Calculation method and device for beam end displacement considering damper under train action

Abstract

The present invention relates to a method and device for calculating beam end displacement under the action of a train, taking into account a damper. The method comprises the following steps: establishing a finite element model based on bridge information and determining a numerical curve for the influence of beam end displacement under the action of a moving unit force based on the finite element model, wherein the numerical curve reflects the relationship between the longitudinal displacement at the beam end and the bridge position where the moving unit force is located; determining the static displacement of the beam end corresponding to the train moving on the bridge based on the physical information of the train and the numerical curve for the influence of the beam end displacement; determining the longitudinal bridge-direction restoring force stiffness and equivalent mass of the bridge based on the dynamic behavior of the bridge structure itself; establishing an equilibrium displacement equation taking into account the damper based on the static displacement of the beam end corresponding to the train moving on the bridge, the longitudinal bridge-direction restoring force stiffness, and the equivalent mass; and solving the longitudinal displacement of the beam end based on the equilibrium displacement equation. This method can improve the accuracy and efficiency of the calculation of the longitudinal displacement of the beam end.

Description

Technical Field

[0001] The present invention relates to the technical field of bridge analysis, and in particular to a method and device for calculating beam end displacement under the action of a train with dampers taken into consideration. Background Art

[0002] With the development of my country's economy and technology, the construction of ultra-long-span railway bridges has grown rapidly. For example, the Changtai Yangtze River Bridge, currently under construction, carries two intercity railway lines and has a main span of 1,176 meters. For ultra-long-span railway bridges, the calculated longitudinal displacement of the beam ends caused by trains passing over them is generally overstated, resulting in larger beam end expansion devices. However, large beam end expansion devices, due to their lack of longitudinal sliding, can compromise train safety.

[0003] The relevant technology for calculating the beam end displacement caused by trains crossing bridges uses static analysis. This method uses the influence line principle to determine the train loading position at the beam end displacement extremes. The train load is then applied to perform a static analysis to obtain the maximum and minimum beam end displacements. However, the static analysis method's disadvantage is that it fails to account for the inertial forces generated by acceleration and the effects of the dampers between the tower and beam. This results in an overstated beam end displacement that is inconsistent with the actual displacement values ​​in the project. Summary of the Invention

[0004] Embodiments of the present invention provide a method and device for calculating the displacement of a beam end under the action of a train, taking into account a damper, so as to improve the accuracy and efficiency of calculating the longitudinal displacement of the beam end.

[0005] An embodiment of the present invention provides a method for calculating beam end displacement under the action of a train, taking into account a damper, characterized in that it includes the steps of:

[0006] Establishing a finite element model based on the bridge information and determining a beam end displacement influence curve under the action of a moving unit force based on the finite element model, wherein the beam end displacement influence curve reflects the relationship between the longitudinal displacement at the beam end and the bridge position where the moving unit force is located;

[0007] Determining the static displacement of the beam end corresponding to the train moving on the bridge according to the physical information of the train and the beam end displacement influence numerical curve;

[0008] Determine the longitudinal restoring stiffness and equivalent mass of the bridge based on the dynamic behavior of the bridge structure itself;

[0009] Based on the static displacement of the beam end corresponding to the train moving on the bridge, the longitudinal bridge restoring force stiffness and the equivalent mass, an equilibrium displacement equation considering the damper is established, and the longitudinal displacement of the beam end is solved based on the equilibrium displacement equation.

[0010] In some embodiments, the physical information of the train includes: the length of the train, the uniformly distributed load of the train, the travel speed of the train, and the travel time of the train; and determining the static displacement of the beam end corresponding to the movement of the train on the bridge based on the physical information of the train and the beam end displacement influence value curve includes the steps of:

[0011] The static displacement of the beam end corresponding to the train moving on the bridge is obtained based on a first formula, wherein the first formula includes:

[0012]

[0013] Where D(t) is the static displacement of the beam end corresponding to the train moving on the bridge, l is the length of the train, t is the train's travel time, q is the uniformly distributed load of the dynamic load, L is the length of the bridge, v is the train's travel speed, and y(t) is the influence curve of the beam end displacement.

