Method for determining dynamic response index of bridge train and electronic equipment

Abstract

The invention provides a method for determining a dynamic response index of a bridge train and electronic equipment, and the method comprises the steps: constructing a finite element model of a bridge according to the basic information of the bridge, and determining a stiffness matrix, a mass matrix and a damping matrix of the bridge; substituting the first temperature into a finite element model of the bridge to obtain the displacement of each node in a plurality of nodes of the bridge based on the first temperature; wherein the first temperature is the temperature of the environment where the bridge is located; constructing a stiffness matrix, a mass matrix and a damping matrix of the train according to the multi-rigid-body dynamic model; and according to the displacement of each node based on the first temperature, the first irregularity value of each node, pile-soil coupling information of the bridge, a rigidity matrix, a mass matrix and a damping matrix of the bridge and a rigidity matrix, a mass matrix and a damping matrix of the train, determining a bridge train dynamic response index. The method can improve the accuracy of determining the dynamic response index of the bridge train.

Description

Technical Field

[0001] The invention relates to the technical field of vehicle-bridge coupled vibration, and in particular to a method for determining a bridge train dynamic response index and electronic equipment. Background Art

[0002] In the process of bridge design, it is necessary to evaluate the stability and safety of trains running on bridges. Usually, the stability and safety of trains running on bridges are evaluated by determining the dynamic response index of bridge trains. However, since the dynamic response index of bridge trains is currently determined based only on the factor of track unevenness, the accuracy of the obtained dynamic response index of bridge trains is low, which in turn makes it impossible to accurately evaluate the stability and safety of trains running on bridges. Summary of the invention

[0003] The present invention provides a method for determining a bridge train dynamic response index and an electronic device, which can improve the accuracy of determining the bridge train dynamic response index, and further improve the accuracy of evaluating the stability and safety of the train running on the bridge.

[0004] In a first aspect, an embodiment of the present application provides a method for determining a bridge train dynamic response index, comprising: constructing a finite element model of the bridge and determining the stiffness matrix, mass matrix and damping matrix of the bridge based on basic information of the bridge; bringing a first temperature into the finite element model of the bridge to obtain the displacement of each of a plurality of nodes of the bridge based on the first temperature; wherein the first temperature is the ambient temperature of the bridge; constructing the stiffness matrix, mass matrix and damping matrix of the train based on a multi-rigid body dynamic model; determining the bridge train dynamic response index based on the displacement of each node based on the first temperature, the first unsmoothness value of each node, the pile-soil coupling information of the bridge, the stiffness matrix, mass matrix and damping matrix of the bridge, and the stiffness matrix, mass matrix and damping matrix of the train.

[0005] Optionally, constructing a finite element model of the bridge and determining the stiffness matrix, mass matrix and damping matrix of the bridge according to basic information of the bridge includes: constructing a finite element model of the bridge according to the basic information of the bridge to obtain the stiffness matrix and mass matrix of each of the multiple units of the bridge; determining the stiffness matrix and mass matrix of the bridge according to the stiffness matrix and mass matrix of each unit; determining the natural vibration characteristic information of the bridge according to the stiffness matrix and mass matrix of the bridge in combination with a subspace iteration method; determining the damping matrix of the bridge according to the natural vibration characteristic information of the bridge, the stiffness matrix and mass matrix of the bridge.

[0006] Optionally, the step of determining the bridge train dynamic response index according to the displacement of each node based on the first temperature, the first unsmoothness value of each node, the pile-soil coupling information of the bridge, the stiffness matrix, mass matrix and damping matrix of the bridge, and the stiffness matrix, mass matrix and damping matrix of the train includes: updating the stiffness matrix of the bridge according to the pile-soil coupling information of the bridge; updating the damping matrix of the bridge according to the updated stiffness matrix of the bridge and the mass matrix of the bridge; determining the first force based on each wheelset according to the displacement of each node based on the first temperature and the first unsmoothness value of each node, and the stiffness of each wheelset in the train; wherein the first force is the force of the bridge on the train; and performing a dynamic displacement determination step, wherein the dynamic displacement determination step includes: determining the first force based on each wheelset, the mass matrix of the bridge and the updated The stiffness matrix and damping matrix of the train are used to determine the dynamic displacement of each node based on the first time step; the second force based on each wheelset is determined according to the dynamic displacement of each node based on the first time step, the displacement of each node based on the first temperature, the first unsmoothness value of each node, and the stiffness of each wheelset in the train; wherein the second force is the force of the train on the bridge; the dynamic response index of the bridge train based on the first time step is determined according to the second force based on each wheelset, the stiffness matrix, the mass matrix and the damping matrix of the train; the second force based on each wheelset is used as the first force based on each wheelset, and the dynamic response index of the bridge train based on the next time step is continuously determined starting from the dynamic displacement determination step until the dynamic response index of the bridge train based on the maximum time step is obtained; wherein the maximum time step is the time step of the train leaving the bridge.

[0007] Optionally, updating the stiffness matrix of the bridge according to the pile-soil coupling information of the bridge includes: determining the equivalent stiffness of each pier bottom node of the bridge according to the pile-soil coupling information of the bridge and in combination with an equivalent stiffness calculation method; wherein the multiple nodes of the bridge include each pier bottom node of the bridge; and updating the stiffness matrix of the bridge according to the equivalent stiffness of each pier bottom node of the bridge.

[0008] Optionally, determining the first force based on each wheelset according to the displacement of each node based on the first temperature, the first roughness value of each node, and the stiffness of each wheelset in the train includes: determining the second roughness value of each node according to the displacement of each node based on the first temperature and the first roughness value of each node; determining the actual position of each node according to the second roughness value of each node and the initial dynamic displacement of each node; determining the first force based on each wheelset according to the actual position of each node and the stiffness of each wheelset.

[0009] Optionally, determining the dynamic displacement of each node based on the first time step according to the first force based on each wheelset, the mass matrix of the bridge, and the updated stiffness matrix and damping matrix of the bridge includes: constructing a kinematic equation of the bridge based on each wheelset according to the first force based on each wheelset, the mass matrix of the bridge, and the updated stiffness matrix and damping matrix of the bridge; solving the kinematic equation of the bridge for each wheelset by the Newmark-β method to obtain the dynamic displacement of each node based on the first time step.

