Dynamic analysis model for linear full-scale anchoring type floating bridge under wave action

Abstract

The invention discloses a dynamic analysis model for a linear full-scale anchored floating bridge under the action of waves, which provides support for dynamic response analysis and vibration control of a large anchored floating bridge structure, and comprises the following steps: firstly, constructing a numerical model of the full-scale anchored floating bridge, and then constructing an environmental load action model; the dynamic analysis model has open source performance and good compatibility and has advantages when solving the complex multi-disaster coupling problem, and the flexible parametric modeling capability of the dynamic analysis model is also beneficial to analysis of the floating bridge structure; the invention further discloses a structural response control method for the dynamic analysis model of the linear full-scale anchored floating bridge under the wave action. According to the dynamic characteristics of the anchoring type floating bridge structure, the tuned mass dampers can be additionally arranged on the cross section of the main beam of the bridge, the vertical acceleration of the main beam of the bridge is controlled by reasonably selecting the parameters, the arrangement number and the arrangement positions of the tuned mass dampers, and therefore the driving comfort is improved.

Description

Technical Field

[0001] The invention relates to the technical field of linear moored floating bridges, and in particular to a dynamic analysis model of a linear full-scale moored floating bridge under wave action. Background Art

[0002] The extremely high construction difficulty and engineering cost of deep-water foundations make it difficult to implement traditional cross-sea bridge solutions. The anchored floating bridge is a new bridge structure system, including mooring cables, floating foundations, floating bridge columns (connecting the main beam and the floating foundation), and bridge main beams. The horizontal tension provided by the anchoring system solves the defect of the anchorless floating bridge relying on the rigid main beam to transmit horizontal forces to the short-distance nearshore. The buoyancy of the pontoon foundation balances the deadweight of the upper structure and the vehicle load. The horizontal tension provided by the anchoring system can overcome the lateral horizontal force and achieve long-distance crossing, which has good application prospects. On the other hand, the floating bridge structure belongs to a new long and flexible structural system with a relatively new structural form and a complex dynamic response mechanism. There are still many unknowns in terms of structural modeling, load action mechanism, and motion response analysis. In particular, how to carry out structural control based on disaster effects needs further research. The main beam in the floating bridge structure is a key component that bears external environmental loads. Its acceleration and velocity response directly affect the overall stability and operational safety of the floating bridge. At the same time, the vibration and impact generated during vehicle driving are also closely related to the acceleration of the main beam. Therefore, in order to reduce the vibration response of the main beam and improve driving comfort, effective control of the main beam acceleration is particularly important. Summary of the invention

[0003] Based on the above shortcomings, the purpose of the present invention is to provide a dynamic analysis model for a linear full-scale anchored floating bridge under wave action. By reasonably designing and simplifying the structural components of the anchored floating bridge, a dynamic analysis model of the full-scale anchored floating bridge structure under different wave load combination conditions is established, thereby providing support for the dynamic response analysis and vibration control of the large-scale anchored floating bridge structure.

[0004] The technical solution adopted by the present invention is as follows: a dynamic analysis model for a linear anchored floating bridge under wave action, and its construction method comprises the following steps:

[0005] S1: Construct a numerical model of a full-scale moored floating bridge:

[0006] (a) Construction of a full-scale numerical model of the anchored floating bridge structure: The open source structural finite element analysis software OpenSees was used to perform full-scale finite element modeling. By analyzing the characteristics of the anchored floating bridge structure system, it was determined that the connection method between the components of the anchored floating bridge was a fully consolidated connection. On this basis, it was determined that the generalized degrees of freedom of the floating bridge column, floating foundation, and bridge main beam were all six degrees of freedom. The specific modeling methods of each structural component are as follows:

[0007] Construct a model of the bridge girder and floating bridge column: set the bridge girder as an elastic beam, define the node mass through mass, set the floating bridge column as rigid, and set its elastic modulus to be 1000 times larger than that of the bridge girder;

[0008] Construct a model of a floating foundation: the floating foundation is set as a rigid body, the node position is selected as the center of gravity of the floating foundation, and the gap connection between the node and the floating bridge column and the mooring cable is considered to be handled by a rigid connection unit. The uniaxial elastic material is assigned to the zero-length unit to represent the spring, and the spring force is used to simulate the buoyancy of the floating foundation. Regarding the value of the spring stiffness, since the spring force is equivalent to the buoyancy of the floating body, that is,

[0009] F 浮 =ρgV 排 =ρgAd;F k = k·d (1)