[0014] In some embodiments, determining the longitudinal restoring stiffness and equivalent mass of the bridge based on the dynamic behavior of the bridge structure itself comprises the steps of:

[0015] Based on the finite element model, a longitudinal force is applied to the main beam and the longitudinal deformation of the main beam is recorded;

[0016] The frequency of the first-order longitudinal bridge drift is determined by modal analysis;

[0017] The longitudinal bridge-directional restoring force stiffness and the equivalent mass are calculated based on the longitudinal bridge-directional force, the longitudinal bridge-directional deformation, and the frequency of the first-order longitudinal bridge-directional drift.

[0018] In some embodiments, the calculating of the longitudinal bridge direction restoring force stiffness and the equivalent mass based on the longitudinal bridge direction force, the longitudinal bridge direction deformation, and the frequency of the first-order longitudinal bridge direction drift comprises the steps of:

[0019] The longitudinal bridge restoring force stiffness and equivalent mass are calculated based on a second formula, wherein the second formula includes: K=F / Δ, M=K / ω 2 , where F is the longitudinal bridge force, Δ is the longitudinal bridge deformation, ω is the frequency of the first-order longitudinal bridge drift, K is the longitudinal bridge restoring force stiffness, and M is the equivalent mass.

[0020] In some embodiments, establishing an equilibrium displacement equation taking into account a damper based on the static displacement of the beam end corresponding to the train moving on the bridge, the longitudinal bridge restoring force stiffness, and the equivalent mass comprises the following steps:

[0021] The equilibrium displacement equation considering the damper is established based on the third formula, and the third formula includes: in,

[0022] n is the number of longitudinal viscous dampers in the entire bridge, C is the damping coefficient of a single viscous damper, α is the damping exponent, and B(t) is the longitudinal displacement of the beam end to be determined.

[0023] In a second aspect, an embodiment of the present invention provides a device for calculating beam end displacement under the action of a train, taking into account a damper, characterized in that it includes:

[0024] Beam end static displacement determination module, which is used to:

[0025] Establishing a finite element model based on the bridge information and determining a beam end displacement influence curve under the action of a moving unit force based on the finite element model, wherein the beam end displacement influence curve reflects the relationship between the longitudinal displacement at the beam end and the bridge position where the moving unit force is located;

[0026] Determining the static displacement of the beam end corresponding to the train moving on the bridge according to the physical information of the train and the beam end displacement influence numerical curve;

[0027] Beam end displacement calculation module, which is used to:

[0028] Determine the longitudinal restoring stiffness and equivalent mass of the bridge based on the dynamic behavior of the bridge structure itself;

[0029] Based on the static displacement of the beam end corresponding to the train moving on the bridge, the longitudinal bridge restoring force stiffness and the equivalent mass, an equilibrium displacement equation considering the damper is established, and the longitudinal displacement of the beam end is solved based on the equilibrium displacement equation.

[0030] In some embodiments, the physical information of the train includes: the length of the train, the uniformly distributed load of the train, the speed of the train, and the travel time of the train;

[0031] The beam end static displacement determination module is also used for:

[0032] The static displacement of the beam end corresponding to the train moving on the bridge is obtained based on a first formula, wherein the first formula includes:

[0033]

[0034] Where D(t) is the static displacement of the beam end corresponding to the train moving on the bridge, l is the length of the train, t is the train's travel time, q is the uniformly distributed load of the dynamic load, L is the length of the bridge, v is the train's travel speed, and y(t) is the influence curve of the beam end displacement.

[0035] In some embodiments, the beam end displacement calculation module is further configured to:

[0036] Based on the finite element model, applying longitudinal bridge force to the main beam and recording the longitudinal bridge deformation of the main beam;

[0037] The frequency of the first-order longitudinal bridge drift is determined by modal analysis;

[0038] The longitudinal bridge direction restoring force stiffness and the equivalent mass are calculated based on the longitudinal bridge direction force, the longitudinal bridge direction deformation, and the frequency of the first-order longitudinal bridge direction drift.

