Sectional bridge wind vibration performance evaluation method and system

Abstract

The invention provides a segmental bridge wind vibration performance evaluation method and system, and relates to the technical field of segmental bridge wind vibration performance. Laser scanning is used for obtaining geometric parameters of a segmental bridge and collecting material characteristics, the geometric parameters and the material characteristics are imported into finite element software, a basic model is established, and boundary conditions are set; modal analysis is executed in finite element software, the natural vibration frequency and the vibration mode are calculated through a Lanczos method, and basic data are provided for wind load analysis; simulating a wind load by using a Davenport wind spectrum, setting a wind speed and a wind direction, and then applying the wind speed and the wind direction to the model; finally, the wind load condition is adjusted, the performance of the bridge under different wind loads is tested, and the displacement, acceleration and stress distribution of the bridge are analyzed and calculated through dynamic response to complete the wind vibration performance evaluation of the segmental bridge.

Description

Technical Field

[0001] The present invention relates to the technical field of wind-induced vibration performance of segmental bridges, and in particular to a method and system for evaluating wind-induced vibration performance of segmental bridges. Background Art

[0002] With the continuous development of modern buildings and infrastructure, the safety and stability of structures in natural environments have become key issues in engineering design. Especially in structures such as high-rise buildings and large bridges, the dynamic response caused by wind loads has a significant impact on the safety and durability of the structure. Traditional static analysis cannot accurately capture the vibration and displacement changes caused by instantaneous wind force, resulting in inaccurate predictions of structural performance under extreme conditions. In addition, although some existing dynamic analysis methods can simulate dynamic responses, they are often complex and time-consuming to calculate, and are sensitive to initial conditions and parameters, which limits their widespread application in actual engineering. Therefore, developing an accurate dynamic analysis model to simulate the structural response under wind loads has become a technical problem that needs to be solved urgently in the engineering field.

[0003] Segmental bridges are made up of multiple prefabricated segments and are widely used in bridge projects spanning longer distances. They have the advantages of fast construction speed, strong structural integrity, and less impact on the construction environment. However, under the action of wind loads, the bridge will vibrate, which may affect the safety and durability of its structure. Therefore, it is crucial to conduct wind-induced vibration performance evaluation, which can identify the main vibration modes and frequencies of the bridge, provide important references for the design and construction stages, and ensure the safety and stability of the bridge. The application of the present invention can help engineers conduct effective wind-induced vibration analysis during the design, construction, and operation stages, improve the wind resistance of the bridge, extend the service life of the bridge, and ensure safe operation under various wind conditions.

[0004] Existing technologies have the following deficiencies in evaluating the wind-induced vibration performance of segmental bridges: traditional numerical simulation methods may not be able to accurately simulate the actual situation under complex wind environments; wind tunnel tests are expensive, and the scaled-down model may result in insufficient accuracy; existing monitoring methods are expensive and difficult to quickly process and analyze data; design standards are usually conservative, which may result in a waste of resources; and traditional vibration control technologies are difficult to cope with multi-modal vibrations. These technologies cannot fully solve the problems of simulating the actual situation under complex wind environments, the similarity between models and actual bridges, the complexity of data processing and analysis, conservative design, and multi-modal vibration control.

[0005] The above information disclosed in this Background section is only for enhancement of understanding of the background of the present disclosure and therefore it may contain information that does not constitute the prior art that is already known to one of ordinary skill in the art. Summary of the invention

[0006] The purpose of the present invention is to provide a method and system for evaluating the wind-induced vibration performance of a segmental bridge, so as to solve the problems raised in the above-mentioned background technology.

[0007] To achieve the above object, the present invention provides the following technical solutions:

[0008] A method for evaluating wind-induced vibration performance of a segmental bridge, comprising the following specific steps:

[0009] Step 1: obtaining geometric parameters and material property data of each segment of the segment bridge to be evaluated, wherein the geometric parameters include cross-sectional area and length data, and the material property data include elastic modulus and material density data;

[0010] Step 2: Establish a basic model in the finite element analysis software, import the geometric parameters and material property data into the finite element analysis software, associate them with the basic model, and set the geometric boundary and load boundary as boundary conditions;

[0011] Step 3: Perform modal analysis in the finite element analysis software, use the Lanczos method to calculate the natural frequency and mode shape, identify the main vibration mode, and obtain the natural frequency, mode shape and participating mass ratio to provide basic data for wind load analysis;

[0012] Step 4: Use the Davenport wind spectrum to simulate wind loads in ANSYS, set specific wind speeds and directions, and apply the simulated wind load conditions to the model;

[0013] Step 5: Adjust the wind load number to test the performance of the segmental bridge under different wind loads. Run a dynamic response analysis under the influence of simulated wind loads to calculate the displacement, acceleration, and stress distribution of the bridge.

[0014] Furthermore, when obtaining the geometric parameters of each segment of the segmental bridge, a laser scanner is used to scan each segment of the segmental bridge to be evaluated to ensure that the scan covers all segments of the bridge, and the three-dimensional point cloud data of each segment of the bridge is obtained. The cross-sectional area A and length L of each segment are obtained based on the three-dimensional point cloud data, and the material property data of the segmental bridge are collected, including the elastic modulus E and material density ρ.

[0015] Furthermore, the logic of setting geometric boundaries and load boundaries as boundary conditions is as follows: set geometric boundary conditions, set fixed constraints at the bridge piers to limit all translations and rotations, allow horizontal movement at the sliding bearings but limit vertical displacement, and set symmetry constraints on the symmetry plane to reduce the amount of calculation; set load boundary conditions, apply wind loads to simulate time-varying loads, and apply uniformly distributed loads or concentrated forces on the bridge deck to simulate vehicle and pedestrian loads on segmental bridges; in summary, the geometric parameters and material property data are imported and associated with the basic model.

