordinate axis component; , Represent the turbulent kinetic energy coefficients The dissipation rate of turbulent kinetic energy per unit mass of fluid The effective diffusion term of , is a constant.

[0065] Step S2. In the computational fluid dynamics simulation software, the vehicle-bridge numerical model for computational fluid dynamics numerical simulation established in step S1 is calculated to obtain the static wind load acting on the train and the bridge during the entire process of the train crossing the bridge (that is, the process of the train passing through the entire bridge) and taking into account the sudden change effect of the wind load in the tower area.

[0066] Wherein, step S2 specifically includes:

[0067] Step S21. Calculate the vehicle-bridge numerical model by computational fluid dynamics simulation software to calculate the three-force coefficient time history of the train crossing the bridge, taking into account the sudden change effect of wind load in the tower area;

[0068] Step S22. According to the three-force coefficient time history calculated in step S21, the static wind load acting on the train and the bridge during the whole process of the train crossing the bridge and taking into account the sudden change effect of the wind load on the tower area is calculated.

[0069] Specifically, during the whole process of the train crossing the bridge, the static wind load acting on the train and the bridge can be defined by static wind resistance, static wind lift and static wind lift moment. Among them, the calculation formula for the static wind load acting on the train and the bridge is:

[0070]

[0071] In the above formula: are the static wind resistance, static wind lift and static wind lift moment acting on the train and bridge in the body axis coordinate system respectively; is the fluid density, generally 1.225 kg / m 3 ; U is the average wind speed, which can be monitored by an anemometer on the bridge; H , B are the height and width of the bridge section or train section, respectively; is the three-force coefficient in the body axis coordinate system, namely the drag coefficient, lift coefficient and lift moment coefficient. The three-force coefficient is obtained by the three-force coefficient time history calculated in the aforementioned step S21.

[0072] like Figure 4 As shown in FIG. 1 , it shows a curve diagram of the three-force coefficients changing with the distance traveled by the train during the entire process of the train crossing the bridge calculated in an exemplary embodiment of the present invention. Figure 4It can be seen that before the train reaches the tower area, that is, before the travel distance is approximately less than 80m, the drag coefficient, lift coefficient and lift moment coefficient all remain basically unchanged; when the train reaches the tower area and passes through the tower area, that is, when the travel distance is approximately between 80-110m, the drag coefficient and lift coefficient both show a state of first increasing slightly, then decreasing sharply, and then increasing again, while the lift moment coefficient is just the opposite, showing a state of first decreasing slightly, then increasing sharply, and then decreasing again; after the train leaves the tower area, that is, after the travel distance is approximately greater than 110m, the drag coefficient, lift coefficient and lift moment coefficient will remain basically unchanged again.

[0073] This also proves that during the entire process of a train crossing a bridge, especially when the train passes through the tower area of ​​the bridge, the aerodynamic force of the train will change sharply due to the sudden change effect of the wind load in the tower area. Therefore, it is necessary to take the sudden change effect of the wind load in the tower area into consideration in order to more accurately evaluate the safety and comfort of the train running on the bridge, especially when passing through the tower area.

[0074] It is worth noting that, in actual calculation, the static wind load acting on the train and the static wind load acting on the bridge can be calculated separately using the above formula. At the same time, the three-force coefficient calculated based on the above step S21 is calculated after considering the sudden change effect of the wind load in the tower area. Therefore, the static wind load acting on the train and the bridge calculated based on the three-force coefficient is also the static wind load after considering the sudden change effect of the wind load in the tower area.

[0075] For example, Figure 5 A curve diagram showing the change of the static wind load on the train over time during the whole process of the train crossing the bridge calculated in an exemplary embodiment of the present invention is shown. The static wind load on the train shown in the figure is also the static wind load that takes into account the sudden change effect of the wind load on the tower area.

[0076] Step S3. Establishing a vehicle-bridge dynamic model; taking the static wind load calculated in step S2 as one of the external excitations and adding it to the vehicle-bridge dynamic model to form a wind-vehicle-bridge-vortex-induced vibration coupling system.