[0010] Optionally, determining the dynamic response index of the bridge train based on the first time step according to the second force based on each wheelset, the stiffness matrix, mass matrix and damping matrix of the train includes: constructing a train kinematic equation based on each wheelset according to the second force based on each wheelset, the stiffness matrix, mass matrix and damping matrix of the train; and solving the train kinematic equation of each wheelset by the Newmark-β method to obtain the dynamic response index of the bridge train based on the first time step.

[0011] In a second aspect, the present application provides a device for determining a bridge train dynamic response index, comprising: a first construction module, for constructing a finite element model of the bridge and determining the stiffness matrix, mass matrix and damping matrix of the bridge based on basic information of the bridge; an introduction module, for introducing a first temperature into the finite element model of the bridge to obtain the displacement of each of the multiple nodes of the bridge based on the first temperature; wherein the first temperature is the ambient temperature of the bridge; a second construction module, for constructing the stiffness matrix, mass matrix and damping matrix of the train based on a multi-rigid body dynamics model; a determination module, for determining the bridge train dynamic response index based on the displacement of each node based on the first temperature, the first unsmoothness value of each node, the pile-soil coupling information of the bridge, the stiffness matrix, mass matrix and damping matrix of the bridge, and the stiffness matrix, mass matrix and damping matrix of the train.

[0012] In a third aspect, the present application provides an electronic device comprising a memory and a processor; the memory is used to store a computer program; the processor is used to implement the method for determining the bridge train dynamic response index described in any one of the first aspects when executing the computer program.

[0013] In a fourth aspect, the present application provides a computer-readable storage medium, characterized in that a computer program is stored on the storage medium, and when the computer program is executed by a processor, the method for determining the bridge train dynamic response index described in any one of the first aspects is implemented.

[0014] The beneficial effects of the method for determining the bridge train dynamic response index of the present invention are:

[0015] By constructing a finite element model of the bridge, determining the stiffness matrix, mass matrix and damping matrix of the bridge, and constructing the stiffness matrix, mass matrix and damping matrix of the train, a data basis is provided for the subsequent determination of the bridge train dynamic response index. By bringing the first temperature (i.e., the ambient temperature of the bridge) into the finite element model of the bridge to obtain the displacement of each of the multiple nodes of the bridge based on the first temperature, the influence of the ambient temperature of the bridge on the displacement of each node of the bridge is determined. According to the displacement of each node based on the first temperature, the first unsmoothness value of each node, the pile-soil coupling information of the bridge, the stiffness matrix, mass matrix and damping matrix of the bridge, and the stiffness matrix, mass matrix and damping matrix of the train, the bridge train dynamic response index can be determined, providing an implementation plan for determining the bridge train dynamic response index.

[0016] Moreover, since the displacement of each node based on the first temperature (indicating the impact of the ambient temperature on the bridge node), the pile-soil coupling information of the bridge and the first roughness value of each node are comprehensively considered when determining the dynamic response index of the bridge train, the dynamic response index of the bridge train is determined from multiple dimensions, which improves the accuracy of determining the dynamic response index of the bridge train, and further improves the accuracy of evaluating the stability and safety of the train running on the bridge. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1 A flow chart of a method for determining a bridge train dynamic response index provided in an embodiment of the present application;

[0018] Figure 2 A schematic cross-sectional view of a cable-stayed bridge provided in an embodiment of the present application;

[0019] Figure 3 A schematic diagram of the deformation of a bridge under a first temperature environment provided in an embodiment of the present application;

[0020] Figure 4A schematic diagram of a flow chart of constructing a finite element model of a bridge and determining a stiffness matrix, a mass matrix and a damping matrix of the bridge provided in an embodiment of the present application;

[0021] Figure 5 A schematic diagram of a process for determining a bridge train dynamic response index provided in an embodiment of the present application;

[0022] Figure 6 A schematic diagram of a pile-soil coupling model provided in an embodiment of the present application;

[0023] Figure 7 A schematic diagram of the structure of a device for determining a bridge train dynamic response index provided in an embodiment of the present application. DETAILED DESCRIPTION

[0024] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the specific embodiments of the present invention are described in detail below in conjunction with the accompanying drawings. Although certain embodiments of the present invention are shown in the accompanying drawings, it should be understood that the present invention can be implemented in various forms and should not be interpreted as being limited to the embodiments described herein. On the contrary, these embodiments are provided to provide a more thorough and complete understanding of the present invention. It should be understood that the drawings and embodiments of the present invention are only for exemplary purposes and are not intended to limit the scope of protection of the present invention.

[0025] It should be understood that the various steps described in the method embodiments of the present invention may be performed in different orders and / or in parallel. In addition, the method embodiments may include additional steps and / or omit the steps shown. The scope of the present invention is not limited in this respect.

[0026] The term "including" and its variations used in this article are open inclusions, that is, "including but not limited to"; the term "based on" means "based at least in part on"; the term "one embodiment" means "at least one embodiment"; the term "another embodiment" means "at least one other embodiment"; the term "some embodiments" means "at least some embodiments"; the term "optionally" means "optional embodiments". The relevant definitions of other terms will be given in the following description. It should be noted that the concepts of "first", "second", etc. mentioned in the present invention are only used to distinguish different devices, modules or units, etc., and are not used to limit the order or interdependence of the functions performed by these devices, modules or units, etc.

[0027] It should be noted that the modifications of "one" and "plurality" mentioned in the present invention are illustrative rather than restrictive, and those skilled in the art should understand that, unless otherwise clearly indicated in the context, it should be understood as "one or more".

[0028] The names of the messages or information exchanged between multiple devices in the embodiments of the present invention are only used for illustrative purposes, and are not used to limit the scope of these messages or information.

[0029] In order to ensure the rationality of bridge design, the stability and safety of train running on the bridge need to be evaluated during the bridge design process. Usually, the stability and safety of train running on the bridge are evaluated by determining the bridge train dynamic response index.