[0016] Furthermore, the method for calculating the natural frequency and mode shape using the Lanczos method is as follows: constructing a stiffness matrix K based on the cross-sectional area, elastic modulus and length data of each segment, and constructing a mass matrix M based on the material density, cross-sectional area and length data of each segment;

[0017] According to the stiffness matrix K and the mass matrix M, the Lanczos method is used to solve the overall eigenvalue λ and vibration mode φ, which are the eigenvectors and the basic equations of modal analysis:

[0018] Kφ=λMφ

[0019] Where φ is the vibration mode vector and λ is the eigenvalue;

[0020] Calculate the natural frequency f from the eigenvalue λ n :

[0021]

[0022] Among them, f n Indicates the nth order natural frequency of the structure, the natural frequency f n Indicates the natural vibration frequency of the structure;

[0023] The vibration mode vector φ is obtained through modal analysis, and the participating mass ratio Γ of each mode is calculated:

[0024]

[0025] Among them, Γ is the participating mass ratio, d is the gravity direction vector, which is the direction of gravity, and φ is the mode vibration vector, which is a unit vector.

[0026] Furthermore, the constructed stiffness matrix K is:

[0027]

[0028] Among them, K i is the stiffness submatrix of the i-th segment. Each submatrix can be calculated through the corresponding node and element properties. The stiffness matrix K of a single segment i It can be calculated by the following formula:

[0029]

[0030] Among them, A i is the cross-sectional area of ​​the ith segment, E i is the elastic modulus of the material of the ith segment, L i is the length of the segment of the i-th segment, i represents the segment number, and j is the number of segments of the segment bridge to be evaluated;

[0031] Similarly, the mass matrix M can also be expressed in the form of a block diagonal matrix, with each block corresponding to a segment of the bridge:

[0032]

[0033] Among them, M i is the stiffness submatrix of the ith segment, each submatrix can be calculated through the corresponding node and element properties; the mass matrix M of a single segment i It can be calculated by the following formula:

[0034] M i =ρ i ·A i ·L i

[0035] Among them, ρ i is the material density of the ith segment, A i is the cross-sectional area of ​​the ith segment, L i is the segment length of the ith segment.

[0036] Furthermore, when using the Davenport wind spectrum in ANSYS to simulate wind loads and apply it to the structural model, the wind speed spectrum density S is first defined. v (f), input the average wind speed U and turbulence intensity coefficient k, and perform modal analysis to obtain the natural vibration frequency f of the structure n , ensure that the frequency range covers the key vibration modes, and then generate random wind speed time history according to the wind speed spectrum, convert the frequency domain wind speed spectrum into time domain wind load through Fourier transform, and convert it into node force or surface force and apply it to the corresponding position. On this basis, perform time history analysis to calculate the response of the structure under wind load, and verify the accuracy of the model through test data, verify the stability under wind load, and use Davenport wind spectrum to calculate the wind speed power spectrum density at different frequencies:

[0037]

[0038] Among them, S v (f) is the wind speed power spectral density, which indicates the power of wind speed changing with frequency, k is the turbulence intensity coefficient, which indicates the intensity of wind turbulence, U is the average wind speed, which refers to the average wind speed measured in a certain period of time, and f is the frequency, which indicates the frequency of wind speed change.

[0039] Furthermore, the Davenport wind spectrum is used to generate wind speed time histories of different intensities by changing the average wind speed U or the turbulence intensity coefficient k, and the wind speed spectrum is converted into the time domain V(t) using the fast Fourier transform (FFT):

[0040] V(t)=F -1 (Sv (f))

[0041] Among them, F -1 stands for Inverse Fourier Transform;

[0042] Wind load calculation:

[0043]

[0044] Among them, F wind (t) is the wind load at time t, ρ wind is the air density, C d is the drag coefficient, A wind represents the windward area, V(t) represents the wind speed at time t, which is derived from the wind speed time history;

[0045] Run a dynamic response analysis under simulated wind loads to model the mechanical behavior and dynamic response of the structure using the finite element equations of motion:

[0046]

[0047] Where C represents the damping effect of the system, i.e., energy dissipation, and {ü(t)} represents the acceleration vector of the system, describing the quadratic change of displacement with time. represents the velocity vector of the system, describing the change of displacement over time, {u(t)} represents the displacement vector of the node in the system, {F total (t)} represents the total external load vector acting on the system.

[0048] The present invention further provides a segmental bridge wind-induced vibration performance evaluation system, the system is used to execute the above-mentioned segmental bridge wind-induced vibration performance evaluation method, comprising:

[0049] The data acquisition module is used to obtain the geometric parameters and material property data of each segment of the segment bridge to be evaluated, wherein the geometric parameters include the cross-sectional area and length, and the material property data include the elastic modulus, material density and Poisson's ratio data, and import these data into the finite element ANSYS software for model construction;

[0050] The model building module is used to build a basic model in the finite element analysis software, import the geometric parameters and material property data into the finite element analysis software, associate them with the basic model, and set the geometric boundary and load boundary as boundary conditions;

[0051] Model analysis module, used to perform modal analysis in ANSYS, calculate the natural frequencies and mode shapes of the bridge using the Lanczos method, and identify the inherent vibration characteristics of the bridge;

[0052] Wind load simulation module, which is used to set wind speed and direction using Davenport wind spectrum, simulate wind load in ANSYS and apply it to the bridge model to simulate the load on the bridge in a real wind field environment;

[0053] The comprehensive evaluation module is used to perform dynamic response analysis, simulate the performance of the bridge under different wind load conditions, evaluate the dynamic performance of the bridge under actual wind conditions, adjust the wind load index, repeatedly simulate the wind field, collect the displacement, acceleration and stress distribution data of the bridge, compare the analysis results with the design standards, and verify the safety and reliability of the structure.