[0010] In the formula, F 浮 is the buoyancy of the floating foundation, ρ is the density of water, g is the acceleration due to gravity, V 排 is the displacement, A and d are the draft area and draft depth of the floating foundation respectively, F k is the spring force equivalent to the buoyancy of the float, and k is the spring stiffness;

[0011] Therefore, the spring stiffness is:

[0012] k=ρgA (2)

[0013] Construct a model of the mooring cable: The mooring line is simulated as a tension-only cable with pre-tension, using a two-node connection unit and an elastic perfect plastic gap uniaxial material. The stiffness k of the cable is cable , calculated from the transverse stiffness of each mooring cluster and the anchor position of the cables, the initial Gap is determined based on the required pretension:

[0014] Gap=-P / k cable (3)

[0015] Where Gap is the initial gap, P is the pretension of each cable;

[0016] At this point, the modeling of structural components in the numerical model of the full-scale moored floating bridge has been completed;

[0017] S2: Constructing the environmental load action model: When the environmental load is considered as a wave load, the forces acting on the floating foundation include wave excitation force and radiation force; among them, the wave excitation force is composed of incident force and diffraction force, and the radiation force is expressed in a form related to the added mass and radiation damping. A single floating foundation hydrodynamic model is established in the hydrodynamic analysis software ANSYS AQWA and hydrodynamic calculations are performed to obtain the added mass, radiation damping, incident force and diffraction force of the floating foundation under different wave frequencies. The incident force and diffraction force of the floating foundation under different wave frequencies are Fourier transformed to obtain the corresponding wave excitation force time history curve, which is applied to the nodes of the floating foundation to simulate the wave excitation force; for the radiation force, the additional mass is superimposed with the mass of the structural node and assigned to each node of the floating foundation for simulation, and the radiation damping is simulated using the damping coefficient in the viscous material.

[0018] Another object of the present invention is to provide a structural response control method for a linear full-scale anchored floating bridge dynamic analysis model under wave action as described above, which is specifically as follows: a tuned mass damper is added as a control device at the cross section of the bridge main beam, and structural dynamic response control is achieved by reasonably selecting the parameters, arrangement quantity and position of the tuned mass damper itself;

[0019] (a) Limitation and mass constraints of the tuned mass damper: The tuned mass damper includes a spring, a mass block and a damper. When designing the tuned mass damper, it is necessary to ensure that its maximum displacement does not exceed the distance between the mass block and the bridge beam to prevent the mass block from colliding with the bridge beam. The mass of the tuned mass damper is limited to 1-3% of the weight of the entire anchored floating bridge structure.

[0020] (b) Modeling implementation of tuned mass damper: The parameters of tuned mass damper include mass M TMD , stiffness K TMD and damping C TMD ,In the modeling, a node and two zero-length elements are used to simulate the tuned mass damper. The specific implementation method is as follows: the tuned mass damper node is connected to the node of the bridge girder using two zero-length elements to simulate the spring stiffness and the damper characteristics respectively, and the mass is applied to the node, and the elastic material and the viscous material are defined to describe the stiffness coefficient of the linear spring and the damping coefficient of the linear damper;

[0021] (c) Determine the structural control frequency and control scheme: The natural frequency of the tuned mass damper needs to be close to the fundamental frequency or excitation frequency of the bridge main beam in order to effectively absorb its energy and achieve the purpose of vibration reduction. Before using the tuned mass damper for control, its natural frequency needs to be determined first. The following steps are used to control the acceleration of the bridge main beam: First, a dynamic response analysis is carried out based on the construction of the full-scale anchored floating bridge structure numerical model to obtain the acceleration time history curve of each node of the bridge main beam. Then, the lateral and vertical acceleration time history curves are Fourier transformed to obtain the acceleration response spectrum of each node and the corresponding dominant frequency. The dominant frequency is the controlled frequency. According to this frequency, the natural frequency of the tuned mass damper is adjusted to be close to it, and then the acceleration response control analysis and research are carried out;

[0022] When selecting a control scheme, the dynamic characteristics and control requirements of the bridge main beam should be combined to reasonably configure the tuned mass damper, and a suitable scheme should be selected between a single tuned mass damper, multiple tuned mass dampers, and multiple tuned mass dampers to achieve the best vibration reduction effect, as follows:

[0023] When the dominant frequency of the bridge girder is unique and the mass of a single tuned mass damper meets the actual installation requirements, a single tuned mass damper control scheme can be adopted. The tuned mass damper is usually arranged at a location with a large dominant modal amplitude, such as the mid-span of the bridge girder, to achieve effective vibration reduction;

[0024] When the dominant frequency of the bridge main beam is unique but the mass of a single tuned mass damper cannot meet the actual installation requirements, a control scheme of multiple tuned mass dampers with the same parameters is adopted. The control task is shared by reasonably arranging multiple small mass dampers. The arrangement method is usually determined according to the controlled modal shape. The specific steps are as follows: based on the construction of the full-scale anchored floating bridge structure numerical model, modal analysis is carried out to obtain the modal frequencies and corresponding modal shapes of each order of the anchored floating bridge, find a modal frequency closest to the dominant frequency of the bridge main beam, determine the modal shape corresponding to the modal frequency as the controlled modal shape, and select the bridge section with a larger amplitude as the arrangement position of the tuned mass damper according to the amplitude distribution of the controlled modal shape;

[0025] For bridge girders with multiple dominant frequencies, multiple tuned mass dampers are used, including multiple tuned mass dampers with different dynamic characteristics. Their layout positions are determined according to the controlled modal shape. The specific steps are similar to the control scheme using multiple tuned mass dampers with the same parameters. The difference is that it is necessary to find the multi-order modal frequencies closest to the dominant frequencies of the bridge girders and determine multiple controlled modal shapes, thereby achieving efficient control of multi-modal vibrations.

[0026] Compared with the prior art, the advantages and beneficial effects of the present invention are as follows: the present invention can reasonably simulate the structural components of an anchored floating bridge, including bridge main beams, floating bridge columns, floating foundations and mooring systems, and provide support for dynamic response analysis and vibration control of large anchored floating bridge structures. It is open source and has good compatibility, and has advantages in solving complex multi-hazard coupling problems. Its flexible parametric modeling capability is also beneficial for analyzing floating bridge structures. The present invention can add a tuned mass damper at the cross-section of the bridge main beam according to the dynamic characteristics of the anchored floating bridge structure, and control the vertical acceleration of the bridge main beam by reasonably selecting the parameters, arrangement quantity and layout position of the tuned mass damper, thereby improving driving comfort. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] Figure 1 To simplify the top view of the floating bridge model;

[0028] Figure 2 It is a schematic diagram of the floating foundation structure model;

[0029] Figure 3 is the additional mass and radiation damping diagram of the floating foundation; where a and b are the additional mass in the translational and rotational directions of the floating foundation, respectively; c and d are the radiation damping in the translational and rotational directions of the floating foundation, respectively;

[0030] Figure 4 is the wave excitation force diagram of the floating foundation when the wave is incident along the y-axis; where a is the wave excitation force in the translation direction of the floating foundation, and b is the wave excitation force in the rotation direction of the floating foundation;

[0031] Figure 5 It is a time history curve of wave force in the sway and heave directions of the moored floating foundation when the wave is incident along the y-axis;

[0032] Figure 6 is a flow chart of the control method of tuned mass damper (TMD);

[0033] Figure 7 It is a schematic diagram of the vertical acceleration comparison of the bridge main beam when the tuned mass damper (TMD) control device parameters are optimized; among them, a is the schematic diagram of the vertical acceleration comparison of the bridge main beam when the mass ratio is variable, and b is the schematic diagram of the vertical acceleration comparison of the bridge main beam when the damping ratio is variable. DETAILED DESCRIPTION

[0034] The present invention will be further described below with reference to the accompanying drawings.

[0035] Example 1

[0036] This embodiment provides a dynamic analysis model for a linear anchored floating bridge under wave action, and its construction method comprises the following steps: S1: numerical modeling of a full-scale anchored floating bridge:

[0037] Select the Norwegian Public Roads Administration (NPRA) for crossing a 5 km wide A conceptual side-anchored straight floating bridge proposed by the Strait is used as an example. The conceptual floating bridge is simplified during the modeling process using OpenSees, and only the floating main bridge section is considered. The simplified anchored floating bridge model is 4.6 kilometers long, and the main beam bridge deck is 18 meters above the water surface as a whole, located on 35 evenly spaced floating foundations. The entire anchored floating bridge superstructure is fixed by 4 mooring clusters, each of which is composed of eight mooring cables, which are symmetrically distributed. The water depth of the floating bridge model is set to 300m, and it is assumed to remain constant along the entire length of the bridge. The boundary conditions of the simplified floating bridge model are: all six degrees of freedom are fully restricted at the south end of the bridge, and translation along the x-axis and rotation around the z-axis are allowed at the north end, where the translational degree of freedom of the bridge along the x-axis is released to allow axial deformation due to thermal effects. The simplified anchored floating bridge model is as follows Figure 1 shown.