[0039] In some embodiments, the beam end displacement calculation module is further configured to:

[0040] The longitudinal bridge restoring force stiffness and equivalent mass are calculated based on a second formula, wherein the second formula includes: K=F / Δ, M=K / ω 2 , where F is the longitudinal bridge force, Δ is the longitudinal bridge deformation, ω is the frequency of the first-order longitudinal bridge drift, K is the longitudinal bridge restoring force stiffness, and M is the equivalent mass.

[0041] In some embodiments, the beam end displacement calculation module is further configured to:

[0042] The equilibrium displacement equation considering the damper is established based on the third formula, and the third formula includes: in,

[0043] n is the number of longitudinal viscous dampers in the entire bridge, C is the damping coefficient of a single viscous damper, α is the damping exponent, and B(t) is the longitudinal displacement of the beam end to be determined.

[0044] The beneficial effects brought about by the technical solution provided by the present invention include:

[0045] An embodiment of the present invention provides a method and device for calculating the beam end displacement under the action of a train, taking into account the damper. Since the inertial force generated by acceleration and the effect of the damper between the tower and the beam are taken into account, the calculated beam end displacement taking into account the damper effect is in good agreement with the actual value. Therefore, when a train passes through an ultra-long span railway bridge, the longitudinal displacement of the beam end can be calculated accurately and efficiently, in line with the actual displacement value of the project, reducing the specifications of the beam end telescopic device and improving the durability of the telescopic device. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the following briefly introduces the drawings required for use in the description of the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0047] Figure 1 A schematic flow chart of a method for calculating beam end displacement under the action of a train with consideration of a damper, provided by an embodiment of the present invention;

[0048] Figure 2A schematic diagram of the bridge-type facade structure of a cable-stayed bridge provided in an embodiment of the present invention;

[0049] Figure 3 A schematic diagram of a numerical curve showing the influence of beam end displacement under a moving unit force provided in an embodiment of the present invention;

[0050] Figure 4 A schematic diagram of a static displacement curve of a beam end provided by an embodiment of the present invention;

[0051] Figure 5 Schematic diagram of beam end displacement curve provided by an embodiment of the present invention

[0052] Figure 6 A schematic structural diagram of a device for calculating beam end displacement taking into account a damper under the action of a train provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0053] To make the objectives, technical solutions, and advantages of the embodiments of the present invention more clear, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts shall fall within the scope of protection of the present invention.

[0054] like Figure 1 As shown, an embodiment of the present invention provides a method for calculating the displacement of a beam end under the action of a train taking into account a damper, characterized in that it includes the steps of:

[0055] S100: establishing a finite element model according to the bridge information and determining a beam end displacement influence numerical curve under the action of a moving unit force based on the finite element model, wherein the beam end displacement influence numerical curve reflects the relationship between the longitudinal displacement at the beam end and the bridge position where the moving unit force is located;

[0056] S200: determining the static displacement of the beam end corresponding to the train moving on the bridge according to the physical information of the train and the beam end displacement influence value curve;

[0057] S300: Determine the longitudinal restoring stiffness and equivalent mass of the bridge based on the dynamic behavior of the bridge structure itself;

[0058] S400: Based on the static displacement of the beam end corresponding to the train moving on the bridge, the longitudinal bridge restoring force stiffness and the equivalent mass, an equilibrium displacement equation considering the damper is established and the longitudinal displacement of the beam end is solved based on the equilibrium displacement equation.

[0059] It should be noted that in S100, the bridge information includes information such as the length of the bridge. When determining the influence curve of the beam end displacement under the action of the moving unit force based on the finite element model, the relationship between the longitudinal displacement at the beam end and the bridge position x where the moving unit force is located can be obtained by performing a moving unit force loading calculation, and the beam end displacement influence curve y(x) can be determined based on this.