[0077] Specifically, the vehicle-bridge dynamics model described in step S3 can be constructed by a bridge finite element model and a train dynamics model. In step S3, the process of establishing the vehicle-bridge dynamics model includes:

[0078] Step S31. According to parameters such as the geometry, material and boundary characteristics of the bridge, a finite element model of the bridge is established in software such as ANSYS, and a mass matrix, a stiffness matrix and a damping matrix of the bridge are assembled.

[0079] Among them, the motion equation of the bridge finite element model can be expressed as:

[0080]

[0081] In the above formula: are the acceleration, velocity and displacement of the bridge subsystem, respectively; They are the mass matrix, damping matrix and stiffness matrix of the bridge subsystem respectively; is the load matrix.

[0082] Step S32. The natural frequency and corresponding vibration mode of the bridge are calculated based on the finite element model of the bridge. Specifically, a modal analysis is performed on the finite element model of the bridge. In the modal analysis, the mass matrix is ​​selected as a lumped mass matrix, and the Lanczos method is used to solve the eigenvalue to obtain the natural frequency and corresponding vibration mode of the bridge.

[0083] Step S33. Perform substructure analysis on the bridge finite element model to ultimately generate a flexible body input file containing relevant information of the bridge finite element model.

[0084] Among them, substructure analysis is to reduce multiple units of the bridge finite element model into one unit, which is represented in the form of a matrix. This unit can be called a super unit. Generally, substructure analysis can include three stages: super unit generation stage (creating super units), super unit use stage (using super units), and super unit expansion stage (expanding results in super units).

[0085] This embodiment mainly involves the first two stages, namely, the super-element generation stage and the super-element use stage. In the super-element generation stage, the mass and stiffness information of the bridge finite element model is included in the super-element to form a structural information file of the bridge finite element model. , and get the geometry file of the bridge finite element model In the process of substructure analysis, it is necessary to reduce the number of degrees of freedom of the bridge finite element model, that is, to select the main nodes. In this embodiment, the Guyan reduction method is used for substructure analysis. When selecting the main nodes, key nodes that can contain the main natural vibration characteristics of the bridge should be selected as much as possible to ensure that the natural vibration frequency difference between the reduced bridge finite element model and the original bridge finite element model is small.

[0086] During the super-element use stage, the modal file of the bridge finite element model can be obtained through modal analysis.

[0087] It can be understood that after substructure analysis and modal analysis, the mass matrix, stiffness matrix, natural frequency and corresponding vibration mode, geometric characteristics, mode and other information of the bridge finite element model are stored in different files respectively, so that they can be exported and used later. Among them, the mass matrix, stiffness matrix, natural frequency and corresponding vibration mode, geometric characteristics, mode and other related information in the bridge finite element model can be read, and a flexible body input file containing these related information can be generated.

[0088] Step S34: Establish a dynamic model of the train based on relevant parameters such as mass, stiffness, damping, etc. of the train.

[0089] As a complex multi-degree-of-freedom spatial vibration system, the vibration of the train can be divided into lateral movement, extension and contraction, floating and sinking, shaking head, nodding head and rolling, etc. The train is generally composed of a car body, a bogie and a wheelset, which can be described by the body in a multi-body system. Among them, the wheelset and the bogie of the train are connected through a primary suspension system (including primary springs, dampers, etc.), and the bogie and the car body are connected through a secondary suspension system (including secondary springs, lateral dampers, vertical dampers, anti-roll torsion bars, anti-snake dampers and lateral stops, etc.). In the primary and secondary suspension systems, springs and dampers provide stiffness and damping respectively, which can be regarded as spring-damper systems. Since the stiffness of the train body, bogie and wheelset is much greater than that of the suspension system, the car body, bogie and wheelset can be regarded as rigid bodies. In addition, the center of mass of each rigid body is symmetrical left-right and front-back.

