A Modal Analysis Method for Vehicle-Axle Coupled Systems Considering Vehicle Speed ​​Effects

Abstract

This invention provides a modal analysis method for vehicle-axle coupled systems considering vehicle speed effects, comprising: defining the vehicle-axle contact point displacement and the relative response between the vehicle's vertical displacement and the vertical displacement of the vehicle-axle contact point; establishing a coordinate transformation matrix based on the relationship between the relative response and the vehicle response, wherein the vehicle response is the vehicle's response relative to its static equilibrium position, and the coordinate transformation matrix is ​​used to transform the response vector defined by the vehicle response in the existing vehicle-axle coupled finite element element into an improved response vector defined by the relative response; transforming the existing vehicle-axle coupled finite element element equations using the coordinate transformation matrix and its time derivative to obtain an improved vehicle-axle coupled finite element element matrix, which explicitly includes speed-related terms caused by the vehicle's forward motion. This invention explicitly incorporates the vehicle speed effect into the system matrix, improving the accuracy of instantaneous modal parameter analysis of vehicle-axle coupled systems under high-speed and strongly coupled conditions.

Description

Technical Field

[0001] This invention relates to the field of vehicle-bridge coupling technology, and specifically provides a vehicle-bridge coupling modal analysis method that considers vehicle speed effects. Background Technology

[0002] As vital transportation infrastructure connecting different regions and traversing man-made or natural obstacles, bridges inevitably suffer from environmental erosion, traffic loads, material aging, and fatigue damage during long-term service, leading to varying degrees of structural performance degradation. To ensure the service safety of bridge structures, various methods for bridge structural health monitoring and condition assessment have been proposed in existing technologies.

[0003] Existing bridge health monitoring technologies typically rely on vibration sensors deployed on the bridge structure or moving vehicles to continuously or indirectly collect dynamic response signals during the bridge's service life. The health status of the bridge structure is then assessed by analyzing the structural dynamic characteristic parameters within the acquired vibration response. Modal parameters such as modal frequency and damping ratio reflect the bridge structure's stiffness, mass distribution, and energy dissipation characteristics, and are crucial indicators for bridge condition identification and damage assessment.

[0004] Under actual operating conditions, bridge vibration response primarily originates from the vehicle-bridge coupled vibration process generated when vehicles pass over the bridge. The vehicle and bridge form a vehicle-bridge coupled system during travel, which exhibits significant time-varying characteristics. Its overall stiffness and mass distribution continuously change as the vehicle moves across the bridge, causing parameters reflecting the bridge's dynamic characteristics, such as modal frequencies and damping ratios, to change with time and vehicle position. Therefore, a reasonable analysis of the evolution of modal parameters in the vehicle-bridge coupled system during vehicle passage is a crucial prerequisite for conducting bridge structural health status assessments based on traffic-induced vibration signals.

[0005] In existing vehicle-bridge coupling analysis methods, vehicle-bridge coupled finite element methods are typically used to model the interaction between the vehicle and the bridge. These elements simultaneously contain the vehicle's and bridge's degrees of freedom, assembling the vehicle and bridge subsystems into a unified finite element equation, thus avoiding iterative solutions between the vehicle and bridge. Therefore, they have been widely used for the dynamic response analysis of vehicle-bridge coupled systems. Furthermore, by combining this with classical modal analysis theory, the system frequencies, damping ratios, and other modal parameters during the vehicle's passage over the bridge can be calculated.

[0006] However, existing vehicle-bridge coupled finite element methods are primarily designed for dynamic response analysis, and their vehicle response is typically defined with reference to the vehicle's static equilibrium position. While this approach is effective for calculating vehicle-bridge coupled dynamic responses, it struggles to explicitly account for the velocity effects caused by the vehicle's forward motion in the system matrix when performing discrete-time modal analysis of the vehicle crossing the bridge. In particular, Coriolis and eccentric terms related to the bridge's contact point inclination and curvature are often not clearly represented in existing vehicle-bridge coupled finite element methods.