[0054] Compared with the prior art, the present invention has the following beneficial effects:

[0055] This technical solution effectively improves the performance evaluation accuracy and reliability of segmental bridges under wind loads through a series of meticulous steps. First, by obtaining the geometric parameters and material property data (such as cross-sectional area, length, elastic modulus and material density, etc.) of the segmental bridge to be evaluated, the high accuracy of the input data is ensured, laying a solid foundation for subsequent analysis. Subsequently, a basic model is established in the finite element analysis software and these data are imported, while setting reasonable geometric boundaries and load boundary conditions to ensure the authenticity of the model and the rationality of the constraints.

[0056] In modal analysis, the Lanczos method is used to calculate the natural frequency and mode shape, identify the main vibration mode, and obtain the data of natural frequency, mode shape and participating mass ratio. This ensures that the response under different vibration modes can be effectively captured, avoids the problem of missing important vibration modes, and provides basic data for wind load analysis. In terms of wind load simulation, the Davenport wind spectrum is used to simulate wind loads in ANSYS, set specific wind speed and wind direction, and apply the simulated wind load conditions to the model, which makes the wind load simulation more realistic and reliable, and provides accurate wind load impact data for subsequent analysis.

[0057] By adjusting the wind load number, testing the performance of the segmental bridge under different wind loads, and finally running the dynamic response analysis to calculate the displacement, acceleration and stress distribution of the bridge, this step ensures that the performance of the bridge can be fully evaluated under different wind load conditions. In summary, this technical solution achieves accurate evaluation of the performance of the segmental bridge under wind load by obtaining accurate data, building a real model, conducting detailed modal analysis and wind load simulation, and performing dynamic response analysis, effectively improving the accuracy and reliability of the analysis. BRIEF DESCRIPTION OF THE DRAWINGS

[0058] Figure 1 It is a schematic diagram of the overall method flow of the present invention;

[0059] Figure 2It is a schematic diagram of the overall system module of the present invention. DETAILED DESCRIPTION

[0060] In order to make the objectives, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with specific embodiments.

[0061] It should be noted that, unless otherwise defined, the technical terms or scientific terms used in the present invention should be understood by people with ordinary skills in the field to which the present invention belongs. The words "first", "second" and similar words used in the present invention do not indicate any order, quantity or importance, but are only used to distinguish different components. "Include" or "comprise" and similar words mean that the elements or objects appearing before the word include the elements or objects listed after the word and their equivalents, without excluding other elements or objects. "Connect" or "connected" and similar words are not limited to physical or mechanical connections, but may include electrical connections, whether direct or indirect. "Up", "down", "left", "right" and the like are only used to indicate relative positional relationships. When the absolute position of the described object changes, the relative positional relationship may also change accordingly.

[0062] Example:

[0063] See also Figure 1 , the present invention provides a technical solution:

[0064] A method for evaluating wind-induced vibration performance of a segmental bridge, comprising the following specific steps:

[0065] Step 1: obtaining geometric parameters and material property data of each segment of the segment bridge to be evaluated, wherein the geometric parameters include cross-sectional area and length data, and the material property data include elastic modulus and material density data;

[0066] The geometric parameters including cross-sectional area and length were obtained by laser scanning, the elastic modulus and material density were obtained through laboratory tests or material specification sheets, the bridge model was constructed in finite element software, and the elastic modulus and material density material properties were imported;

[0067] Use laser scanners to scan all sections of the bridge in all directions to ensure that all structural surfaces are covered. Use laser beams to measure the distance of points on the surface of objects to generate 3D point cloud data. Cut sections at different positions from the 3D model. The 3D point cloud data obtained by scanning is a file containing a large number of coordinate points. Use FARO Scene, Leica Cyclone, Trimble RealWorks and other software to process and analyze point cloud data. Import the point cloud data files (.LAS, .PTS, .E57 and other formats) obtained by the scanner into the software to remove noise and redundant points, and purify by filtering and eliminating isolated points.

[0068] Average filtering calculates the average value of the neighborhood points of each point and uses it to replace the value of the point to smooth the data:

[0069]

[0070] Among them, P i ′ is the updated point, P j is a point in the neighborhood, and N is the number of points in the neighborhood;

[0071] Median filtering replaces the value of a point with the median of the neighborhood points. It is suitable for removing isolated noise, calculating the median of the points in the neighborhood and assigning it to the center point.

[0072] Statistical filtering removes points with large deviations by calculating the average distance from each point to its neighboring points:

[0073]

[0074] Among them, P i Indicates the point currently being processed;

[0075] Surface fitting, by fitting point cloud data to a geometric surface and removing mismatched points, usually uses the least squares method:

[0076]

[0077] Among them, f(x i ,y i ,z i ) represents the fitted geometric surface, z i is the actual point cloud data;

[0078] If multiple scans are performed, the point cloud data from different perspectives need to be aligned and merged:

[0079] Key point matching, by identifying common feature points in different scans and aligning them using feature point matching algorithms (such as SIFT and SURF);

[0080] The iterative closest point algorithm adjusts the position and angle of the point cloud by continuously calculating the closest point pairs of two sets of point clouds and minimizing their distance:

[0081]

[0082] Among them, P p is a point in the fixed point cloud, Q p is the moving point cloud with P pThe nearest point; after completing the alignment, merge multiple point cloud data and remove duplicate points in the overlapping area. Voxel Grid Downsampling can be used to reduce redundant points. In the case of multi-view scanning, use a global optimization algorithm (such as global ICP) to ensure the consistency between all scanned point clouds and avoid local optimal solutions;

[0083] The cross-sectional area A is extracted from the point cloud on the cross section, and the contour of the cross section is identified using the built-in tools of the software, and the area of ​​the cross section is calculated through a fitting algorithm; the length L marks the start and end points of the segment in the software, and the distance between the two points is directly calculated using the measurement tool; the extracted geometric parameter data is exported to a software format that can be used for subsequent analysis, such as CSV or Excel.