[0030] Since the unevenness of bridge tracks is an important factor causing train vibration, and the train vibration caused by uneven tracks increases exponentially with the increase of train speed, and may even cause train derailment in severe cases. Therefore, track unevenness will affect the stability and safety of train operation on bridges. Thus, in related technologies, the bridge train dynamic response index is determined based on track unevenness, so as to evaluate the stability and safety of train operation on bridges according to the bridge train dynamic response index.

[0031] However, since the bridge train dynamic response index is determined based only on the factor of track unevenness, the obtained bridge train dynamic response index is of low accuracy, which makes it impossible to accurately evaluate the stability and safety of the train running on the bridge.

[0032] During the use of bridges, it was found that the construction environment of the bridge will affect the stability and safety of trains running on the bridge. For example, when the bridge is built in an extreme temperature environment, the extreme temperature will cause fatigue and deformation of the bridge structure, and the deformation of the bridge will affect the stability and safety of the train running on the bridge, and in severe cases it will even endanger the driving safety of the train. For another example, the pile-soil coupling effect is also an important factor to be considered in bridge construction. When the bridge load is large, the inertia force of the bridge body will react on the foundation to cause corresponding deformation, especially for bridges on soft foundations. Due to the displacement of the soil layer, the actual displacement of the bridge structure is different from the displacement assumed in the rigid foundation model. In addition, most bridges are in soft soil layers. Therefore, the pile-soil coupling effect on the stability and safety of trains running on bridges cannot be ignored.

[0033] Based on this, the embodiment of the present application provides a method for determining the dynamic response index of a bridge train. In this method, the dynamic response index of the bridge train is determined by comprehensively considering the unevenness of the bridge, the pile-soil coupling effect and the ambient temperature of the bridge, so as to improve the accuracy of determining the dynamic response index of the bridge train, and further improve the accuracy of evaluating the stability and safety of the train running on the bridge.

[0034] Figure 1The present invention provides a flow chart of a method for determining a bridge train dynamic response index, which can be executed by an electronic device, including but not limited to a desktop computer, a notebook computer, a tablet computer, and other devices with data processing capabilities. Figure 1 As shown, the method may include the following steps:

[0035] 110. Based on the basic information of the bridge, construct the finite element model of the bridge and determine the stiffness matrix, mass matrix and damping matrix of the bridge.

[0036] In the embodiment of the present application, the bridge is composed of multiple structures, including but not limited to bridge towers, main beams, cable-stayed cables, etc. The bridge includes multiple nodes, the number and positions of the multiple nodes can be set by the designer, and the nodes in the bridge can be understood as points used to calibrate the positions of various structures in the bridge. Two adjacent nodes constitute a unit. The multiple nodes of the bridge may include, for example, multiple nodes on the bridge tower, multiple nodes on the main beam, multiple nodes on the cable-stayed cables, etc.

[0037] Based on this, the basic information of the bridge includes but is not limited to the position of each of the multiple nodes of the bridge, the information of each of the multiple units composed of the multiple nodes, the support and constraint information between the various structures of the bridge, etc. The information of each unit includes but is not limited to the material and cross-sectional shape of each unit, etc. The support and constraint information between the various structures of the bridge can be, for example, the connection mode between the various structures in the bridge.

[0038] For example, Figure 2 The cross-sectional diagram of a cable-stayed bridge provided in the embodiment of the present application is shown in FIG. Figure 2 As shown, the cable-stayed bridge includes an upper deck, a lower deck, two bridge towers and cable-stayed cables located between the upper deck and the lower deck. The multiple nodes of the cable-stayed bridge include multiple nodes of the upper deck, multiple nodes of the lower deck and multiple nodes of the two bridge towers. The upper deck adopts an orthotropic steel bridge deck structure with a dense beam system, the lower deck adopts an integral steel box structure, the two bridge towers are made of concrete, the cross-sections of the two bridge towers are single-box single-chamber cross-sections, the cable-stayed cables are arranged in a double-cable harp shape, and the cable-stayed cables adopt 1860MPa-grade parallel steel wire cable-stayed cables.

[0039] After obtaining the basic information of the bridge, a finite element model of the bridge can be constructed based on the basic information of the bridge and in combination with the construction method of the finite element model to obtain the mass matrix and stiffness matrix of each of the multiple units of the bridge, and the damping matrix of the bridge can be determined based on the mass matrix and stiffness matrix of each of the multiple units of the bridge.

[0040] It should be noted that the specific implementation process of step 110 will be described below and will not be repeated here.

[0041] 120. The first temperature is introduced into the finite element model of the bridge to obtain the displacement of each of the plurality of nodes of the bridge based on the first temperature.

[0042] In the embodiment of the present application, the first temperature is the ambient temperature of the bridge. The first temperature may be, for example, 30 degrees, 10 degrees, 0 degrees, etc., which is specifically determined according to the ambient temperature of the bridge.

[0043] By bringing the first temperature into the finite element model of the bridge, the finite element model of the bridge can output the displacement of each node based on the first temperature. In other words, the displacement of each node of the bridge at the first temperature can be determined through 120.

[0044] For example, Figure 3 This is a schematic diagram of the deformation of the bridge under the first temperature environment provided by the embodiment of the present application. Figure 3 As shown, the horizontal direction indicates the mileage of the bridge, and the vertical direction indicates the vertical deformation of the bridge. ① indicates the deformation of the bridge deck at the first temperature, ② indicates the deformation of the main tower of the bridge at the first temperature, ③ indicates the deformation of the entire bridge at the first temperature, ④ indicates the total deformation of ①, ②, ③ and ⑤, and ⑤ indicates the deformation of the cable of the bridge at the first temperature.

[0045] 130. Based on the multi-rigid body dynamics model, construct the stiffness matrix, mass matrix and damping matrix of the train.