[0007] Therefore, when vehicle speed is high, vehicle mass is large, or vehicle-axle coupling is strong, directly using existing vehicle-axle coupling finite element methods for dynamic analysis may fail to accurately describe the influence of vehicle speed on the evolution of modal frequencies and damping ratios of the vehicle-axle coupling system. To address this, it is necessary to propose an improved finite element method suitable for modal analysis of vehicle-axle coupling systems. This method allows the vehicle's forward motion and its resulting velocity-related effects to be explicitly incorporated into the vehicle-axle coupling system matrix, thereby improving the rationality and accuracy of time-varying modal parameter analysis of the vehicle-axle coupling system. Summary of the Invention

[0008] To overcome the above-mentioned shortcomings, this invention is proposed to provide a solution or at least a partial solution to the problems that existing vehicle-bridge coupled finite element methods are mainly geared towards dynamic response analysis and are difficult to explicitly consider vehicle speed effects when used for instantaneous modal analysis of vehicle-bridge coupled systems.

[0009] In a first aspect, the present invention provides a vehicle-bridge coupled modal analysis method considering vehicle speed effects, comprising the following steps: Define the displacement of the axle contact point, and the relative response between the vehicle's vertical displacement and the vertical displacement of the axle contact point; Based on the relationship between the relative response and the vehicle response, a coordinate transformation matrix is ​​established; wherein, the vehicle response is the response of the vehicle relative to the static equilibrium position, and the coordinate transformation matrix is ​​used to transform the response vector defined by the vehicle response in the existing vehicle-bridge coupled finite element element into an improved response vector defined by the relative response. Using the coordinate transformation matrix and its time derivative, the existing vehicle-bridge coupled finite element equations are transformed to obtain an improved vehicle-bridge coupled finite element matrix, which explicitly includes velocity-related terms caused by the vehicle's forward motion.

[0010] Preferably, the relative response between the vehicle's vertical displacement and the vertical displacement of the axle contact point is the difference between the vehicle's vertical displacement and the vertical displacement of the axle contact point: .

[0011] in, This represents the vertical displacement at the axle contact point. This represents the vertical displacement of the vehicle.

[0012] Preferably, the vehicle response is the absolute displacement of the vehicle relative to its static equilibrium position.

[0013] Preferably, the coordinate transformation matrix The expression is: in, This is the identity matrix corresponding to the number of degrees of freedom of the bridge element nodes. Let the interpolation function vector of the beam element at the contact point be denoted as . Parameters for controlling the response reference mode.

[0014] Preferably, the time derivative of the coordinate transformation matrix includes the first-order time derivative. and second-order time derivative This is used to incorporate the vehicle's forward speed into the improved unit matrix.

[0015] Preferably, the expression for the improved vehicle-bridge coupled finite element matrix is: in, , , These represent the mass matrix, damping matrix, and stiffness matrix of the improved vehicle-axle coupled finite element element. This is the improved element load vector.

[0016] Preferably, the displacement of the axle contact point is defined, including: Suppose that at a certain moment, the vehicle is located within a certain element of the bridge, and its local coordinates are... Its position in the overall bridge coordinate system is The vertical displacement of the contact point between the vehicle and the bridge is obtained by interpolating the bridge node displacement of this element: in, This represents the vertical displacement at the axle contact point. Let the interpolation function vector of the beam element at the contact point be denoted as . This represents the vertical displacement of the vehicle. This represents the displacement vector of the bridge node.

[0017] Preferably, it further includes: assembling the improved vehicle-bridge coupled finite element unit with conventional bridge beam units, and the overall motion equation of the vehicle-bridge coupled system is as follows: in, , , These are the overall mass matrix, overall damping matrix, and overall stiffness matrix of the vehicle-axle coupling system, respectively. This is the overall response vector that includes the vehicle's relative response and the bridge node response; This represents the overall load vector.

[0018] Preferably, it further includes: establishing an instantaneous eigenvalue problem based on the overall matrix: The complex eigenvalues ​​of the vehicle-bridge coupled system are obtained by solving. ; For the complex eigenvalues , is represented as: in, For the first Instantaneous circular frequency of the stepped axle coupling system This corresponds to the instantaneous damping ratio; The instantaneous damping ratio Instantaneous frequency Calculated from complex eigenvalues: .