[0084] Step 2: Establish a basic model in the finite element analysis software, import the geometric parameters and material property data into the finite element analysis software, associate them with the basic model, and set the geometric boundary and load boundary as boundary conditions;

[0085] The logic of setting geometric boundaries and load boundaries as boundary conditions is as follows: set geometric boundary conditions, set fixed constraints at the bridge piers to limit all translations and rotations, allow horizontal movement at the sliding bearings but limit vertical displacement, and set symmetry constraints on the symmetry plane to reduce the amount of calculation; set load boundary conditions, apply wind loads to simulate time-varying loads, and apply uniformly distributed loads or concentrated forces on the bridge deck to simulate vehicle and pedestrian loads on segmental bridges; in summary, import and associate geometric parameters and material property data into the basic model;

[0086] Apply constraints to all degrees of freedom (including translation and rotation) at the bridge pier foundation, fix the support, and make all displacements and rotations zero: u x =u y =u z =0,θ x =θ y =θ z =0; where u x ,u y ,u z Displacement along x, y, z directions, θ x ,θ y ,θ z Rotation around the x, y, and z axes;

[0087] Sliding support, allows horizontal movement, but limits vertical displacement, and the displacement in one direction is zero: u z =0,θ x =θ y =θ z =0; where u x ,u yFree;

[0088] Apply symmetry conditions on the symmetry plane to reduce the amount of calculation: n =0, where u n is the normal displacement (perpendicular to the symmetry plane);

[0089] Load boundaries, wind loads, simulation of time-varying loads:

[0090] F w (t) = F0sin(ω(t-t0))

[0091] Among them, F0 is the maximum wind load, ω is the angular frequency;

[0092] Uniform load on the bridge deck, simulating vehicle and pedestrian loads: q(x) = q0, which means that the load along the length x of the bridge is uniformly distributed, that is, the load on each unit length is the same. q0 is the uniform load intensity, which means the uniform load per unit length, usually expressed in force units (such as Newton / meter);

[0093] First, it is necessary to understand the specific purpose of the bridge (for example, highway bridge, railway bridge, pedestrian bridge, etc.) and traffic flow, which includes information such as the type of vehicles, weight and pedestrian flow that may pass on the bridge; use traffic flow surveys and vehicle weight statistics to collect the actual load conditions that the bridge may face, which can be obtained through traffic monitoring systems, weighing data, etc.; determine the standard uniform load value according to the relevant bridge design specifications; for example, the "Highway Bridge Design Specifications" (such as China's "General Specifications for Highway Bridge and Culvert Design") will provide standard load values ​​and distribution conditions for different types of bridges. These specifications are summarized based on a large amount of empirical data and engineering practice; simplify the complex actual load conditions into uniformly distributed loads. In this process, calculations can be performed according to the formulas and methods in the design specifications to ensure that the design values ​​can cover the most unfavorable load conditions. The specific steps are as follows: According to the traffic flow survey and design specifications, determine the maximum load P that the bridge design needs to withstand. Based on the bridge length L, the uniform load q0 can be calculated by evenly distributing the maximum load:

[0094]

[0095] Among them, P is the total load of the bridge over the design length L; the final calculated uniform load q0 needs to be compared with the recommended value in the design specification, and checked and adjusted according to the actual situation to ensure the safety and reliability of the bridge under various use conditions; In summary, the determination of the uniform load q0 is a process that comprehensively considers the actual traffic flow, design specifications and empirical data. By reasonably setting q0, it can be ensured that the bridge design can withstand the maximum possible load in actual use;

[0096] Concentrated force on the bridge deck, simulating concentrated loads:

[0097]

[0098] Among them, F i is the i-th concentrated force, δ is the Dirac function;

[0099] The geometric and material property data are associated with the model, σ=E∈, where σ is stress and ∈ is strain. After importing these parameters into the basic model, a series of calculations and analyses are performed to ensure the safety and stability of the bridge design.

[0100] Step 3: Perform modal analysis in the finite element analysis software, use the Lanczos method to calculate the natural frequency and mode shape, identify the main vibration mode, and obtain the natural frequency, mode shape and participating mass ratio to provide basic data for wind load analysis;

[0101] The method for calculating the natural frequency and mode shape using the Lanczos method is as follows: construct the stiffness matrix K based on the cross-sectional area, elastic modulus and length data of each segment, and construct the mass matrix M based on the material density, cross-sectional area and length data of each segment;

[0102] According to the stiffness matrix K and the mass matrix M, the Lanczos method is used to solve the overall eigenvalue λ and vibration mode φ, which are the eigenvectors and the basic equations of modal analysis:

[0103] Kφ=λMφ

[0104] Where φ is the vibration mode vector and λ is the eigenvalue;

[0105] Calculate the natural frequency f from the eigenvalue λ n :

[0106]

[0107] Among them, f n Indicates the nth order natural frequency of the structure, the natural frequency f n Indicates the natural vibration frequency of the structure;