[0046] For example, the train adopts a multi-rigid body dynamics model, and the train may include a car body and two bogies. Without considering the freedom of the train wheelset and considering the 5 degrees of freedom of each component, namely, lateral, vertical, rolling, nodding and shaking, the train has a total of 15 degrees of freedom. Based on this, the stiffness matrix, mass matrix and damping matrix of the train may be as follows:

[0047] The mass matrix M of the train V This can be shown as follows:

[0048]

[0049] in,

[0050] M c is the vehicle mass, I cx is the moment of inertia of the train around the X axis, I cy is the moment of inertia of the vehicle body around the Y axis, I cz is the moment of inertia of the vehicle body around the Z axis, M t is the bogie mass, I tx is the moment of inertia of the bogie around the X axis, I ty is the moment of inertia of the bogie around the Y axis, I tz is the moment of inertia of the rack around the Z axis.

[0051] The damping matrix C of the train V This can be shown as follows:

[0052]

[0053] in,

[0054]

[0055] Among them, C tx is the secondary suspension longitudinal damping (bogie side), C ty is the suspension lateral damping (bogie side), C tz is the secondary suspension vertical damping (bogie side), H cb is the distance between the center of mass of the vehicle body and the center of mass of the bolster, d sc is half of the lateral spacing of the secondary vertical shock absorbers, l c is half of the train gauge, d sk It is half of the lateral spacing of the central spring, H bt C is the distance between the center of mass of the bolster and the center of mass of the bogie, px is the primary suspension longitudinal damping (per axle box), C py is the primary suspension lateral damping (per axle box), C pz is the primary suspension vertical damping (per axle box), H tw is the distance between the center of mass of the bogie and the center of mass of the wheelset, d wc It is half of the lateral spacing of the axle box damper, d wk is half of the lateral spacing of the axle box spring, l t It is half of the fixed wheelbase of the train.

[0056] The stiffness matrix K of the train V This can be shown as follows:

[0057]

[0058] in,

[0059]

[0060] Among them, K tx is the secondary suspension longitudinal stiffness (bogie side), K ty is the lateral stiffness of the secondary suspension (on the bogie side), K tz is the secondary suspension vertical stiffness (bogie side), K px is the primary suspension longitudinal stiffness (per axle box), K py is the lateral stiffness of the primary suspension (per axle box), K pz is the vertical stiffness of the primary suspension (per axle box).

[0061] It should be noted that the above description of the stiffness matrix, mass matrix and damping matrix of the train is merely exemplary and is not intended to limit the construction of the stiffness matrix, mass matrix and damping matrix of the train in this application.

[0062] 140. Determine the bridge train dynamic response index based on the displacement of each node based on the first temperature, the first unsmoothness value of each node, the pile-soil coupling information of the bridge, the stiffness matrix, mass matrix and damping matrix of the bridge, and the stiffness matrix, mass matrix and damping matrix of the train.

[0063] Exemplarily, the train kinematic equation and the bridge kinematic equation can be constructed according to the displacement of each node based on the first temperature, the first irregularity value of each node, the pile-soil coupling information of the bridge, the stiffness matrix, mass matrix and damping matrix of the bridge and the stiffness matrix, mass matrix and damping matrix of the train, so as to obtain the bridge train dynamic response index by solving the train kinematic equation and the bridge kinematic equation. The specific implementation process will be described below and will not be repeated here.

[0064] The bridge train dynamic response index may include a bridge train dynamic response index based on each time step in a plurality of time steps. The number of the plurality of time steps may be determined according to the length of the bridge, the speed of the train, and the step length of the time step.

[0065] The bridge train dynamic response index based on one time step includes but is not limited to the acceleration, velocity and displacement of the train calculated based on each wheelset of the train at the time step.

[0066] It should be noted that the acceleration, velocity and displacement of a train based on a wheelset may be calculated by the force exerted by the train on the bridge at the wheelset.

[0067] By determining the bridge train dynamic response index and comparing the bridge train dynamic response index with the bridge train dynamic response index standard, the running stability and safety of the train on the bridge can be evaluated based on the comparison results.

[0068] As can be seen from the above, by constructing the finite element model of the bridge, determining the stiffness matrix, mass matrix and damping matrix of the bridge, and constructing the stiffness matrix, mass matrix and damping matrix of the train, a data basis is provided for the subsequent determination of the bridge train dynamic response index. By bringing the first temperature (i.e., the ambient temperature of the bridge) into the finite element model of the bridge to obtain the displacement of each of the multiple nodes of the bridge based on the first temperature, the influence of the ambient temperature of the bridge on the displacement of each node of the bridge is determined. According to the displacement of each node based on the first temperature, the first irregularity value of each node, the pile-soil coupling information of the bridge, the stiffness matrix, mass matrix and damping matrix of the bridge, and the stiffness matrix, mass matrix and damping matrix of the train, the bridge train dynamic response index can be determined, providing an implementation plan for determining the bridge train dynamic response index.

[0069] Moreover, since the displacement of each node based on the first temperature (indicating the impact of the ambient temperature on the bridge node), the pile-soil coupling information of the bridge and the first roughness value of each node are comprehensively considered when determining the dynamic response index of the bridge train, the dynamic response index of the bridge train is determined from multiple dimensions, which improves the accuracy of determining the dynamic response index of the bridge train, and further improves the accuracy of evaluating the stability and safety of the train running on the bridge.

[0070] Figure 4 A schematic diagram of a process for constructing a finite element model of a bridge and determining the stiffness matrix, mass matrix and damping matrix of the bridge provided in an embodiment of the present application. Figure 4 As shown, based on the basic information of the bridge, the process of constructing the finite element model of the bridge and determining the stiffness matrix, mass matrix and damping matrix of the bridge can be as follows:

[0071] 410. According to the basic information of the bridge, a finite element model of the bridge is constructed to obtain the stiffness matrix and mass matrix of each unit in the multiple units of the bridge.

[0072] A finite element model of the bridge is constructed according to the basic information of the bridge and in combination with the construction method of the finite element model. After the finite element model of the bridge is obtained, the stiffness matrix and mass matrix of each unit of the multiple units of the bridge are obtained in combination with mathematical calculations.

[0073] For example, the stiffness matrix K of a unit of a bridge is BL This can be shown as follows:

[0074]

[0075] Where E is the elastic modulus of the material of the unit, G is the shear modulus of the material of the unit, and I X ,I Z ,I Yare the moments of inertia about the local coordinate system X, Y, and Z axes, respectively, X ,I Z ,I Y It can be obtained based on the cross-sectional characteristics of each unit, where L is the length of the unit and A is the cross-sectional area of ​​the unit.