[0060] It is understandable that the embodiment of the present invention uses finite elements to determine the numerical curve of the influence of the beam end displacement under the action of a moving unit force, and then combines the physical information of the train to determine the static displacement value of the beam end when the train is moving on the bridge. According to the dynamic mechanical behavior of the bridge structure itself, the equivalent mass and restoring stiffness are determined, and the equilibrium displacement equation considering the damper is established using dynamic theory. The equilibrium displacement solved by the equilibrium displacement equation is the longitudinal displacement of the beam end considering the damper. The calculated beam end displacement considering the damper effect is in good agreement with the actual value, so that when a train passes through an ultra-large span railway bridge, the calculation of the longitudinal displacement of the beam end is accurate and efficient, in line with the actual displacement value of the project, reducing the specifications of the beam end telescopic device and improving the durability of the telescopic device. At the same time, the calculation time is only a few minutes, which improves the calculation efficiency of engineering personnel.

[0061] In some embodiments, the physical information of the train in step S200 includes: the length of the train, the uniformly distributed load of the train, the speed of the train, and the travel time of the train. S200 can obtain the static displacement of the beam end corresponding to the movement of the train on the bridge according to a first formula, and the first formula includes:

[0062]

[0063] Where D(t) is the static displacement of the beam end corresponding to the train moving on the bridge, l is the length of the train, t is the train's travel time, q is the uniformly distributed load of the train, L is the length of the bridge, v is the train's travel speed, and y(t) is the numerical curve of the beam end displacement influence.

[0064] In some embodiments, step S300 includes:

[0065] S310: Applying a longitudinal force to the main beam based on the finite element model and recording the longitudinal deformation of the main beam;

[0066] S320: Determine the frequency of the first-order longitudinal bridge drift through modal analysis;

[0067] S330: Calculate the longitudinal bridge-direction restoring force stiffness and equivalent mass based on the longitudinal bridge-direction force, the longitudinal bridge-direction deformation, and the frequency of the first-order longitudinal bridge-direction drift.

[0068] Furthermore, S330 may calculate the longitudinal bridge restoring force stiffness and equivalent mass based on a second formula, and the second formula includes: K = F / Δ, M = K / ω 2 , where F is the longitudinal bridge force, Δ is the longitudinal bridge deformation, ω is the frequency of the first-order longitudinal bridge drift, K is the longitudinal bridge restoring force stiffness, and M is the equivalent mass.

[0069] Furthermore, S400 may establish a balanced displacement equation considering the damper based on a third formula, and the third formula includes: in,

[0070] n is the number of longitudinal viscous dampers in the entire bridge, C is the damping coefficient of a single viscous damper, α is the damping exponent, and B(t) is the longitudinal displacement of the beam end to be determined.

[0071] In a specific embodiment, taking a double-tower five-span railway cable-stayed bridge as an example, the bridge facade is arranged as follows: Figure 2 As shown, the cable-stayed bridge consists of four structural components: a main girder 1, pylons 2, stay cables 3, and piers 6. Longitudinal movable bearings 5 ​​are located between the main girder 1, the bridge sections 6, and the pylons 2. Viscous dampers 7 are located between the pylons 2 and the main girder 1. Four viscous dampers are located on either side of each pylon, for a total of 16 viscous dampers across the entire bridge. The span arrangement of the cable-stayed bridge is (140+490+1176+490+140) meters, with a total length of 2436 meters.

[0072] Based on Figure 1 The specific calculation process is as follows:

[0073] Based on S100, a finite element calculation model of the bridge was established. The longitudinal length of the bridge was L = 2436m. A moving unit force loading calculation was performed to obtain a numerical curve y(x) showing the relationship between the longitudinal displacement at the beam end and the bridge position x where the moving unit force is applied.

[0074] Based on S200, the train length is l = 550m, the uniformly distributed load of the train is q = 64kN / m, and the train speed is set to v = 150km / h. The time when the train enters the bridge is 0, and the train reaches the bridge position x = vt at time t. According to the relationship x = vt, the numerical curve y(x) is converted into the numerical curve y(t) of the beam end displacement influence, as shown in the following example: Figure 3 The time it takes for the train to leave the bridge is (L+l) / v=71.6s. At the same time, the static displacement D(t) at the beam end can be calculated according to the first formula, as follows: Figure 4 shown.