[0108] The vibration mode vector φ is obtained through modal analysis, and the participating mass ratio Γ of each mode is calculated:

[0109]

[0110] Among them, Γ is the participating mass ratio, d is the gravity direction vector, which is the direction of gravity, and φ is the modal vibration vector, which is a unit vector. By calculating the participating mass ratio, we can determine which modes contribute the most to the total response of the structure, and then optimize the design and analysis process;

[0111] The constructed stiffness matrix K is:

[0112]

[0113] Among them, K i is the stiffness submatrix of the i-th segment. Each submatrix can be calculated through the corresponding node and element properties. The stiffness matrix K of a single segment i It can be calculated by the following formula:

[0114]

[0115] Among them, A i is the cross-sectional area of ​​the ith segment, E i is the elastic modulus of the material of the ith segment, L i is the length of the segment of the i-th segment, i represents the segment number, and j is the number of segments of the segment bridge to be evaluated;

[0116] Similarly, the mass matrix M can also be expressed in the form of a block diagonal matrix, with each block corresponding to a segment of the bridge:

[0117]

[0118] Among them, M i is the stiffness submatrix of the ith segment, each submatrix can be calculated through the corresponding node and element properties; the mass matrix M of a single segment i It can be calculated by the following formula:

[0119] M i =ρ i ·A i ·L i

[0120] Among them, ρ i is the material density of the ith segment, A i is the cross-sectional area of ​​the ith segment, L i is the segment length of the ith segment

[0121] The number of rows and columns of the stiffness matrix K and the mass matrix M depends on the number of nodes of the unit and the number of degrees of freedom of each node. For beam units: usually each node has 6 degrees of freedom (3 translational degrees of freedom and 3 rotational degrees of freedom), and there are two nodes at both ends. Therefore, for beam units, there are a total of 2×6=12 degrees of freedom. Therefore, the stiffness matrix K and mass matrix M for beam units are both 12×12 square matrices, where each K i and M i is a 12×12 stiffness submatrix, each K i and M iThe submatrix reflects the mechanical properties of a single segment. For shell elements or solid elements, the matrix size varies depending on the number of node degrees of freedom and the number of nodes. For example, for an eight-node solid element, each node has three translational degrees of freedom, so the size of the stiffness matrix and the mass matrix is ​​24×24 (i.e., 8×3=24 degrees of freedom). Both the stiffness matrix and the mass matrix will be 24×24 square matrices, where each K i and M i is the 24×24 stiffness submatrix;

[0122] The number of rows and columns of the stiffness matrix K and the mass matrix M also depends on the unit type and the number of nodes. They contain multiple elements. For linear units, two-dimensional triangular units (plane stress / strain) are 6×6, and for three-dimensional tetrahedral units are 12×12. For complex units (shell units or solid units), the matrix size will be larger. The specific size depends on the number of nodes and degrees of freedom of each unit. Each node usually has several degrees of freedom (DOF), such as 1 DOF in one dimension, 2 DOF (displacement in three directions) in two dimensions, and 3 DOF in three dimensions. The dimension of the matrix is: number of nodes × number of DOFs per node. The stiffness and mass matrices are not a single element, but are composed of multiple elements, reflecting the interaction between different nodes. The size and structure of the matrix reflect the interaction between nodes, ensuring the balance and coordination between nodes and units in the analysis.

[0123] Step 4: Use the Davenport wind spectrum to simulate wind loads in ANSYS, set specific wind speeds and directions, and apply the simulated wind load conditions to the model;

[0124] When using Davenport wind spectrum in ANSYS to simulate wind loads and apply them to structural models, first define the wind speed spectrum density S v (f), input the average wind speed U and turbulence intensity coefficient k, and perform modal analysis to obtain the natural vibration frequency f of the structure n , ensure that the frequency range covers the key vibration modes, and then generate random wind speed time history according to the wind speed spectrum, convert the frequency domain wind speed spectrum into time domain wind load through Fourier transform, and convert it into node force or surface force and apply it to the corresponding position. On this basis, perform time history analysis to calculate the response of the structure under wind load, and verify the accuracy of the model through test data, verify the stability under wind load, and use Davenport wind spectrum to calculate the wind speed power spectrum density at different frequencies:

[0125]

[0126] Among them, S v(f) is the wind speed power spectrum density, which indicates the power of wind speed changing with frequency, k is the turbulence intensity coefficient, which indicates the intensity of wind turbulence, U is the average wind speed, which refers to the average wind speed measured in a certain period of time, and f is the frequency, which indicates the frequency of wind speed change. n The frequency related to the natural frequency of the bridge reflects the natural vibration characteristics of the structure. This formula converts the wind speed spectrum in the frequency domain into the wind speed time history in the time domain, which is used to generate simulation data of wind speed changes over time, as the basis for subsequent wind load calculations. This formula is based on the atmospheric boundary layer turbulence theory and is used to describe the frequency spectrum characteristics of atmospheric turbulence. Through experimental data and theoretical analysis, the relationship between wind speed and frequency is established. The Davenport wind spectrum can be used to simulate wind speed changes in a real environment, and wind load conditions can be applied to the structural model to help predict the dynamic response caused by wind, providing a basis for design and analysis;

[0127] S v (f) describes the energy density of wind speed at different frequencies, reflecting the fluctuation characteristics of turbulent wind speed. Low frequencies usually represent long-term changes (such as large-scale climate patterns), while high frequencies represent short-term fluctuations (such as turbulence). The larger the value, the greater the wind speed fluctuation energy at that frequency, which means that the wind has a more significant impact on that frequency. In structural design, it is necessary to pay attention to whether these frequencies are close to the natural frequencies of the structure to avoid resonance.