[0019] Secondly, the present invention discloses a modal analysis system for a vehicle-bridge coupling system considering vehicle speed effects, comprising: The acquisition module is used to define the displacement of the axle contact point and the relative response between the vehicle vertical displacement and the vertical displacement of the axle contact point. The matrix construction module is used to establish a coordinate transformation matrix based on the relationship between the relative response and the vehicle response; wherein, the vehicle response is the response of the vehicle relative to the static equilibrium position, and the coordinate transformation matrix is ​​used to transform the response vector defined by the vehicle response in the existing vehicle-bridge coupled finite element element into an improved response vector defined by the relative response; The transformation module is used to transform the existing vehicle-bridge coupled finite element equations using the coordinate transformation matrix and its time derivative to obtain an improved vehicle-bridge coupled finite element matrix, which explicitly includes velocity-related terms caused by the vehicle's forward motion.

[0020] The beneficial effects of this invention are as follows: 1. By extracting the displacement of the vehicle-bridge contact point and the vertical relative response between the vehicle and the contact point, the single absolute response description method is abandoned, which can truly reflect the dynamic deformation and position change law of the wheel and bridge contact surface during vehicle travel, and closely match the spatial displacement characteristics of the actual vehicle crossing the bridge.

[0021] 2. By reconstructing the response vector expression using a coordinate transformation matrix, the original response system based on the vehicle's absolute static balance position is transformed into a relative response characterization system. This standardizes the definition of variables in the vehicle-bridge coupling system and effectively avoids modeling errors caused by inconsistent response benchmarks.

[0022] 3. The improved unit matrix explicitly embeds the speed-related terms caused by the vehicle's forward motion, making up for the shortcoming of the traditional vehicle-bridge coupled finite element model that ignores the coupling effect of driving speed, and can fully reflect the dynamic mechanical effects such as vehicle inertia and motion drag effect. Attached Figure Description

[0023] The disclosure of this invention will become more readily understood with reference to the accompanying drawings. It will be readily understood by those skilled in the art that these drawings are for illustrative purposes only and are not intended to limit the scope of protection of this invention. Furthermore, similar numbers in the drawings are used to denote similar components, wherein: Figure 1 This is a schematic diagram of a vehicle-axle coupling system according to an embodiment of the present invention; wherein, Figure 1 (a) shows the overall vehicle-bridge coupling model when a vehicle crosses a bridge. Figure 1 (b) shows the vehicle-bridge coupled finite element unit formed by the interaction between the vehicle and the bridge unit.

[0024] Figure 2 This is a schematic diagram illustrating a scenario of multiple vehicles crossing a bridge at a predetermined speed, according to an embodiment of the present invention. Vehicles traveling longitudinally along the bridge should maintain a predetermined distance from each other. .

[0025] Figure 3 This is a comparison diagram of frequency identification results obtained based on synchronous extraction transformation according to an embodiment of the present invention and theoretical calculation results; wherein, Figure 3 (a) Corresponding vehicle speed Low-speed operating conditions Figure 3 (b) Corresponding vehicle speed High-speed operating conditions; Figure 4 This is a flowchart illustrating a modal analysis method for a vehicle-bridge coupling system considering vehicle speed effects, according to an embodiment of the present invention. Detailed Implementation

[0026] Some embodiments of the present invention will now be described with reference to the accompanying drawings. Those skilled in the art should understand that these embodiments are merely illustrative of the technical principles of the present invention and are not intended to limit the scope of protection of the present invention.

[0027] Example 1 like Figure 1As shown, the bridge structure is discretized into several beam elements. For bridge areas not affected by vehicles, conventional bridge elements are used for modeling; for bridge elements corresponding to vehicle locations, vehicle-bridge coupled finite element elements are constructed.

[0028] In one specific embodiment, the bridge can adopt a Bernoulli-Euler beam model, where each beam element has two nodes, each node including a vertical displacement degree of freedom and a rotational degree of freedom. The vehicle can be simplified as a single-degree-of-freedom spring-damped-mass system, including the vehicle mass. Vehicle suspension stiffness and vehicle suspension damping The vehicle travels at a constant speed. By bridge.

[0029] For the vehicle-bridge coupled finite element element containing the vehicle, its bridge node displacement vector is denoted as... The vertical displacement of the vehicle is denoted as The element response vector commonly used in existing vehicle-axle coupled finite element elements is... It can be written as: Among them, subscript Indicates a quantity at the unit level, using subscripts. This represents quantities based on the existing vehicle-bridge coupled finite element unit form.