[0090] Generally, a train can be divided into three types: car body, bogie, and wheelset, with a total of 7 rigid bodies. The springs, dampers and other components in the primary and secondary suspension systems can be regarded as force elements. At this time, the entire train can be regarded as a rigid body-spring-damper model. Among them, in a single carriage of the train, the car body and two bogies are connected to the inertial coordinate system in space through railway hinges and have 6 degrees of freedom. Since there is one constraint on each of the left and right wheels in the wheelset, it has 4 degrees of freedom in space. The connection mainly considers the primary spring, secondary spring, vertical damper, lateral damper, lateral stopper, anti-snake damper, anti-roll torsion bar, etc., which are all simulated by force elements; the stiffness and damping of these force elements are set to linear or nonlinear according to the actual situation. In this embodiment, a single carriage has a total of 34 degrees of freedom, and the single carriage is then connected by a coupler to form a vehicle marshaling to finally form a train dynamics model.

[0091] Step S35. Import the flexible body input file from the bridge finite element model and the train dynamics model into multi-body dynamics software such as SIMPACK to form a vehicle-bridge dynamics model.

[0092] In step S3, in addition to the static wind load calculated in step S2, the external excitation added to the vehicle-bridge dynamics model may further include buffeting force, track irregularity and vortex-induced vibration acting on the bridge.

[0093] Specifically, the buffeting force acting on the bridge can be defined by buffeting resistance, buffeting lift force and buffeting lift moment based on the quasi-steady assumption. The calculation formula of the buffeting force acting on the bridge is:

[0094]

[0095] In the above formula: are the buffeting resistance, buffeting lift and buffeting lift moment acting on the bridge respectively; is the fluid density; U is the average wind speed; B is the width of the bridge section; are the drag coefficient, lift coefficient and lift moment coefficient respectively; They are the derivative of the drag coefficient, the derivative of the lift coefficient, and the derivative of the lift moment coefficient respectively; u , w are the fluctuating wind speeds in the transverse and vertical directions acting on the bridge respectively; The time-domain aerodynamic admittance function is used to modify the quasi-steady buffeting force model to take into account the unsteady characteristics of the buffeting force.

[0096] As for track unevenness, when a train passes through the track structure on a bridge, it is disturbed by the track and the train will vibrate. The force generated by the train vibration and the train's own weight are transmitted to the bridge structure through the wheel-rail interaction, causing the bridge to vibrate. Therefore, the excitation of the wheel-rail system is an important excitation source of the system. The excitation of the wheel-rail system can be divided into deterministic excitation and non-deterministic excitation. Deterministic excitation is caused by certain specific factors of the train or track, such as wheel scratches, misaligned rail joints, low track joints, etc. Non-deterministic excitation is mainly due to the random unevenness of the track geometry. The actual line geometry is affected by many factors and shows obvious randomness, so it is also called random excitation.

[0097] Track irregularity is a stable Gauss random process. After determining the power spectrum density function, it can be generated by the trigonometric series superposition method, the principle of which is:

[0098]

[0099] In the above formula: is the sequence of track unevenness generated; is the power spectral density function of a given track irregularity; For the i The frequencies considered are, , N is the number of frequencies considered; is the bandwidth of the frequency interval; In response to i The phase of the frequency, The values ​​are evenly distributed between.

[0100] Furthermore, track irregularities are usually described by a power spectral density function. Preferably, the track irregularities simulated by the low-interference track spectrum of the German high-speed railway are used as one of the external excitations. Vertical irregularities, horizontal irregularities and directional irregularities are considered. Different track irregularities are applied to the left and right tracks of the bridge respectively in the form of track excitation, and speed and acceleration excitations are considered.