[0128] S v (f) is proportional to U, so the larger the average wind speed U, the greater the wind speed power spectrum density S v (f) will also increase. Higher average wind speed means greater wind energy input, which affects the dynamic response of the structure. v (f) is proportional to k. The larger the turbulence intensity coefficient, the more violent the wind fluctuation. v (f) will also increase, affecting the random vibration of the structure and possibly leading to a greater dynamic response; frequency f n The size of S v (f) The energy density at a specific frequency determines the degree of influence of that frequency on the structure;

[0129] The Davenport wind spectrum is used to generate wind speed time histories of different intensities by changing the average wind speed U or the turbulence intensity coefficient k, and the wind speed spectrum is converted into the time domain V(t) using the Fast Fourier Transform (FFT):

[0130] V(t)=F -1 (S v (f))

[0131] Among them, F -1It stands for Inverse Fourier Transform, which converts the wind speed spectrum in the frequency domain into the wind speed time history in the time domain, and is used to generate simulation data of wind speed variation over time, which serves as the basis for subsequent wind load calculations;

[0132] Wind load calculation:

[0133]

[0134] Among them, F wind (t) is the wind load at time t, ρ wind is the air density, C d is the drag coefficient, A wind represents the windward area, V(t) represents the wind speed at time t, which is derived from the wind speed time history. According to the wind speed spectrum, the wind speed time history is converted into the actual load acting on the structure and applied to the nodes of the structural model, considering the spatial and temporal changes of the wind speed;

[0135] F wind (t) reflects the wind load on the structure surface (such as the side of the bridge) at time t. The larger the value, the greater the force exerted by the wind on the structure, which will cause more significant structural response. Specifically:

[0136] Wind load is proportional to air density, drag coefficient, windward area and wind speed. Air density ρ wind The larger the wind load F is, the greater the wind load F is under the same wind speed. wind (t) is larger; C d It reflects the resistance of the surface shape of the structure to wind. The larger the resistance coefficient, the greater the wind resistance of the structure. Therefore, the wind load F wind (t) is also larger; the area A of the structure exposed to the wind wind The larger it is, the greater the wind force; V(t) is proportional to the square of the wind speed. The greater the wind speed, the wind load increases exponentially.

[0137] Step 5: Adjust the wind load number to test the performance of the segmental bridge under different wind loads. Run dynamic response analysis under the influence of simulated wind loads to calculate the displacement, acceleration and stress distribution of the bridge.

[0138] Run a dynamic response analysis under simulated wind loads to model the mechanical behavior and dynamic response of the structure using the finite element equations of motion:

[0139]

[0140] Among them, M is the mass matrix, which describes the mass distribution of the structure, K is the stiffness matrix, which describes the elastic properties of the structure, C represents the damping effect of the system, that is, energy dissipation, {ü(t)} represents the acceleration vector of the system, which describes the quadratic change of displacement with time, represents the velocity vector of the system, describing the change of displacement over time, {u(t)} represents the displacement vector of the node in the system, {F total (t)} represents the total external load vector acting on the system. This equation systematically describes the dynamic behavior of the structure under various external forces and can be used for time history analysis to help predict and analyze the deformation, vibration and stability of the structure;

[0141] {F total (t)} reflects the combined effect of all external forces acting on the structure at time t, including wind loads and other possible external loads, such as earthquake forces, vehicle loads, etc.;

[0142] {F total An important component of (t)} is the wind load F wind (t), which represents the effect of wind on the structure. On bridges, wind loads affect the vibration, stability and structural stress of the bridge deck. Other loads include static loads (such as deadweight) and dynamic loads (such as traffic loads and earthquake forces). These loads and wind loads jointly affect the dynamic response of the structure;

[0143] The total external load vector {F total The larger the (t)}, the greater the total external force on the structure, which may cause more significant displacement, stress and vibration response. It is necessary to ensure that the design of the structure can withstand these loads to ensure safety and functionality. The total load directly affects the displacement response of the structure. The larger the load, the more significant the displacement. The larger the total load, the greater the stress and strain generated, which affects the safety and durability of the structure. High loads may lead to higher speeds and accelerations, which in turn affect the vibration characteristics.

[0144] The damping effect is usually expressed by the damping matrix C, which describes the energy dissipation of the system. There are many ways to obtain C using the Rayleigh damping model. The mathematical formula is:

[0145] C=aM+bK

[0146] Among them, a and b are damping coefficients, which need to be adjusted according to the structural characteristic frequency and experimental data, M is the mass matrix, K is the stiffness matrix, and the Rayleigh damping model assumes that the damping is a linear combination of mass and stiffness. This method is suitable for most engineering applications.

[0147] Basic mechanical formulas of bridges;

[0148] σ=E·ε

[0149] Among them, σ is the internal force reflection of the force acting on the material, which is caused by the external load and obtained by deformation measurement, ε is the degree of deformation of the material under the action of external force, and E is the elastic modulus, which is an indicator of the rigidity of the material;

[0150] Strain ε can be measured directly by strain gauges installed on the material. These devices record the deformation of the material under the action of external forces and can be calculated from the geometric deformation:

[0151]

[0152] Among them, ΔL is the length change of the material after deformation, and L0 is the original length of the material;

[0153] In numerical solutions, numerical integration methods (Newmark-beta method) are often used to obtain the time response of displacement, velocity and acceleration. Displacement update:

[0154]

[0155] Speed ​​Update:

[0156]

[0157] Among them, β and γ are method parameters, and β = 0.25 and γ = 0.5 are usually taken to ensure numerical stability;

[0158] Acceleration update: Using the equations of motion:

[0159]

[0160] Solving for the acceleration:

[0161]

[0162] In bridge analysis, calculating displacement, velocity, acceleration and stress distribution is the key to ensuring bridge safety, stability and durability. Displacement ensures that the bridge will not deform too much under load to avoid affecting the function and appearance of the bridge. Velocity evaluates dynamic response, especially under dynamic loads such as earthquakes or wind, to understand the vibration characteristics of the bridge. Acceleration analyzes the dynamic behavior of the bridge to ensure comfort and safety, especially when responding to emergencies. Stress distribution identifies possible stress concentration areas to prevent material yielding or fracture and ensure structural safety. By analyzing these parameters, design optimization, maintenance planning and safety assessment can be guided to ensure the safety and reliability of the bridge throughout its service life.