[0030] like Figure 4 As shown, the present invention provides a modal analysis method for a vehicle-bridge coupling system considering vehicle speed effects, comprising: S1. Define the displacement of the axle contact point and the relative response between the vehicle's vertical displacement and the vertical displacement of the axle contact point.

[0031] In one specific implementation, suppose the vehicle is located within a certain unit of the bridge at a certain moment, and its local coordinates are... Its position in the overall bridge coordinate system is The vertical displacement of the contact point between the vehicle and the bridge is obtained by interpolating the bridge node displacement of this element: in, This represents the vertical displacement at the axle contact point. This is the interpolation function vector for the beam element at the contact point.

[0032] As the vehicle moves along the bridge, the position of the contact point changes over time. It is also a function that changes over time. (Regarding...) By taking the time derivative, the velocity at the contact point can be obtained: Further By taking the second time derivative, we can obtain the acceleration at the contact point: in, and Let represent the first and second derivatives of the interpolation function with respect to spatial coordinates, respectively. In the above expressions, It is related to the forward motion of the vehicle and the change in the slope of the bridge deformation, and can be associated with the Coriolis effect. Related to vehicle speed and bridge deformation curvature, it corresponds to the centrifugal effect term. Therefore, the vehicle speed effect can be explicitly reflected in the modal analysis of the vehicle-bridge coupled system.

[0033] Unlike existing vehicle-axle coupled finite element methods that typically define vehicle response relative to the static equilibrium position, this implementation redefines vehicle response as the relative response of the vehicle's vertical displacement to the displacement of the axle contact point: Right now: in, This refers to the relative response of the vehicle to the axle contact point. Parameters for controlling the response reference mode.

[0034] when At that time, there were: At this point, the vehicle response degenerates into the form of the vehicle response in the existing vehicle-bridge coupled finite element element, that is, the vehicle response is referenced to the static equilibrium position.

[0035] when At that time, there were: At this point, the vehicle response is the relative response of the vehicle mass block with respect to the axle contact point. Since the axle contact point moves with the vehicle's forward motion, this definition allows the velocity-related terms caused by the vehicle's forward motion to be included in the axle coupling system matrix. Therefore, in this embodiment, it is preferable to take... .

[0036] It should be noted that the method for obtaining the contact point displacement is not limited to the interpolation method described above; other finite element interpolation methods can also be used, such as Hermite interpolation or higher-order shape functions. As long as the vertical displacement at the vehicle-axle contact point can be obtained, it falls within the scope of protection of this invention.

[0037] S2. Based on the relationship between the relative response and the vehicle response, establish a coordinate transformation matrix; wherein, the vehicle response is the response of the vehicle relative to the static equilibrium position, and the coordinate transformation matrix is ​​used to transform the response vector defined by the vehicle response in the existing vehicle-bridge coupled finite element element into an improved response vector defined by the relative response.

[0038] In one specific implementation, based on vehicle relative response The response vector of the improved vehicle-axle coupled finite element is defined as follows: Its relationship with the original response vector The coordinate transformation relationship between them is as follows: Wherein, coordinate transformation matrix for: In the formula, This is the identity matrix corresponding to the number of degrees of freedom of the bridge unit nodes.

[0039] because As the vehicle's contact point position changes, and the vehicle's contact point position changes over time, therefore when hour, This is a time-varying matrix. Therefore, the relationships between the velocity and acceleration vectors are as follows: in, and These are the first and second time derivatives of the coordinate transformation matrix, respectively. It is precisely because of the existence of these two time derivative terms that the vehicle speed... And its related terms can be incorporated into the improved unit matrix.

[0040] S3. Using the coordinate transformation matrix and its time derivative, the existing vehicle-bridge coupled finite element equations are transformed to obtain an improved vehicle-bridge coupled finite element matrix, which explicitly includes velocity-related terms caused by the vehicle's forward motion.

[0041] In a specific implementation, the existing vehicle-axle coupled finite element element can typically be written in the following form: in, , , These are the mass matrix, damping matrix, and stiffness matrix of the original vehicle-axle coupled finite element element. This is the original element load vector.