[0038] Construct a linear full-scale anchored floating bridge structure numerical model: Use the open source structural finite element analysis software OpenSees to perform finite element modeling of the full-scale anchored floating bridge structure. By analyzing the characteristics of the floating bridge structure system, it is determined that the connection method between the various components of the floating bridge is a fully consolidated connection. On this basis, it is determined that the generalized degrees of freedom of the floating bridge column, floating foundation, and bridge main beam are all six degrees of freedom, and reasonable assumptions and simplifications are made in the numerical model. The specific modeling methods of each structural component are as follows:

[0039] Construct the model of the bridge girder and floating bridge column: Set the bridge girder as an elastic beam, use the elastic beam column element to simulate, and define the node mass by mass. Consider the floating bridge column as rigid, and assume that its elastic modulus is 1000 times larger than that of the bridge girder;

[0040] Construct a model of a floating foundation: Set the floating foundation as a rigid body, and select the node position as the center of gravity of the floating foundation. Consider using a rigidLink Beam to handle the gap connection between the node and the floating bridge column and the mooring cable. Assign the uniaxial elastic material to the zero-length element to represent the spring, and use the spring force to simulate the buoyancy of the floating foundation. Regarding the value of the spring stiffness, since the spring force is equivalent to the buoyancy of the floating body, that is,

[0041] F 浮 =ρ·g·V 排=ρ·g·A·d; F k = k·d (1)

[0042] In the formula, F 浮 is the buoyancy of the floating foundation, ρ is the density of water, g is the acceleration due to gravity, V 排 is the displacement, A and d are the draft area and draft depth of the floating foundation respectively, F k is the spring force equivalent to the buoyancy of the float, and k is the spring stiffness;

[0043] Therefore, the spring stiffness is:

[0044] k=ρgA (2)

[0045] Modeling the mooring cable: The mooring line is simulated as a cable that only pulls but does not compress, taking into account the pre-tension. The simulation is performed using a two-node link element and an elastic-perfectly plastic gap uniaxial material (ElasticPPGap material for short). The stiffness of the cable is calculated from the lateral stiffness of each mooring cluster and the anchor position of the cable. The initial gap is determined based on the required pre-tension:

[0046] Gap=-P / k cable (3)

[0047] Where Gap is the initial gap, P is the pretension of each cable;

[0048] At this point, the modeling of structural components in the numerical model of the linear full-scale anchored floating bridge is completed.

[0049] S2: Constructing the environmental load action model: When the environmental load is considered as a wave load, the forces acting on the floating foundation include wave excitation force and radiation force. Among them, the wave excitation force is composed of incident force (Froude-Krylov force, FK force) and diffraction force, and the radiation force is expressed in a form related to the added mass and radiation damping. In order to calculate these forces acting on the floating foundation, a single floating foundation hydrodynamic model is established in the hydrodynamic analysis software ANSYS AQWA and hydrodynamic calculations are performed to obtain the added mass and radiation damping of the floating foundation under different wave frequencies as well as the incident force and diffraction force. Here, the model data of the floating foundation comes from the simplified floating bridge mentioned above, and is divided into an anchored floating foundation and a non-anchored floating foundation according to whether it is connected to the mooring system. The schematic diagram of the structural model of the floating foundation is shown in the figure. Figure 2 As shown. Figure 3The curves of the added mass and radiation damping of the anchored floating foundation and the non-anchored floating foundation in the six degrees of freedom directions as a function of the wave frequency are shown. In addition, when the wave is incident along the y-axis (i.e., the sway direction), the curves of the wave excitation force on the anchored floating foundation and the non-anchored floating foundation as a function of the wave frequency are shown in the figure below. Figure 4 shown.

[0050] In order to simulate these forces in the finite element model, the incident force and diffraction force of the floating foundation at different wave frequencies obtained based on AQWA are Fourier transformed to obtain the corresponding wave-induced force time history curves, which are applied to the nodes of the floating foundation to simulate the wave-induced force. For the radiation force, the additional mass is superimposed with the mass of the structural node and assigned to each node of the floating foundation for simulation, and the radiation damping is simulated using the damping coefficient in the viscous material.