[0075] Based on S300, in the finite element model established in S100, a longitudinal force F = 1000N is applied to the main beam, and the longitudinal deformation of the main beam Δ = = 7.894×10 -6=m; modal analysis was performed to determine the frequency of the first-order longitudinal drift to be ω = 0.708 rad / s. The longitudinal restoration stiffness K = 126666616 N / m and the equivalent mass M = 2.521×10 8 kg.

[0076] Based on S400, the number of longitudinal viscous dampers 7 in the entire bridge is n = 16, the damping coefficient of a single viscous damper is C = 3400, and the damping exponent α = 0.2. The equilibrium displacement B(t) (i.e., the longitudinal displacement of the beam end) considering the effect of the viscous damper is solved according to the third formula, as follows: Figure 5 shown.

[0077] Figure 4 、 Figure 5 By comparison, the maximum static displacement of the beam end is 0.1m, and considering the damper effect, the longitudinal displacement of the beam end is only 0.003m. The actual longitudinal displacement of the beam end when the train passes the bridge is 0.004m, which is in good agreement.

[0078] The embodiment of the present invention facilitates the reduction of specifications of the beam end telescopic device through the refined calculation of the displacement of the train passing the bridge end, thereby increasing the service life of the beam end telescopic device and ensuring the formation safety of the train.

[0079] On the other hand, Figure 6 As shown, an embodiment of the present invention further provides a device for calculating beam end displacement under the action of a train, taking into account a damper, comprising:

[0080] Beam end static displacement determination module, which is used to:

[0081] Establishing a finite element model based on the bridge information and determining a beam end displacement influence curve under the action of a moving unit force based on the finite element model, wherein the beam end displacement influence curve reflects the relationship between the longitudinal displacement at the beam end and the bridge position where the moving unit force is located;

[0082] Determining the static displacement of the beam end corresponding to the train moving on the bridge according to the physical information of the train and the beam end displacement influence numerical curve;

[0083] Beam end displacement calculation module, which is used to:

[0084] Determine the longitudinal restoring stiffness and equivalent mass of the bridge based on the dynamic behavior of the bridge structure itself;

[0085] Based on the static displacement of the beam end corresponding to the train moving on the bridge, the longitudinal bridge restoring force stiffness and the equivalent mass, an equilibrium displacement equation considering the damper is established, and the longitudinal displacement of the beam end is solved based on the equilibrium displacement equation.

[0086] In some embodiments, the physical information of the train includes: the length of the train, the uniformly distributed load of the train, the speed of the train, and the travel time of the train;

[0087] The module for determining static displacements at beam ends is also used for:

[0088] The static displacement of the beam end corresponding to the train moving on the bridge is obtained based on a first formula, wherein the first formula includes:

[0089]

[0090] Where D(t) is the static displacement of the beam end corresponding to the train moving on the bridge, l is the length of the train, t is the train's travel time, q is the uniformly distributed load of the dynamic load, L is the length of the bridge, v is the train's travel speed, and y(t) is the influence curve of the beam end displacement.

[0091] In some embodiments, the beam end displacement calculation module is further configured to:

[0092] Based on the finite element model, longitudinal forces are applied to the main beam and the longitudinal deformation of the main beam is recorded.

[0093] The frequency of the first-order longitudinal bridge drift is determined by modal analysis;

[0094] The longitudinal bridge restoring force stiffness and the equivalent mass are calculated based on the longitudinal bridge force, the longitudinal bridge deformation, and the frequency of the first-order longitudinal bridge drift.

[0095] In some embodiments, the beam end displacement calculation module is further configured to:

[0096] The longitudinal bridge restoring force stiffness and equivalent mass are calculated based on the second formula, and the second formula includes: K = F / Δ, M = K / ω 2 , where F is the longitudinal bridge force, Δ is the longitudinal bridge deformation, ω is the frequency of the first-order longitudinal bridge drift, K is the longitudinal bridge restoring force stiffness, and M is the equivalent mass.