[0042] Specifically, the original vehicle-axle coupled finite element equation can be expressed as: in, For vehicle quality, For vehicle suspension damping, For vehicle suspension stiffness, The vehicle's forward speed; , , These are the mass matrix, damping matrix, and stiffness matrix of the bridge beam element, respectively; the original element load vector can be expressed as: , This represents the external load vector acting on the bridge element nodes. The acceleration is due to gravity. The original vehicle-bridge coupled finite element element described above can unify the vehicle's degrees of freedom and the bridge's nodal degrees of freedom into the same element equation, thus it can be well used for the dynamic response analysis of vehicle-bridge coupled systems. However, the vehicle response in this element is based on the vehicle's static equilibrium position, and it is mainly suitable for dynamic response calculations. When it is directly used for the instantaneous modal analysis of discrete moments during the vehicle's passage across the bridge, the velocity-related effects caused by the vehicle's forward motion are not fully and explicitly reflected in the element matrix.

[0043] Specifically, as can be seen from the above matrix form, the mass matrix of the original vehicle-axle coupled finite element unit is... Regardless of vehicle position and forward speed; simultaneously, when the vehicle suspension damping At that time, the damping matrix and stiffness matrix of the original element are related to the vehicle speed. The related items also disappeared.

[0044] Substituting the above time-varying coordinate transformation relationship into the original vehicle-axle coupled finite element equation, we can obtain the improved vehicle-axle coupled finite element equation: in, , , These represent the mass matrix, damping matrix, and stiffness matrix of the improved vehicle-axle coupled finite element element. This is the improved element load vector.

[0045] The improved element matrix and the original element matrix satisfy the following relationship: Through the above transformation, the original vehicle-axle coupled finite element element is improved into a vehicle-axle coupled finite element element suitable for modal analysis. Because , and All of these are related to the vehicle's position and speed, so the improved mass matrix, damping matrix, and stiffness matrix can change as the vehicle moves forward.

[0046] When preferred When the improved unit equation is obtained, it can be expressed as: in, , , These are the mass matrix, damping matrix, and stiffness matrix of the bridge beam element, respectively.

[0047] As can be seen from the above expression, the improved vehicle-axle coupled finite element element explicitly includes: and The terms are of equal velocity. The former is related to vehicle velocity and bridge deformation slope, while the latter is related to the square of vehicle velocity and bridge deformation curvature. Therefore, they can be used to reflect the influence of vehicle forward motion on the modal characteristics of the vehicle-bridge coupling system.

[0048] In one embodiment, the method further includes: during the process of a vehicle crossing a bridge, the bridge element corresponding to the vehicle's location adopts the improved vehicle-bridge coupled finite element described above; the remaining bridge elements that are not in contact with the vehicle adopt conventional beam elements.

[0049] By assembling the improved vehicle-bridge coupled finite element unit with the conventional bridge beam unit according to the finite element assembly rules, the overall motion equation of the vehicle-bridge coupled system can be obtained: in, , , These are the overall mass matrix, overall damping matrix, and overall stiffness matrix of the vehicle-axle coupling system, respectively. This is the overall response vector that includes the vehicle's relative response and the bridge node response; This represents the overall load vector. As the vehicle moves along the bridge, the element containing the vehicle-bridge contact point and its local location continuously change. Therefore, the interpolation function needs to be updated at each calculation time or at each vehicle position. , , The vehicle-bridge coupling finite element matrix is ​​updated and improved accordingly. Therefore, the overall matrix... , , It becomes a time-varying matrix that changes with the vehicle's position and speed.

[0050] In one embodiment, the method further includes: at any discrete moment during the vehicle's passage across the bridge, constructing a corresponding improved vehicle-bridge coupled finite element matrix based on the vehicle's position and speed at that moment, and assembling it to obtain the overall system matrix. Then, the instantaneous eigenvalue problem of the vehicle-bridge coupled system is established: The complex eigenvalues ​​of the vehicle-bridge coupled system are obtained by solving. For the first The complex eigenvalues ​​of order one can be expressed as: in, For the first Instantaneous circular frequency of the stepped axle coupling system This represents the corresponding instantaneous damping ratio.

[0051] It can be calculated from complex eigenvalues: Furthermore, the instantaneous frequency can be expressed as: By calculating multiple instantaneous characteristic values ​​of a vehicle throughout the entire process of crossing a bridge, the evolution curves of modal parameters such as frequency and damping ratio of the vehicle-bridge coupling system as a function of vehicle position or time can be obtained.