[0076] The mass matrix M of a bridge unit BL This can be shown as follows:

[0077]

[0078] Where ρ is the density of the material of the unit, A is the cross-sectional area of ​​the unit, L is the length of the unit, and I X is the moment of inertia about the local coordinate system X, Y, and Z axes.

[0079] 420. Based on the stiffness matrix and mass matrix of each unit, determine the stiffness matrix and mass matrix of the bridge.

[0080] In the embodiment of the present application, the stiffness matrices of all units are combined to obtain the stiffness matrix of the bridge. The mass matrices of all units are combined to obtain the mass matrix of the bridge.

[0081] 430. Based on the stiffness matrix and mass matrix of the bridge and combined with the subspace iteration method, the natural vibration characteristic information of the bridge is determined.

[0082] For example, the natural vibration characteristic information of the bridge may include the vibration period, vibration frequency and vibration shape of the bridge at each modal order.

[0083] Specifically, the process of determining the natural vibration characteristic information of the beam by the subspace iteration method can be as follows:

[0084] First, generate the iterative formula, which can be shown as follows:

[0085] [δ][M B ][ψ]0=[ψ]1

[0086] Among them, [δ] is the bridge flexibility matrix, [δ] is the inverse matrix of the bridge stiffness matrix, [M B ] is the mass matrix of the bridge, [ψ] indicates the initial shape matrix of the bridge, [ψ] is a matrix with dimensions of n rows and s columns, n is the dimension of the stiffness matrix K of the bridge, s is the first s-order vibration mode of the bridge, in this embodiment s is 20, the shape matrix value is a randomly generated non-zero matrix, and the subscript below [ψ] is the number of iterations.

[0087] After the first iteration through the above formula, Perform normalization.

[0088] Then, the generalized stiffness matrix of the bridge is obtained according to the following formula: and the generalized mass matrix of the bridge

[0089] Among them, K B is the stiffness matrix of the bridge.

[0090] Solve the formation and vibration frequency according to the following formula:

[0091]

[0092] Where {q} is the generalized coordinate amplitude of the vibration mode. In order to ensure that the above equation has a solution, the following formula must hold.

[0093]

[0094] By solving the above formula, we can get the vibration period ω, and the vibration frequency can be determined by the vibration period ω. Substituting ω into {q} can be solved, and the vibration mode [Φ]1 after the first iteration can be obtained by using [Φ]1=[ψ]1{q}. In this way, the following Table 1 can be obtained. Repeat the above process 3-5 times to repeatedly iterate and replace the values ​​in Table 1, and determine the data in Table 1 obtained from the last iteration as the natural vibration characteristic information of the bridge.

[0095]

[0096]

[0097] Table 1

[0098] It should be noted that the data in Table 1 above will be updated once for each iteration. Through multiple iterations, the obtained data can be more in line with the actual situation of the bridge.

[0099] 440. Determine the damping matrix of the bridge based on the natural vibration characteristic information of the bridge, the stiffness matrix and the mass matrix of the bridge.

[0100] Exemplarily, the stiffness matrix of the bridge is calculated by the following formula:

[0101] C B =α c M B +β c K B

[0102] Among them, C B is the damping matrix of the bridge, M B is the mass matrix of the bridge, K B is the stiffness matrix of the bridge.

[0103]

[0104] Among them, ω i ,ω j are the vibration frequencies of the i-th and j-th vibration modes respectively; α c , β c is the Rayleigh damping linear combination parameter, ζ i , j are the damping ratios corresponding to the i-th and j-th order vibration modes, respectively, and are both 0.005 in this embodiment.

[0105] It should be noted that the values ​​of i and j can be selected from the modal orders in Table 1. Usually, i and j have different values.

[0106] Obviously, α can be calculated by Table 1 and the above formula c , β c . Then according to α c , β c Calculate C B .

[0107] Figure 5 A schematic diagram of a process for determining a bridge train dynamic response index provided in an embodiment of the present application. Figure 5 As shown, the process of determining the bridge train dynamic response index can be as follows:

[0108] 510. Update the stiffness matrix of the bridge based on the pile-soil coupling information of the bridge.

[0109] Exemplarily, the implementation process of 510 may be as follows:

[0110] First, according to the pile-soil coupling information of the bridge and in combination with the equivalent stiffness calculation method, the equivalent stiffness of each bridge pier bottom node of the bridge is determined. The multiple nodes of the bridge may include each bridge pier bottom node of the bridge.

[0111] Specifically, under the premise of considering the pile-soil coupling, Penzien's simplified method is adopted to use the interaction between mass and spring to replace the mutual influence between pile and foundation in actual situations. It is assumed that the soil is a uniform isotropic linear elastic horizontal layer and the damping is independent of frequency. The properties of each layer of soil can be different. The properties of the lateral soil are independent of each other in two orthogonal directions. The soil resistance is uncoupled in the axial, lateral and torsional directions, and it belongs to a small displacement problem.

[0112] For example, Figure 6 A schematic diagram of the pile-soil coupling model provided in an embodiment of the present application. Figure 6 The bridge cap 601, bridge pier 602, and pile-soil equivalent spring 603 are shown. Figure 6In , the pile-soil coupling information is equivalent to the pile-soil equivalent spring 603. In this way, the equivalent stiffness of each bridge pier bottom node of the bridge can be determined by calculating the stiffness of the pile-soil equivalent spring 603 at each bridge pier bottom node.

[0113] Based on this, the equivalent stiffness of each pier bottom node can be calculated by the following formula:

[0114]

[0115] Among them, k s is the equivalent stiffness of the Zth pier bottom node, p s =Aσ zx , A=ab p , σ zx =m z x z , A is the vertical cross-sectional area of ​​the pile at the bottom node of the Zth pier, σ zx is the lateral resistance of the soil at the bottom node of the Zth pier to the pile, a is the thickness of the soil layer at the bottom node of the Zth pier, b p Calculate the width of the pile at the bottom node of the Zth pier, m z Mainly derived from the measurement data in actual engineering, x z is the lateral displacement of the pile foundation at the bottom node of the Zth pier.