[0101] As for vortex-induced vibration, it is a limited-amplitude vibration with self-excited properties under the action of vortex excitation force. A lot of work has been carried out at home and abroad on the study of vortex excitation force of long-span bridge main beams, and dozens of theoretical models have been established, including simple harmonic force model, empirical linear model, lift oscillator model, etc. Although there is still a lack of a unified model that can accurately and comprehensively describe the vortex-induced vibration phenomenon, one thing is clear: vortex vibration is unanimously considered to be a vibration form that is approximately equal-amplitude stable. Each particle oscillates in time, but the spatial distribution of its peak amplitude does not change, similar to a standing wave. Therefore, the canonical normalized main beam vertical vibration mode vector can be multiplied by the vortex-induced vibration amplitude, and the influence of the initial phase can be considered to determine the vortex-induced vibration of the main beam, that is:

[0102]

[0103] In the above formula: is the displacement time history of vortex-induced vibration; A is the vortex-induced vibration amplitude; is the vibration mode vector corresponding to the vertical frequency of vortex-induced vibration; is the vibration frequency of vortex-induced vibration; It is the initial phase of vortex-induced vibration when the train runs to the side span of the bridge.

[0104] In actual operation, the vibration mode, amplitude and frequency of the bridge when vortex-induced vibration occurs are obtained through the monitoring system on the bridge, and the corresponding parameters are substituted into the above formula to obtain the following: Figure 6 The curve diagram shown is a graph of the vertical displacement of the bridge mid-span caused by vortex-induced vibration varying with time, which can then determine the displacement caused by the vortex-induced vibration of the bridge.

[0105] On this basis, the step S3 further includes: taking the displacement generated by the vortex-induced vibration of the bridge as one of the external excitations and adding it to the nodes of the bridge main beam in the vehicle-bridge dynamics model.

[0106] It is worth noting that this embodiment fully considers the coupling between the train and the bridge under the vortex-induced vibration state by directly adding the vortex-induced vibration to the bridge in the form of displacement. Compared with the known evaluation methods, for example, the method disclosed in the patent document with application number "CN202410907916.9" and named "A windmill-bridge coupling calculation method considering bridge vortex vibration" adopts the method of adding vortex-induced vibration to track irregularity. This method can more carefully evaluate the influence of vortex-induced vibration on the dynamic response of the vehicle-bridge system.

[0107] Further, based on the wind-vehicle-bridge-vortex-induced vibration coupling system obtained in step S3, the vibration analysis method disclosed in this embodiment may also include:

[0108] Step S4. Calculate the dynamic responses of the train and the bridge in the wind-vehicle-bridge-vortex-induced vibration coupling system, so as to obtain the safety and comfort evaluation index of the train based on the dynamic response calculation of the train and the bridge, so as to evaluate the safety and comfort of the train when running on the bridge.

[0109] Specifically, the wind-vehicle-bridge-vortex-induced vibration coupling system includes a bridge subsystem and a train subsystem. The motion differential equations of the bridge subsystem and the train subsystem are expressed as:

[0110]

[0111] In the above two formulas: are the acceleration, velocity and displacement of the bridge subsystem, respectively; are the acceleration, velocity and displacement of the train subsystem respectively; They are the mass matrix, damping matrix and stiffness matrix of the bridge subsystem respectively; They are the mass matrix, damping matrix and stiffness matrix of the train subsystem respectively; , are the interaction forces between the train and the bridge respectively; is the wind load acting on the bridge; is the wind load acting on the train.

[0112] It can be understood that the dynamic response of the train and the bridge in the wind-vehicle-bridge-vortex-induced vibration coupling system can be calculated through the motion differential equations of the above-mentioned bridge subsystem and train subsystem, so as to calculate the safety and comfort evaluation indicators of the train through the dynamic responses of the two.

[0113] Among them, the train safety evaluation indicators include derailment coefficient (Q / P), wheel load reduction rate and the axle lateral force (H).

[0114] Specifically, the derailment coefficient is the ratio of the wheel-rail lateral force Q to the vertical force P. In the calculation, the derailment coefficient is a value that changes over time. In order to assess whether it exceeds the limit, its maximum value is generally compared with the limit value specified in the standard. In other words, the larger the derailment coefficient, the higher the possibility of wheel-rail separation.