[0052] It should be noted that the above embodiments are illustrated using a single-degree-of-freedom vehicle model and a beam bridge model as examples, but the present invention is not limited thereto. In other embodiments, the vehicle model can be extended to a multi-degree-of-freedom vehicle model, and the bridge model can be extended to a spatial beam, slab, beam-slab composite structure, or other finite element models. As long as the technical concept of defining the vehicle response relative to the vehicle-bridge contact point and explicitly introducing the vehicle speed effect into the vehicle-bridge coupling element matrix through time-varying coordinate transformation is adopted, it should fall within the protection scope of the present invention.

[0053] Furthermore, this invention can be used not only to calculate the instantaneous frequency of the vehicle-bridge coupling system during vehicle passage across a bridge, but also to calculate the instantaneous damping ratio, modal evolution law, and the influence of velocity effect on modal parameters. In addition, this invention can be combined with traffic-induced vibration signals collected by bridge sensors or moving vehicle sensors to provide theoretical simulation and calculation support for application scenarios such as bridge structural health monitoring, modal parameter identification, and vehicle scanning detection.

[0054] In one possible implementation, the modal analysis method for vehicle-axle coupling systems that considers vehicle speed effects includes: (1) Input bridge and vehicle parameters, including bridge length, cross-sectional parameters, elastic modulus, mass distribution, damping parameters, boundary conditions, vehicle mass, suspension stiffness, suspension damping and vehicle speed; (2) Divide the bridge into several beam elements and determine the mass matrix, damping matrix and stiffness matrix of each beam element; (3) Determine the bridge unit where the vehicle is located and its local coordinates within that unit based on the vehicle's current position; (4) Calculate the interpolation function at the vehicle contact point. and its spatial first derivative and second derivative ; (5) Based on the definition of the relative response of the vehicle to the axle contact point, construct the improved vehicle-axle coupled finite element mass matrix, damping matrix and stiffness matrix at the current vehicle position; (6) Assemble the improved vehicle-bridge coupling finite element with the other conventional bridge beam elements to obtain the overall mass matrix, overall damping matrix and overall stiffness matrix of the vehicle-bridge coupling system at the current moment; (7) Based on the total mass matrix, total damping matrix and total stiffness matrix at the current moment, establish the instantaneous eigenvalue problem, solve the complex eigenvalues ​​of the vehicle-bridge coupling system, and calculate the instantaneous frequency and instantaneous damping ratio of the system from the complex eigenvalues; (8) Update the vehicle position and repeat steps (3) to (7) until the vehicle leaves the bridge; (9) Output the evolution results of the vehicle-bridge coupling system modal frequency and damping ratio as the vehicle position or time changes during the entire process of the vehicle passing through the bridge.

[0055] To verify the effectiveness of the improved vehicle-bridge coupling finite element unit described in this invention in modal analysis of vehicle-bridge coupling systems, this embodiment constructs a numerical simulation scenario of multiple vehicles passing through a bridge in a cycle, and compares the theoretical modal analysis results obtained based on the improved unit of this invention with the frequency results obtained by identifying the bridge acceleration response signal.

[0056] In this embodiment, as Figure 2 As shown, an idealized series of equally spaced vehicles are set up at a constant speed. The distance between adjacent vehicles via the bridge is By using this multi-vehicle scenario, the acceleration response signal at the mid-span of the bridge can be obtained for any time length, thereby reducing the impact of the finite signal length on the frequency resolution in time-frequency analysis.

[0057] In this embodiment, the bridge is modeled as a simply supported beam. The bridge length is: The mass per unit length of the bridge is The elastic modulus of the bridge is: The moment of inertia of the bridge section is: The bridge damping ratio is: The first-order natural frequency of the bridge is: In the finite element modeling, the bridge is divided into 10 beam elements, each using the Euler-Bernoulli beam element form. Each node contains vertical displacement and rotation degrees of freedom. For bridge elements at vehicle locations, the improved vehicle-bridge coupled finite element method described in this invention is used for modeling; for bridge areas not affected by vehicles, conventional bridge beam elements are used. The time step in the dynamic response calculation is: In this embodiment, an idealized, equally spaced train of vehicles crosses the bridge at a constant speed. The spacing between adjacent vehicles is: Each vehicle is simplified to a single-degree-of-freedom spring-damped mass system. The vehicle mass is taken as: The vehicle suspension stiffness is taken as: The vehicle damping ratio is taken as: This embodiment considers two vehicle speed conditions: low-speed condition. High-speed operating conditions: High-speed operation is used to amplify the speed effect caused by the vehicle's forward motion, thereby more clearly verifying the advantages of the improved unit of this invention.