[0116] It should be noted that the pile-soil coupling information of the bridge may include the thickness of the soil layer at the bottom node of each pier, the calculated width of the pile column, and the measurement data in the actual project.

[0117] Then, the stiffness matrix of the bridge is updated according to the equivalent stiffness of each pier bottom node of the bridge.

[0118] The update process is as follows:

[0119] The equivalent stiffness of each pier bottom node is summed with the stiffness of the corresponding pier bottom node in the stiffness matrix of the bridge to obtain the equivalent stiffness and the sum of the stiffness of each pier bottom node. In addition, the stiffness of the corresponding pier bottom node in the stiffness matrix of the bridge is replaced by the equivalent stiffness and the sum of the stiffness of each pier bottom node to achieve the update of the stiffness matrix of the bridge.

[0120] 520. Update the damping matrix of the bridge according to the updated stiffness matrix of the bridge and the mass matrix of the bridge. Specifically, the damping matrix of the bridge can be updated according to the relevant processes in 430 and 440, which will not be described in detail here.

[0121] 530. Determine a first force based on each wheelset according to the displacement of each node based on the first temperature, the first unsmoothness value of each node, and the stiffness of each wheelset in the train.

[0122] The first force is the force of the bridge on the train. It should be noted that the first force based on each wheelset can be understood as the first force at each wheelset.

[0123] The specific implementation process of 530 can be as follows:

[0124] First, a second unsmoothness value of each node is determined according to a displacement of each node based on the first temperature and a first unsmoothness value of each node.

[0125] Exemplarily, the second roughness value of each node may be determined by the following formula:

[0126] r i =r i1 +r i2

[0127] Among them, r i is the second unsmoothness value of the ith node, r i1 is the first uneven value of the i-th node, r i2 is the displacement of the i-th node based on the first temperature.

[0128] It should be noted that the first unsmoothness value of each node may be provided to the device by a designer.

[0129] Then, the actual position of each node is determined according to the second irregularity value of each node and the initial dynamic displacement of each node.

[0130] Exemplarily, the actual position of each node can be determined by the following formula:

[0131] D Bi =X Bi +r i

[0132] Among them, D Bi is the actual position of the ith node, X Bi is the initial dynamic displacement of the ith node, r i is the second roughness value of the i-th node.

[0133] Finally, the first force based on each wheelset is determined according to the actual position of each node and the stiffness of each wheelset.

[0134] Exemplarily, the first force based on each wheelset may be determined by the following formula:

[0135] F(B-V)wi =k wi ×D B

[0136] Among them, k wi is the stiffness of the wi-th wheelset of the train, D B is the actual position of the bridge space, F (B-V)wi is the first force acting on the wi-th wheelset. D B is a position vector composed of the actual positions of multiple nodes. That is to say, first determine D according to the actual position of each node B , and then, the first force based on each wheelset is determined according to the above formula.

[0137] 540. Execute a dynamic displacement determination step, wherein the dynamic displacement determination step may include: determining the dynamic displacement of each node based on the first time step according to a first force based on each wheelset, a mass matrix of the bridge, and an updated stiffness matrix and damping matrix of the bridge.

[0138] The specific implementation process of 540 can be as follows:

[0139] First, the kinematic equation of the bridge based on each wheelset is constructed according to the first force based on each wheelset, the mass matrix of the bridge, and the updated stiffness matrix and damping matrix of the bridge.

[0140] Exemplarily, the bridge kinematic equation for each wheelset may be as follows:

[0141]

[0142] Among them, M B is the mass matrix of the bridge, C B is the updated damping matrix of the bridge, K B is the updated stiffness matrix of the bridge, F (B-V)wi is the first force of the wi-th wheelset, X Bwi is the displacement of the bridge based on the wi-th wheelset, is the speed of the bridge based on the wi-th wheelset, is the acceleration of the bridge based on the wi-th wheelset.

[0143] Then, the kinematic equations of the bridge for each wheelset are solved by the Newmark-β method to obtain the dynamic displacement of each node based on the first time step.

[0144] A displacement based on the first time step can be calculated through the bridge kinematic equation of a wheelset, and the displacement based on the first time step can include the dynamic displacement of each node based on the first time step under the wheelset.

[0145] The purpose of solving the bridge kinematic equations for each wheelset is to obtain X Bwi , and The specific solution process can be shown as follows:

[0146] By calculating the integral format:

[0147]

[0148] To solve the bridge kinematic equations for each wheelset.

[0149] Among them, α and β are integration parameters, α is taken as 0.25, β is taken as 0.5, Δt is the step size of the time step; n is the nth time step, 0≤n≤N, N can be determined according to Δt, train speed and length of the bridge, the first time step refers to n=1, and the maximum time step refers to n=N.

[0150] X Bwi , and As X n , Substitute into the integral format to solve the bridge kinematic equations for each wheelset.

[0151] In the above formula Utilizing X n+1 To represent, then respectively Substitute into the bridge subsystem dynamics equation at n+1 time step and simplify to obtain X n+1 The solution formula is:

[0152]

[0153] Among them, F n+1 is the bridge node load at time step n+1, which can be calculated based on F (B-V)wi Here, M, C, and K are the mass matrix, updated damping matrix, and updated stiffness matrix of the bridge, respectively.

[0154] X n+1 The solution formula is:

[0155]

[0156] In the formula, a6=Δt(1-β), a7=βΔt, solving the above equation yields X n+1 ;

[0157] The solution formula is:

[0158]

[0159] Obviously, the above formula can be used to obtain X n+1 Among them, X n+1 Can indicate the displacement based on the n+1th time step, Can indicate the speed based on the n+1th time step, May indicate the acceleration based on the n+1th time step.

[0160] In summary, the dynamic displacement of each node based on the first time step can be determined according to the above principles.

[0161] 550. Determine the second force based on each wheelset according to the dynamic displacement of each node based on the first time step, the displacement of each node based on the first temperature, the first unsmoothness value of each node, and the stiffness of each wheelset in the train. The second force is the force of the train on the bridge. It should be noted that the implementation principle of 550 is similar to that of 530, and will not be repeated here.