[0115] In addition, according to the "High-speed EMU Vehicle Test Specifications", when the train speed is above 200 km / h, the derailment coefficient Q / P < 0.8. The "High-speed Railway Design Specifications" (TB 10621-2014) stipulates that the critical value of the derailment coefficient for trains with a design speed of 250~350km / h is also 0.8.

[0116] The wheel weight reduction ratio is used to assess the safety of the train when the lateral force is close to zero. The wheel weight reduction ratio is the ratio of the wheel weight reduction ΔP on the reduced side to the average deadweight wheel of the wheelset. The ratio is:

[0117]

[0118] In the above formula: are the static wheel weights of the left and right wheels respectively; is the vertical force of the wheel on the unloaded side. In the absence of unbalanced load, the static wheel weight of each wheel is the same, that is: .

[0119] In addition, the "High-speed EMU Vehicle Test Specification" stipulates that: in quasi-static state, ; Dynamically, At the same time, the "High-speed Railway Design Code" (TB 10621-2014) stipulates: In this embodiment, the limit standard value of the wheel load reduction rate is: .

[0120] The axle lateral force is the sum of the wheel-rail lateral forces on both sides of the wheelset, that is: , where Q1 and Q2 are the wheel-rail lateral forces on both sides of the wheelset. The "High-speed Railway Design Code" (TB 10621-2014) stipulates that the limit of wheel axle lateral force is:

[0121]

[0122] In the above formula: H is the lateral force of the wheel axle; is the static axle weight.

[0123] The train comfort evaluation indexes include body vibration acceleration and running stability. Among them, body vibration acceleration mainly reflects the magnitude of train vibration, while running stability comprehensively considers the influence of body vibration acceleration magnitude, frequency, etc.

[0124] In the "Test Methods and Evaluation Standards for Railway Locomotive Dynamic Performance" (TB / T 2360-93), the maximum vehicle body vibration acceleration is stipulated as follows: in the vertical direction, the vehicle body vibration acceleration ; In the lateral direction, the vehicle body vibration acceleration .

[0125] The running stability of the train can be evaluated using the Sperling index and can be calculated as follows:

[0126]

[0127] In the above formula: W Indicates the running stability of the train; is the vehicle body vibration acceleration; is the vibration frequency; is a correction function related to the vibration frequency.

[0128] In addition, the Sperling index level in the "Railway Vehicle Dynamics Performance Evaluation and Test Evaluation Specification" (GB 5599-85) can be used to evaluate the vertical and lateral stability of the train. The details are shown in the following table:

[0129] Train running stability evaluation comparison table

[0130]

[0131] In summary, it can be seen that the wind-vehicle-bridge-vortex-induced vibration analysis method considering the sudden change of wind load in the tower area disclosed in this embodiment, by taking the static wind load and vortex-induced vibration that take into account the sudden change effect of wind load in the tower area as external excitations, forms a wind-vehicle-bridge-vortex-induced vibration coupling system. Compared with the known methods for evaluating the safety and comfort of trains running on bridges under vortex-induced vibration conditions, the present invention can more accurately evaluate the dynamic response of trains running on bridges, especially the safety and comfort when crossing the tower area.

[0132] At the same time, this embodiment fully considers the coupling between the train and the bridge under the vortex-induced vibration state by directly adding the vortex-induced vibration to the bridge in the form of displacement, and can more carefully evaluate the impact of the vortex-induced vibration on the dynamic response of the vehicle-bridge system.