[0058] For each vehicle speed condition, two types of vehicle-axle coupled finite element elements were used for modal analysis: the first type was the original vehicle-axle coupled finite element element, with the vehicle response referenced to the static equilibrium position, i.e. The second type is the improved vehicle-axle coupling finite element described in this invention, corresponding to the vehicle response defined relative to the vehicle-axle contact point, i.e. For each discrete moment during the vehicle's passage across the bridge, the overall mass matrix, damping matrix, and stiffness matrix corresponding to the two models are assembled respectively, and the instantaneous eigenvalue problem is solved to obtain the theoretical instantaneous bridge frequency of the vehicle-bridge coupled system.

[0059] Simultaneously, the bridge mid-span acceleration response signal was obtained based on vehicle-bridge coupled dynamic response analysis, and a synchronous extraction and transformation method was adopted (corresponding to...). Figure 3 The acceleration signal (identified by the "results") is subjected to time-frequency analysis to identify the bridge frequency variation over time from the response signal. Then, the frequency results obtained from signal identification are compared with the theoretical frequency results obtained from the original unit and the improved unit of this invention, respectively.

[0060] like Figure 3 As shown, in low-speed operating conditions Below, the theoretical system coupling bridge frequencies obtained from both unit calculations are approximately The frequency results obtained from the acceleration signal identification are also close to... Since the vehicle speed effect is relatively weak at this time, and the time-frequency analysis resolution is limited, the difference between the results obtained by the original unit and the improved unit of this invention is not significant.

[0061] High-speed operating conditions Below, the bridge frequency identified by the mid-span acceleration signal of the bridge agrees well with the theoretical results obtained by the improved vehicle-bridge coupled finite element method of this invention (approximately). In contrast, the frequency results obtained from the original vehicle-axle coupled finite element method (which are still approximately...) There is a significant difference between the results and the signal recognition results. The reason is that, in the original unit, the Coriolis effect and centrifugal effect caused by the vehicle's forward motion relative to the static equilibrium position were not fully reflected in the instantaneous modal analysis, resulting in the theoretical frequency results being insensitive to changes in vehicle speed.

[0062] As can be seen from the above embodiments, when the vehicle speed is low, the vehicle speed effect has little impact on the modal analysis results of the vehicle-axle coupled system, and acceptable results can still be obtained using the original vehicle-axle coupled finite element element. However, when the vehicle speed is high, the speed-related effect caused by the vehicle's forward motion cannot be ignored. The improved vehicle-axle coupled finite element element described in this invention can more reasonably reflect the frequency evolution law of the vehicle-axle coupled system. Therefore, this embodiment verifies the advantages of this invention for modal analysis of vehicle-axle coupled systems under high-speed or strong vehicle-axle coupling conditions.

[0063] Example 2 This invention discloses a modal analysis system for a vehicle-axle coupling system considering vehicle speed effects, comprising: The acquisition module is used to define the displacement of the axle contact point and the relative response between the vehicle vertical displacement and the vertical displacement of the axle contact point. The matrix construction module is used to establish a coordinate transformation matrix based on the relationship between the relative response and the vehicle response; wherein, the vehicle response is the response of the vehicle relative to the static equilibrium position, and the coordinate transformation matrix is ​​used to transform the response vector defined by the vehicle response in the existing vehicle-bridge coupled finite element element into an improved response vector defined by the relative response; The transformation module is used to transform the existing vehicle-bridge coupled finite element equations using the coordinate transformation matrix and its time derivative to obtain an improved vehicle-bridge coupled finite element matrix, which explicitly includes velocity-related terms caused by the vehicle's forward motion.

[0064] The technical solution of the present invention has been described in conjunction with the preferred embodiments shown in the accompanying drawings. However, it will be readily understood by those skilled in the art that the scope of protection of the present invention is obviously not limited to these specific embodiments. Without departing from the principles and objectives of the present invention, those skilled in the art can make equivalent changes or substitutions to the original technical features, specific structures, materials, connection methods, arrangement methods, etc., and the technical solutions after these changes or substitutions will all fall within the scope of protection of the present invention.