[0163] See also Figure 2 The present invention further provides a segmental bridge wind-induced vibration performance evaluation system, the system is used to execute the above-mentioned segmental bridge wind-induced vibration performance evaluation method, comprising:

[0164] The data acquisition module is used to obtain the geometric parameters and material property data of each segment of the segment bridge to be evaluated, wherein the geometric parameters include the cross-sectional area and length, and the material property data include the elastic modulus, material density and Poisson's ratio data, and import these data into the finite element ANSYS software for model construction;

[0165] The model building module is used to build a basic model in the finite element analysis software, import the geometric parameters and material property data into the finite element analysis software, associate them with the basic model, and set the geometric boundary and load boundary as boundary conditions;

[0166] Model analysis module, used to perform modal analysis in ANSYS, calculate the natural frequencies and mode shapes of the bridge using the Lanczos method, and identify the inherent vibration characteristics of the bridge;

[0167] Wind load simulation module, which is used to set wind speed and direction using Davenport wind spectrum, simulate wind load in ANSYS and apply it to the bridge model to simulate the load on the bridge in a real wind field environment;

[0168] The comprehensive evaluation module is used to perform dynamic response analysis, simulate the performance of the bridge under different wind load conditions, evaluate the dynamic performance of the bridge under actual wind conditions, adjust the wind load index, repeatedly simulate the wind field, collect the displacement, acceleration and stress distribution data of the bridge, compare the analysis results with the design standards, and verify the safety and reliability of the structure.

[0169] The above formulas are all dimensionless and numerical calculations. The formula is a formula for the most recent real situation obtained by collecting a large amount of data and performing software simulation. The preset parameters in the formula are set by technicians in this field according to actual conditions.

[0170] The above embodiments may be implemented in whole or in part by software, hardware, firmware or any other combination thereof. When implemented by software, the above embodiments may be implemented in whole or in part in the form of a computer program product. Those skilled in the art may appreciate that the units and algorithm steps of each example described in conjunction with the embodiments disclosed herein may be implemented by electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are performed by hardware or software methods depends on the specific application and design constraints of the technical solution.

[0171] The units described as separate components may or may not be physically separated, and the components shown as units may or may not be physical units, and may be located in one place or distributed on multiple network units. Some or all of the units may be selected according to actual needs to achieve the purpose of the solution of this embodiment.

[0172] The above description is only a specific implementation manner of the present application, but the protection scope of the present application is not limited thereto. Any technician familiar with the technical field can easily think of changes or substitutions within the technical scope disclosed in the present application, which should be included in the protection scope of the present application.

Claims

1. A method for evaluating the wind-induced vibration performance of a segmental bridge, characterized in that: The specific steps include: Step 1: obtaining geometric parameters and material property data of each segment of the segment bridge to be evaluated, wherein the geometric parameters include cross-sectional area and length data, and the material property data include elastic modulus and material density data; Step 2: Establish a basic model in the finite element analysis software, import the geometric parameters and material property data into the finite element analysis software, associate them with the basic model, and set the geometric boundary and load boundary as boundary conditions; Step 3: Perform modal analysis in the finite element analysis software, use the Lanczos method to calculate the natural frequency and mode shape, identify the main vibration mode, and obtain the natural frequency, mode shape and participating mass ratio to provide basic data for wind load analysis; Step 4: Use the Davenport wind spectrum to simulate wind loads in ANSYS, set specific wind speeds and directions, and apply the simulated wind load conditions to the model; Step 5: Adjust the wind load number to test the performance of the segmental bridge under different wind loads. Run a dynamic response analysis under the influence of simulated wind loads to calculate the displacement, acceleration, and stress distribution of the bridge.

2. The wind-induced vibration performance evaluation method for a segmental bridge according to claim 1 is characterized by: In step 1, when obtaining the geometric parameters of each segment of the segmental bridge, use a laser scanner to scan each segment of the segmental bridge to be evaluated, ensure that the scan covers all segments of the bridge, obtain the three-dimensional point cloud data of each segment of the bridge, obtain the cross-sectional area A and length L of each segment based on the three-dimensional point cloud data, and collect the material property data of the segmental bridge including the elastic modulus E and material density ρ.

3. The wind-induced vibration performance evaluation method for a segmental bridge according to claim 1 is characterized by: In step 2, the logic of setting the geometric boundary and load boundary as boundary conditions is as follows: set the geometric boundary conditions, set fixed constraints at the bridge pier foundation to restrict all translations and rotations, allow horizontal movement at the sliding support but restrict vertical displacement, and set symmetry constraints on the symmetry plane; Set load boundary conditions, apply wind loads, simulate time-varying loads, and apply uniform loads or concentrated forces on the bridge deck to simulate vehicle and pedestrian loads on segmental bridges; In summary, the geometric parameters and material property data are imported and associated to the base model.