[0097] In some embodiments, the beam end displacement calculation module is further configured to:

[0098] The equilibrium displacement equation considering the damper is established based on the third formula, which includes: Where n is the number of longitudinal viscous dampers in the entire bridge, C is the damping coefficient of a single viscous damper, α is the damping exponent, and B(t) is the longitudinal displacement of the beam end to be determined.

[0099] It can be understood that the technical effects that can be achieved by the above-mentioned device embodiment are the same as the technical effects that can be achieved by the method embodiment.

[0100] It will be understood by those skilled in the art that all or some of the steps, systems, and functional modules / units in the methods disclosed above may be implemented as software, firmware, hardware, and appropriate combinations thereof. In a hardware implementation, the division between the functional modules / units mentioned in the above description does not necessarily correspond to the division of physical components; for example, a physical component may have multiple functions, or a function or step may be performed by several physical components in cooperation. Some or all physical components may be implemented as software executed by a processor, such as a central processing unit, a digital signal processor, or a microprocessor, or may be implemented as hardware, or may be implemented as an integrated circuit, such as an application-specific integrated circuit. Such software may be distributed on a computer-readable storage medium, which may include a computer-readable storage medium (or a non-transitory medium) and a communication medium (or a temporary medium).

[0101] It should be noted that, in the present invention, relational terms such as "first" and "second" are merely used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply the existence of any such actual relationship or order between these entities or operations. Moreover, the terms "include", "comprise" or any other variants thereof are intended to cover non-exclusive inclusion, so that a process, method, article or device comprising a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, article or device. In the absence of further restrictions, an element defined by the sentence "comprising a ..." does not exclude the presence of other identical elements in the process, method, article or device comprising the element.

[0102] The foregoing description is intended only to provide specific embodiments of the present invention, which will enable those skilled in the art to understand and implement the present invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention is not intended to be limited to the embodiments shown herein, but is intended to be accorded the widest scope consistent with the principles and novel features claimed herein.

Claims

1. A method for calculating the displacement of beam ends under train action with consideration of dampers, characterized in that: It includes the steps of: Establishing a finite element model based on the bridge information and determining a beam end displacement influence curve under the action of a moving unit force based on the finite element model, wherein the beam end displacement influence curve reflects the relationship between the longitudinal displacement at the beam end and the bridge position where the moving unit force is located; Determining the static displacement of the beam end corresponding to the train moving on the bridge according to the physical information of the train and the beam end displacement influence numerical curve; Determine the longitudinal restoring stiffness and equivalent mass of the bridge based on the dynamic behavior of the bridge structure itself; Establishing an equilibrium displacement equation taking into account the damper based on the static displacement of the beam end corresponding to the train moving on the bridge, the longitudinal bridge restoring force stiffness, and the equivalent mass, and solving the longitudinal displacement of the beam end based on the equilibrium displacement equation; The method includes establishing an equilibrium displacement equation taking into account a damper based on the static displacement of the beam end corresponding to the train moving on the bridge, the longitudinal bridge restoring force stiffness, and the equivalent mass, including the following steps: The equilibrium displacement equation considering the damper is established based on the third formula, and the third formula includes: ,in, n is the number of longitudinal viscous dampers in the entire bridge, C is the damping coefficient of a single viscous damper, is the damping index, B ( t ) is the longitudinal displacement of the beam end to be determined.

2. The method for calculating the beam end displacement under the action of a train taking into account the damper as claimed in claim 1, characterized in that: The physical information of the train includes: the length of the train, the uniformly distributed load of the train, the running speed of the train, and the running time of the train; and determining the static displacement of the beam end corresponding to the movement of the train on the bridge based on the physical information of the train and the beam end displacement influence value curve includes the following steps: The static displacement of the beam end corresponding to the train moving on the bridge is obtained based on a first formula, wherein the first formula includes: ， in, is the static displacement of the beam end corresponding to the train moving on the bridge, is the length of the train, is the train's running time, is the uniformly distributed load of the dynamic load, is the length of the bridge, v is the train speed, is the numerical curve of the influence of beam end displacement.