Claims

1. A modal analysis method for a vehicle-bridge coupled system considering vehicle speed effects, characterized in that, Includes the following steps: Define the displacement of the axle contact point, and the relative response between the vehicle's vertical displacement and the vertical displacement of the axle contact point; Based on the relationship between the relative response and the vehicle response, a coordinate transformation matrix is ​​established; wherein, the vehicle response is the response of the vehicle relative to the static equilibrium position, and the coordinate transformation matrix is ​​used to transform the response vector defined by the vehicle response in the existing vehicle-bridge coupled finite element element into an improved response vector defined by the relative response. Using the coordinate transformation matrix and its time derivative, the existing vehicle-bridge coupled finite element equations are transformed to obtain an improved vehicle-bridge coupled finite element matrix, which explicitly includes velocity-related terms caused by the vehicle's forward motion.

2. The method according to claim 1, characterized in that, The relative response between the vehicle's vertical displacement and the vertical displacement of the axle contact point The difference between the vehicle's vertical displacement and the vertical displacement at the axle contact point: 。 in, This represents the vertical displacement at the axle contact point. This represents the vertical displacement of the vehicle.

3. The method according to claim 2, characterized in that, The vehicle response is the absolute displacement of the vehicle relative to its static equilibrium position.

4. The method according to claim 1, characterized in that, The coordinate transformation matrix The expression is: in, This is the identity matrix corresponding to the number of degrees of freedom of the bridge element nodes. Let the interpolation function vector of the beam element at the contact point be denoted as . Parameters for controlling the response reference mode.

5. The method according to claim 4, characterized in that, The time derivative of the coordinate transformation matrix includes the first-order time derivative. and second-order time derivative This is used to incorporate the vehicle's forward speed into the improved unit matrix.

6. The method according to claim 5, characterized in that, The improved expression for the vehicle-axle coupled finite element matrix is ​​as follows: in, , , These represent the mass matrix, damping matrix, and stiffness matrix of the improved vehicle-axle coupled finite element element. This is the improved element load vector.

7. The method according to claim 1, characterized in that, Define the displacement of the axle contact point, including: Suppose that at a certain moment, the vehicle is located within a certain element of the bridge, and its local coordinates are... Its position in the overall bridge coordinate system is The vertical displacement of the contact point between the vehicle and the bridge is obtained by interpolating the bridge node displacement of this element: in, This represents the vertical displacement at the axle contact point. Let the interpolation function vector of the beam element at the contact point be denoted as . This represents the vertical displacement of the vehicle. This represents the displacement vector of the bridge node.

8. The method according to claim 1, characterized in that, Also includes: The improved vehicle-bridge coupled finite element unit is assembled with conventional bridge beam elements. The overall motion equation of the vehicle-bridge coupled system is as follows: in, , , These are the overall mass matrix, overall damping matrix, and overall stiffness matrix of the vehicle-axle coupling system, respectively. This is the overall response vector that includes the vehicle's relative response and the bridge node response; This represents the overall load vector.

9. The method according to claim 1, characterized in that, Also includes: The problem of establishing instantaneous eigenvalues ​​based on the overall matrix: The complex eigenvalues ​​of the vehicle-bridge coupled system are obtained by solving. ; For the complex eigenvalues , is represented as: in, For the first Instantaneous circular frequency of the stepped axle coupling system This corresponds to the instantaneous damping ratio; The instantaneous damping ratio Instantaneous frequency Calculated from complex eigenvalues: 。 10. A modal analysis system for a vehicle-bridge coupling system considering vehicle speed effects, characterized in that, include: The acquisition module is used to define the displacement of the axle contact point and the relative response between the vehicle vertical displacement and the vertical displacement of the axle contact point. The matrix construction module is used to establish a coordinate transformation matrix based on the relationship between the relative response and the vehicle response; wherein, the vehicle response is the response of the vehicle relative to the static equilibrium position, and the coordinate transformation matrix is ​​used to transform the response vector defined by the vehicle response in the existing vehicle-bridge coupled finite element element into an improved response vector defined by the relative response; The transformation module is used to transform the existing vehicle-bridge coupled finite element equations using the coordinate transformation matrix and its time derivative to obtain an improved vehicle-bridge coupled finite element matrix, which explicitly includes velocity-related terms caused by the vehicle's forward motion.

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