4. The wind-induced vibration performance evaluation method for a segmental bridge according to claim 1 is characterized by: In step 3, the method of calculating the natural frequency and mode shape using the Lanczos method is: The stiffness matrix K is constructed based on the cross-sectional area, elastic modulus and length data of each segment, and the mass matrix M is constructed based on the material density, cross-sectional area and length data of each segment; According to the stiffness matrix K and the mass matrix M, the Lanczos method is used to solve the overall eigenvalue λ and vibration mode φ, which are the eigenvectors and the basic equations of modal analysis: Kφ=λMφ Where φ is the vibration mode vector and λ is the eigenvalue; Calculate the natural frequency f from the eigenvalue λ n : Among them, f n Indicates the nth order natural frequency of the structure, the natural frequency f n Indicates the natural vibration frequency of the structure; The vibration mode vector φ is obtained through modal analysis, and the participating mass ratio Γ of each mode is calculated: Among them, Γ is the participating mass ratio, d is the gravity direction vector, which is the direction of gravity, and φ is the mode vibration vector, which is a unit vector.

5. The wind-induced vibration performance evaluation method for a segmental bridge according to claim 4 is characterized in that: The constructed stiffness matrix K is: Among them, K i is the stiffness submatrix of the i-th segment. Each submatrix can be calculated through the corresponding node and element properties. The stiffness matrix K of a single segment i It can be calculated by the following formula: Among them, A i is the cross-sectional area of ​​the ith segment, E i is the elastic modulus of the material of the ith segment, L i is the length of the i-th segment, i represents the segment number, and j is the number of segments of the segment bridge to be evaluated; Similarly, the mass matrix M can also be expressed in the form of a block diagonal matrix, with each block corresponding to a segment of the bridge: Among them, M i is the stiffness submatrix of the ith segment, each submatrix can be calculated through the corresponding node and element properties; the mass matrix M of a single segment i It can be calculated by the following formula: M i =ρ i ·A i ·L i Among them, ρ i is the material density of the ith segment, A i is the cross-sectional area of ​​the ith segment, L i is the segment length of the ith segment.

6. The wind-induced vibration performance evaluation method of a segmental bridge according to claim 4 is characterized by: In step 4, when using the Davenport wind spectrum in ANSYS to simulate wind loads and apply them to the structural model, first define the wind speed spectrum density S v (f), input the average wind speed U and turbulence intensity coefficient k, and perform modal analysis to obtain the natural vibration frequency f of the structure n , ensure that the frequency range covers the key vibration modes, and then generate random wind speed time history according to the wind speed spectrum, convert the frequency domain wind speed spectrum into time domain wind load through Fourier transform, and convert it into node force or surface force and apply it to the corresponding position. On this basis, perform time history analysis to calculate the response of the structure under wind load, and verify the accuracy of the model through test data, verify the stability under wind load, and use Davenport wind spectrum to calculate the wind speed power spectrum density at different frequencies: Among them, S v (f) is the wind speed power spectral density, which indicates the power of wind speed changing with frequency, k is the turbulence intensity coefficient, which indicates the intensity of wind turbulence, U is the average wind speed, which refers to the average wind speed measured in a certain period of time, and f is the frequency, which indicates the frequency of wind speed change.

7. The method for evaluating wind-induced vibration performance of a segmental bridge according to claim 6, characterized in that: In step 5, the Davenport wind spectrum is used to generate wind speed time histories of different intensities by changing the average wind speed U or the turbulence intensity coefficient k, and the wind speed spectrum is converted into the time domain V(t) using the fast Fourier transform: V(t)=F -1 (S v (f)) Among them, F -1 stands for Inverse Fourier Transform; Wind load calculation: Among them, F wind (t) is the wind load at time t, ρ wind is the air density, C d is the drag coefficient, A wind represents the windward area, V(t) represents the wind speed at time t, which is derived from the wind speed time history; Run a dynamic response analysis under simulated wind loads to model the mechanical behavior and dynamic response of the structure using the finite element equations of motion: Where C represents the damping effect of the system, i.e., energy dissipation, represents the acceleration vector of the system, describing the quadratic change of displacement with time, represents the velocity vector of the system, describing the change of displacement over time, {u(t)} represents the displacement vector of the node in the system, {F total (t)} represents the total external load vector acting on the system.

8. A wind-induced vibration performance evaluation system for a segmental bridge, characterized in that: The system is used to execute a method for evaluating wind-induced vibration performance of a segmental bridge according to any one of claims 1 to 7: The data acquisition module is used to obtain the geometric parameters and material property data of each segment of the segment bridge to be evaluated, wherein the geometric parameters include the cross-sectional area and length, and the material property data include the elastic modulus, material density and Poisson's ratio data, and import these data into the finite element ANSYS software for model construction; The model building module is used to build a basic model in the finite element analysis software, import the geometric parameters and material property data into the finite element analysis software, associate them with the basic model, and set the geometric boundary and load boundary as boundary conditions; Model analysis module, used to perform modal analysis in ANSYS, calculate the natural frequencies and mode shapes of the bridge using the Lanczos method, and identify the inherent vibration characteristics of the bridge; Wind load simulation module, which is used to set wind speed and direction using Davenport wind spectrum, simulate wind load in ANSYS and apply it to the bridge model to simulate the load on the bridge in a real wind field environment; The comprehensive evaluation module is used to perform dynamic response analysis, simulate the performance of the bridge under different wind load conditions, evaluate the dynamic performance of the bridge under actual wind conditions, adjust the wind load index, repeatedly simulate the wind field, collect the displacement, acceleration and stress distribution data of the bridge, compare the analysis results with the design standards, and verify the safety and reliability of the structure.

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