[0051] Taking into account the wave conditions of the fjord where the conceptual floating bridge is located, the sea conditions of once in a hundred years and the extreme wave conditions, the regular waves are divided into variable wave height conditions WH1~5 (6s-2m, 6s-3m, 6s-4m, 6s-5m, 6s-6m) and variable wave period conditions WP1~5 (2m-6s, 2m-7s, 2m-8s, 2m-9s, 2m-10s). Taking the variable period conditions WP1~5 as an example, when the wave is incident along the y-axis, the wave force perpendicular to the wave incident direction, that is, the longitudinal direction (surge direction), is small and can be ignored. Therefore, the wave excitation force time history curves of the moored floating foundation in the transverse (surge direction) and vertical (heaving direction) directions are given, as shown in Figure 1. Figure 5 shown.

[0052] Example 2

[0053] This embodiment provides a structural response control method for a linear full-scale anchored floating bridge dynamic analysis model under wave action as described in Embodiment 1, which is specifically as follows:

[0054] The bridge girder in the floating bridge structure is a key component that bears the external environmental load. Its acceleration and speed response directly affect the overall stability and operational safety of the floating bridge. At the same time, the vibration and impact generated during vehicle driving are also closely related to the acceleration of the bridge girder. Therefore, in order to reduce the vibration response of the bridge girder and improve driving comfort, effective control of its acceleration is particularly important. To this end, a tuned mass damper can be added to the cross-section of the bridge girder as a control device, and the structural dynamic response control can be achieved by reasonably selecting the parameters of the tuned mass damper itself, the number of arrangements and the position;

[0055] (a) Limit and mass constraints of tuned mass damper: Tuned mass damper (TMD), also known as dynamic vibration absorber, is a passive control device consisting of a spring, a mass block and a damper. TMDs generally have limit requirements. When designing a tuned mass damper, it is necessary to ensure that its maximum displacement does not exceed the distance between the mass block and the bridge beam to prevent the mass block from colliding with the bridge beam. In addition, the mass of the tuned mass damper is usually limited to 1-3% of the weight of the entire moored pontoon structure to control costs and achieve feasibility.

[0056] (b) Modeling implementation of tuned mass damper: The parameters of tuned mass damper include mass M TMD , stiffness K TMD and damping C TMD In the modeling, a node and two zero-length elements are used to simulate the tuned mass damper. The specific implementation method is: two zero-length elements are used to connect the tuned mass damper node to the node of the bridge main beam to simulate the spring stiffness and damper characteristics respectively, and the mass is applied to the node. The elastic material and viscous material are defined to describe the stiffness coefficient of the linear spring and the damping coefficient of the linear damper respectively.

[0057] (c) Determine the structural control frequency and control scheme: In this embodiment, a study on the control of a tuned mass damper and its optimization control is carried out for a once-in-a-century sea condition (WP1 condition). The specific flow chart of the control method based on the tuned mass damper is as follows: Figure 6 As shown. In order to improve driving comfort, this example focuses on controlling the vertical acceleration response of the bridge girder. First, the acceleration time history curves of each node of the bridge girder are analyzed by Fourier transform to obtain the acceleration response spectrum and dominant frequency of each node. The study found that under the action of regular waves, the vertical acceleration response of the bridge girder presents the characteristics of a single dominant frequency, so two control schemes, a single tuned mass damper and a multi-tuned mass damper, can be selected. The results show that the multi-tuned mass damper control scheme can achieve better control effects by reasonably determining the number and layout of TMDs according to the modal shape corresponding to the dominant frequency. Further research shows that when the multi-tuned mass damper control scheme is used for parameter optimization, the design variables including mass ratio and damping ratio will affect the control effect of the tuned mass damper to a certain extent. Within the range of 1%-3% of the mass ratio, when the mass ratio is 3%, the tuned mass damper shows the best control effect. At the same time, the adjustment of the damping ratio also has an important influence on the control efficiency. A smaller damping ratio can significantly improve the control efficiency of the tuned mass damper. Figure 7 The comparison of the vertical acceleration of the bridge girder during the tuning mass damper parameter optimization process is shown, which intuitively reflects the optimization effect.