[0162] 560. According to the second force based on each wheelset, the stiffness matrix, mass matrix and damping matrix of the train, the dynamic response index of the bridge train based on the first time step is determined.

[0163] The specific implementation process of 560 can be as follows:

[0164] Firstly, according to the second force based on each wheelset, the stiffness matrix, mass matrix and damping matrix of the train, the kinematic equation of the train based on each wheelset is constructed.

[0165] Exemplarily, the train kinematic equation for each wheelset may be as follows:

[0166]

[0167] Among them, M V is the mass matrix of the train, C V is the damping matrix of the train, K V is the stiffness matrix of the train, F (V-B)wi is the second force of the wi-th wheelset, X Vwi is the displacement of the train based on the wi-th wheelset, is the speed of the train based on the wi-th wheelset, is the acceleration of the train based on the wi-th wheelset.

[0168] Then, the train kinematic equations of each wheelset are solved by the Newmark-β method to obtain the bridge train dynamic response index based on the first time step.

[0169] A bridge train dynamic response index based on the first time step can be calculated through the train kinematic equation of a wheelset, and the bridge train dynamic response index based on the first time step may include the acceleration, speed and position of the train under the wheelset.

[0170] The purpose of solving the train kinematic equations for each wheelset is to obtain X Vwi , and The specific solution process can be shown as follows:

[0171] By calculating the integral format:

[0172]

[0173] To solve the train kinematic equations for each wheelset.

[0174] Among them, α and β are integration parameters, α is taken as 0.25, β is taken as 0.5, Δt is the step size of the time step; n is the nth time step, 0≤n≤N, N can be determined according to Δt, train speed and length of the bridge, the first time step refers to n=1, and the maximum time step refers to n=N.

[0175] X Vwi , and As X n , Substitute into the integral format to solve the train kinematic equations for each wheelset.

[0176] In the above formula Utilizing X n+1 To represent, then respectively Substitute into the bridge subsystem dynamics equation at n+1 time step and simplify to obtain X n+1 The solution formula is:

[0177]

[0178] Among them, F n+1 is the bridge node load at time step n+1, which can be calculated based on F (V-B)wi Here, M, C, and K are the mass matrix, damping matrix, and stiffness matrix of the train, respectively.

[0179] X n+1 The solution formula is:

[0180]

[0181] In the formula, a6=Δt(1-β), a7=βΔt, solving the above equation yields X n+1 ;

[0182] The solution formula is:

[0183]

[0184] Obviously, the above formula can be used to obtain X n+1 Among them, X n+1 Can indicate the displacement based on the n+1th time step, Can indicate the speed based on the n+1th time step, May indicate the acceleration based on the n+1th time step.

[0185] In summary, the bridge train dynamic response index based on the first time step can be determined according to the above principles.

[0186] 570. The second force based on each wheelset is used as the first force based on each wheelset, and the bridge train dynamic response index based on the next time step is determined continuously from the dynamic displacement determination step until the bridge train dynamic response index based on the maximum time step is obtained; wherein the maximum time step is the time step when the train leaves the bridge.

[0187] Figure 7 This is a schematic diagram of a structure of a device for determining a bridge train dynamic response index provided in an embodiment of the present application. Figure 7 As shown, the bridge train dynamic response index determination device 700 may include:

[0188] A first construction model 710 is used to construct a finite element model of the bridge and determine a stiffness matrix, a mass matrix and a damping matrix of the bridge according to basic information of the bridge;

[0189] An input module 720 is used to input the first temperature into the finite element model of the bridge to obtain a displacement of each of a plurality of nodes of the bridge based on the first temperature;

[0190] Wherein, the first temperature is the ambient temperature of the bridge;

[0191] The second construction module 730 is used to construct the stiffness matrix, mass matrix and damping matrix of the train according to the multi-rigid body dynamics model;

[0192] The determination module 740 is used to determine the bridge train dynamic response index based on the displacement of each node based on the first temperature, the first unsmoothness value of each node, the pile-soil coupling information of the bridge, the stiffness matrix, mass matrix and damping matrix of the bridge, and the stiffness matrix, mass matrix and damping matrix of the train.

[0193] It should be noted that the implementation principle and effect of the above-mentioned device for determining the dynamic response index of a bridge train are similar to the implementation principle and effect of the above-mentioned method for determining the dynamic response index of a bridge train, and will not be repeated here.

[0194] An embodiment of the present application also provides an electronic device, including a memory and a processor; the memory is used to store a computer program; the processor is used to implement the method for determining the bridge train dynamic response index as described above when executing the computer program.

[0195] An embodiment of the present application also provides a computer-readable storage medium, on which a computer program is stored. When the computer program is executed by a processor, the method for determining the bridge train dynamic response index as described above is implemented.

[0196] A person of ordinary skill in the art can understand that all or part of the processes in the controller in the above-mentioned embodiments can be completed by instructing the relevant hardware through a computer program, and the program can be stored in a computer-readable storage medium. When the program is executed, it can include the processes of the embodiments of the above-mentioned methods. Among them, the storage medium can be a disk, an optical disk, a read-only memory (ROM) or a random access memory (RAM), etc. In the present application, the unit described as a separate component may or may not be physically separated, and the component displayed as a unit may or may not be a physical unit, that is, it may be located in one place, or it may be arranged on multiple network units. Some or all of the units can be selected according to actual needs to achieve the purpose of the embodiment of the present invention. In addition, each functional unit in each embodiment of the present invention can be integrated in a processing unit, or each unit can exist physically separately, or two or more units can be integrated in one unit. The above-mentioned integrated unit can be implemented in the form of hardware or in the form of software functional units.

[0197] Although the present invention is disclosed as above, the protection scope of the present invention is not limited thereto. Those skilled in the art may make various changes and modifications without departing from the spirit and scope of the present invention, and these changes and modifications will fall within the protection scope of the present invention.