[0133] The above are only preferred embodiments of the present invention and are not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A wind-vehicle-bridge-vortex-induced vibration analysis method considering sudden changes in wind loads in the tower area, characterized in that: The steps include: Step S1. Establishing a vehicle-bridge numerical model for computational fluid dynamics numerical simulation; Step S2. Calculate the vehicle-bridge numerical model established in step S1 to calculate the static wind load acting on the train and the bridge during the entire process of the train crossing the bridge and taking into account the sudden change effect of the wind load on the tower area; Step S3. Establishing a vehicle-bridge dynamic model; taking the static wind load calculated in step S2 as one of the external excitations and adding it to the vehicle-bridge dynamic model to form a wind-vehicle-bridge-vortex-induced vibration coupling system; Step S2 specifically includes: Step S21. Calculate the train-bridge numerical model to obtain the time history of the three-force coefficients taking into account the sudden change effect of wind load in the tower area during the whole process of the train crossing the bridge; Step S22. According to the three-force coefficient time history calculated in step S21, the static wind load acting on the train and the bridge during the whole process of the train crossing the bridge and taking into account the sudden change effect of the wind load in the tower area is calculated; The step S3 also includes: taking the displacement generated by the vortex-induced vibration of the bridge as one of the external excitations and adding it to the nodes of the bridge main beam in the vehicle-bridge dynamics model.

2. The wind-vehicle-bridge-vortex-induced vibration analysis method considering the sudden change of wind load in the tower area according to claim 1 is characterized in that: In step S1, the process of establishing the vehicle-bridge numerical model includes: Step S11. Establishing a three-dimensional geometric model of the vehicle-bridge according to the structural parameters of the bridge and the train; Step S12. Meshing the vehicle-bridge three-dimensional geometric model established in step S11, and using overlapping meshes to simulate the movement of the train; Step S13. Importing the three-dimensional geometric model of the vehicle-bridge meshed in step S12 into computational fluid dynamics software, defining initial variables and boundary conditions, and performing iterative calculations by solving NS equations and turbulence equations to obtain a vehicle-bridge numerical model; In the rectangular coordinate system, the NS equation is: In the above formula: is the fluid density; x , y , z They represent the coordinate axes in the rectangular coordinate system respectively; u 1. u 2. u 3 are the velocity of the fluid in the rectangular coordinate system x , y , z Three components below the axis; t For time; p is the hydrostatic pressure; is the fluid dynamic viscosity coefficient; The turbulence equation is: In the above two formulas: is the fluid density; k is the turbulent kinetic energy coefficient; The turbulence kinetic energy coefficient k The empirical formula of is the dissipation rate of turbulent kinetic energy per unit mass of fluid; is the velocity component; t For time; , is the coordinate axis component; , Represent the turbulent kinetic energy coefficients k The dissipation rate of turbulent kinetic energy per unit mass of fluid The effective diffusion term of , is a constant.

3. The wind-vehicle-bridge-vortex-induced vibration analysis method considering the sudden change of wind load in the tower area according to claim 1 is characterized in that: In step S3, the process of establishing the vehicle-bridge dynamics model includes: Step S31. Establishing a finite element model of a bridge, and assembling a mass matrix, a stiffness matrix, and a damping matrix of the bridge; Step S32. Calculating the natural frequency and corresponding vibration mode of the bridge according to the finite element model of the bridge; Step S33. Performing substructure analysis on the bridge finite element model to ultimately generate a flexible body input file of the bridge finite element model containing relevant information; Step S34. Establishing a train dynamics model; Step S35. Import the flexible body input file from the bridge finite element model and the train dynamics model into the multi-body dynamics software to form a vehicle-bridge dynamics model.

4. The wind-vehicle-bridge-vortex-induced vibration analysis method considering the sudden change of wind load in the tower area according to claim 3 is characterized in that: In step S33, the relevant information includes mass matrix, stiffness matrix, natural frequency and corresponding vibration mode, and geometric characteristics.

5. The wind-vehicle-bridge-vortex-induced vibration analysis method considering the sudden change of wind load in the tower area according to claim 1 is characterized in that: In step S3, the external excitation also includes buffeting force acting on the bridge and track unevenness.

6. The wind-vehicle-bridge-vortex-induced vibration analysis method considering the sudden change of wind load in the tower area according to claim 1 is characterized in that: Also includes: Step S4. Calculate the dynamic responses of the train and the bridge in the wind-vehicle-bridge-vortex-induced vibration coupling system to obtain the safety and comfort evaluation index of the train based on the dynamic response calculation of the train and the bridge.

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