3. The method for calculating the beam end displacement under the action of a train taking into account the damper as claimed in claim 2, characterized in that: The method of determining the longitudinal restoring force stiffness and equivalent mass of the bridge according to the dynamic behavior of the bridge structure itself includes the following steps: Based on the finite element model, a longitudinal force is applied to the main beam and the longitudinal deformation of the main beam is recorded; The frequency of the first-order longitudinal bridge drift is determined by modal analysis; The longitudinal bridge-directional restoring force stiffness and the equivalent mass are calculated based on the longitudinal bridge-directional force, the longitudinal bridge-directional deformation, and the frequency of the first-order longitudinal bridge-directional drift.

4. The method for calculating the beam end displacement under the action of a train taking into account the damper as claimed in claim 3, characterized in that: The calculating of the longitudinal bridge direction restoring force stiffness and equivalent mass based on the longitudinal bridge direction force, the longitudinal bridge direction deformation, and the frequency of the first-order longitudinal bridge direction drift comprises the steps of: The longitudinal bridge restoring force stiffness and equivalent mass are calculated based on a second formula, wherein the second formula includes: ,in, is the longitudinal bridge force, The longitudinal deformation of the bridge is is the frequency of the first-order longitudinal bridge drift, is the longitudinal bridge restoring stiffness, is equivalent mass.

5. A device for calculating beam end displacement under train action taking into account dampers, characterized in that: It includes: Beam end static displacement determination module, which is used to: Establishing a finite element model based on the bridge information and determining a beam end displacement influence curve under the action of a moving unit force based on the finite element model, wherein the beam end displacement influence curve reflects the relationship between the longitudinal displacement at the beam end and the bridge position where the moving unit force is located; Determining the static displacement of the beam end corresponding to the train moving on the bridge according to the physical information of the train and the beam end displacement influence numerical curve; Beam end displacement calculation module, which is used to: Determine the longitudinal restoring stiffness and equivalent mass of the bridge based on the dynamic behavior of the bridge structure itself; Establishing an equilibrium displacement equation taking into account the damper based on the static displacement of the beam end corresponding to the train moving on the bridge, the longitudinal bridge restoring force stiffness, and the equivalent mass, and solving the longitudinal displacement of the beam end based on the equilibrium displacement equation; The beam end displacement calculation module is also used for: The equilibrium displacement equation considering the damper is established based on the third formula, and the third formula includes: ,in, n is the number of longitudinal viscous dampers in the entire bridge, C is the damping coefficient of a single viscous damper, is the damping index, B ( t ) is the longitudinal displacement of the beam end to be determined.

6. The device for calculating beam end displacement under train action with consideration of dampers as claimed in claim 5, characterized in that: The physical information of the train includes: the length of the train, the uniformly distributed load of the train, the running speed of the train and the running time of the train; The beam end static displacement determination module is also used for: The static displacement of the beam end corresponding to the train moving on the bridge is obtained based on a first formula, wherein the first formula includes: ， in, is the static displacement of the beam end corresponding to the train moving on the bridge, is the length of the train, is the train's running time, is the uniformly distributed load of the dynamic load, is the length of the bridge, v is the train speed, is the numerical curve of the influence of beam end displacement.

7. The device for calculating beam end displacement under train action with consideration of dampers as claimed in claim 6, characterized in that: The beam end displacement calculation module is also used for: Based on the finite element model, applying longitudinal bridge force to the main beam and recording the longitudinal bridge deformation of the main beam; The frequency of the first-order longitudinal bridge drift is determined by modal analysis; The longitudinal bridge direction restoring force stiffness and the equivalent mass are calculated based on the longitudinal bridge direction force, the longitudinal bridge direction deformation, and the frequency of the first-order longitudinal bridge direction drift.

8. The device for calculating beam end displacement under train action with consideration of dampers as claimed in claim 7, characterized in that: The beam end displacement calculation module is also used for: The longitudinal bridge restoring force stiffness and equivalent mass are calculated based on a second formula, wherein the second formula includes: ,in, is the longitudinal bridge force, The longitudinal deformation of the bridge is is the frequency of the first-order longitudinal bridge drift, is the longitudinal bridge restoring stiffness, is equivalent mass.

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