Claims

1. A method for determining a bridge train dynamic response index, characterized in that: include: According to the basic information of the bridge, a finite element model of the bridge is constructed and a stiffness matrix, a mass matrix and a damping matrix of the bridge are determined; Bringing a first temperature into a finite element model of the bridge to obtain a displacement of each of a plurality of nodes of the bridge based on the first temperature; Wherein, the first temperature is the ambient temperature of the bridge; According to the multi-rigid body dynamics model, the stiffness matrix, mass matrix and damping matrix of the train are constructed; The bridge train dynamic response index is determined according to the displacement of each node based on the first temperature, the first irregularity value of each node, the pile-soil coupling information of the bridge, the stiffness matrix, mass matrix and damping matrix of the bridge, and the stiffness matrix, mass matrix and damping matrix of the train.

2. The method according to claim 1, characterized in that The step of constructing a finite element model of the bridge and determining a stiffness matrix, a mass matrix and a damping matrix of the bridge according to basic information of the bridge comprises: According to the basic information of the bridge, a finite element model of the bridge is constructed to obtain a stiffness matrix and a mass matrix of each unit in a plurality of units of the bridge; Determine the stiffness matrix and mass matrix of the bridge according to the stiffness matrix and mass matrix of each unit; According to the stiffness matrix and mass matrix of the bridge and in combination with a subspace iteration method, natural vibration characteristic information of the bridge is determined; The damping matrix of the bridge is determined according to the natural vibration characteristic information of the bridge, the stiffness matrix and the mass matrix of the bridge.

3. The method according to claim 1, characterized in that Determining the bridge train dynamic response index according to the displacement of each node based on the first temperature, the first irregularity value of each node, the pile-soil coupling information of the bridge, the stiffness matrix, mass matrix and damping matrix of the bridge, and the stiffness matrix, mass matrix and damping matrix of the train includes: updating the stiffness matrix of the bridge according to the pile-soil coupling information of the bridge; updating the damping matrix of the bridge according to the updated stiffness matrix of the bridge and the mass matrix of the bridge; Determine a first force based on each wheelset according to the displacement of each node based on the first temperature, the first unsmoothness value of each node, and the stiffness of each wheelset in the train; Wherein, the first force is the force acting on the train by the bridge; Executing a dynamic displacement determination step, wherein the dynamic displacement determination step comprises: determining the dynamic displacement of each node based on the first time step according to the first force based on each wheelset, the mass matrix of the bridge, and the updated stiffness matrix and damping matrix of the bridge; Determine a second force based on each wheelset according to the dynamic displacement of each node based on the first time step, the displacement of each node based on the first temperature, the first unsmoothness value of each node, and the stiffness of each wheelset in the train; Wherein, the second force is the force exerted by the train on the bridge; Determining a dynamic response index of the bridge train based on the first time step according to the second force based on each wheelset, the stiffness matrix, the mass matrix and the damping matrix of the train; Using the second force based on each wheelset as the first force based on each wheelset, and continuing to determine the bridge train dynamic response index based on the next time step from the dynamic displacement determination step until the bridge train dynamic response index based on the maximum time step is obtained; The maximum time step is the time step for the train to leave the bridge.

4. The method according to claim 3, characterized in that The updating of the stiffness matrix of the bridge according to the pile-soil coupling information of the bridge comprises: Determine the equivalent stiffness of each pier bottom node of the bridge according to the pile-soil coupling information of the bridge and in combination with an equivalent stiffness calculation method; Wherein, the plurality of nodes of the bridge include each pier bottom node of the bridge; The stiffness matrix of the bridge is updated according to the equivalent stiffness of each pier bottom node of the bridge.

5. The method according to claim 3, characterized in that: Determining the first force based on each wheelset according to the displacement of each node based on the first temperature, the first unsmoothness value of each node, and the stiffness of each wheelset in the train comprises: Determine a second roughness value of each node according to the displacement of each node based on the first temperature and the first roughness value of each node; Determining the actual position of each node according to the second unsmoothness value of each node and the initial dynamic displacement of each node; According to the actual position of each node and the stiffness of each wheelset, a first force based on each wheelset is determined.

6. The method according to claim 3, characterized in that Determining the dynamic displacement of each node based on the first time step according to the first force based on each wheelset, the mass matrix of the bridge, and the updated stiffness matrix and damping matrix of the bridge comprises: Constructing a kinematic equation of the bridge based on each wheelset according to the first force based on each wheelset, the mass matrix of the bridge, and the updated stiffness matrix and damping matrix of the bridge; The bridge kinematic equations of each wheelset are solved by the Newmark-β method to obtain the dynamic displacement of each node based on the first time step.

7. The method according to claim 3, characterized in that Determining the bridge train dynamic response index based on the first time step according to the second force based on each wheelset, the stiffness matrix, the mass matrix and the damping matrix of the train comprises: Constructing a train kinematics equation based on each wheelset according to the second force based on each wheelset, the stiffness matrix, the mass matrix and the damping matrix of the train; The train kinematic equation of each wheelset is solved by the Newmark-β method to obtain the bridge train dynamic response index based on the first time step.

8. A device for determining a bridge train dynamic response index, characterized in that: include: A first construction module is used to construct a finite element model of the bridge and determine a stiffness matrix, a mass matrix and a damping matrix of the bridge according to basic information of the bridge; An input module, used for inputting a first temperature into a finite element model of the bridge to obtain a displacement of each of a plurality of nodes of the bridge based on the first temperature; Wherein, the first temperature is the ambient temperature of the bridge; The second construction module is used to construct the stiffness matrix, mass matrix and damping matrix of the train according to the multi-rigid body dynamics model; A determination module is used to determine the bridge train dynamic response index according to the displacement of each node based on the first temperature, the first unsmoothness value of each node, the pile-soil coupling information of the bridge, the stiffness matrix, mass matrix and damping matrix of the bridge, and the stiffness matrix, mass matrix and damping matrix of the train.

9. An electronic device, characterized in that: including memory and processor; The memory is used to store computer programs; The processor is used to implement the method for determining the bridge train dynamic response index according to any one of claims 1 to 7 when executing the computer program.

10. A computer-readable storage medium, characterized in that: The storage medium stores a computer program, and when the computer program is executed by a processor, the method for determining a bridge train dynamic response index according to any one of claims 1 to 7 is implemented.

Images