Claims

1. A dynamic analysis model for a linear full-scale moored floating bridge under wave action, characterized in that: The construction method is as follows: S1: Construct a linear full-scale numerical model of the anchored floating bridge structure: Use the open source structural finite element analysis software OpenSees to perform full-scale finite element modeling. By analyzing the characteristics of the anchored floating bridge structure system, it is determined that the connection method between the components of the anchored floating bridge is a fully consolidated connection. On this basis, it is determined that the generalized degrees of freedom of the floating bridge column, floating foundation, and bridge main beam are all six degrees of freedom. The specific modeling methods of each structural component are as follows: Construct a model of the bridge girder and floating bridge column: set the bridge girder as an elastic beam, define the node mass through mass, set the floating bridge column as rigid, and set its elastic modulus to be 1000 times larger than that of the bridge girder; Construct a model of a floating foundation: the floating foundation is set as a rigid body, the node position is selected as the center of gravity of the floating foundation, and the gap connection between the node and the floating bridge column and the mooring cable is considered to be handled by a rigid connection unit. The uniaxial elastic material is assigned to the zero-length unit to represent the spring, and the spring force is used to simulate the buoyancy of the floating foundation. Regarding the value of the spring stiffness, since the spring force is equivalent to the buoyancy of the floating body, that is, F 浮 =ρgV 排 =ρgAd;F k =k·d (1) In the formula, F 浮 is the buoyancy of the floating foundation, ρ is the density of water, g is the acceleration due to gravity, V 排 is the displacement, A and d are the draft area and draft depth of the floating foundation respectively, F k is the spring force equivalent to the buoyancy of the float, and k is the spring stiffness; Therefore, the spring stiffness is: k=ρgA (2) Construct a model of the mooring cable: The mooring line is simulated as a tension-only cable with pre-tension, using a two-node connection unit and an elastic perfect plastic gap uniaxial material. The stiffness k of the cable is cable , calculated from the transverse stiffness of each mooring cluster and the anchor position of the cables, the initial Gap is determined based on the required pretension: Gap=-P / k cable (3) Where Gap is the initial gap, P is the pretension of each cable; At this point, the modeling of structural components in the numerical model of the linear full-scale anchored floating bridge is completed; S2: Constructing the environmental load action model: When the environmental load is considered as a wave load, the forces acting on the floating foundation include wave excitation force and radiation force; among them, the wave excitation force is composed of incident force and diffraction force, and the radiation force is expressed in a form related to the added mass and radiation damping. A single floating foundation hydrodynamic model is established in the hydrodynamic analysis software ANSYS AQWA and hydrodynamic calculations are performed to obtain the added mass, radiation damping, incident force and diffraction force of the floating foundation under different wave frequencies. The incident force and diffraction force of the floating foundation under different wave frequencies are Fourier transformed to obtain the corresponding wave excitation force time history curve, which is applied to the nodes of the floating foundation to simulate the wave excitation force; for the radiation force, the additional mass is superimposed with the mass of the structural node and assigned to each node of the floating foundation for simulation, and the radiation damping is simulated using the damping coefficient in the viscous material.

2. The structural response control method of a linear full-scale anchored floating bridge dynamic analysis model according to claim 1 is characterized in that: The method is as follows: a tuned mass damper is added as a control device at the cross section of the bridge main beam, specifically including the following: (a) Limitation and mass constraints of the tuned mass damper: The tuned mass damper includes a spring, a mass block and a damper. When designing the tuned mass damper, it is necessary to ensure that its maximum displacement does not exceed the distance between the mass block and the bridge beam to prevent the mass block from colliding with the bridge beam. The mass of the tuned mass damper is limited to 1-3% of the weight of the entire anchored floating bridge structure. (b) Modeling implementation of tuned mass damper: The parameters of tuned mass damper include mass M TMD , stiffness K TMD and damping C TMD ,In the modeling, a node and two zero-length elements are used to simulate the tuned mass damper. The specific implementation method is as follows: the tuned mass damper node is connected to the node of the bridge girder using two zero-length elements to simulate the spring stiffness and the damper characteristics respectively, and the mass is applied to the node, and the elastic material and the viscous material are defined to describe the stiffness coefficient of the linear spring and the damping coefficient of the linear damper; (c) Determine the structural control frequency and control scheme: The natural frequency of the tuned mass damper needs to be close to the fundamental frequency or excitation frequency of the bridge main beam in order to effectively absorb its energy and achieve the purpose of vibration reduction. Before using the tuned mass damper for control, its natural frequency needs to be determined first. The following steps are used to control the acceleration of the bridge main beam: First, based on the construction of the linear full-scale anchored floating bridge structure numerical model, a dynamic response analysis is carried out to obtain the acceleration time history curve of each node of the bridge main beam. Subsequently, the lateral and vertical acceleration time history curves are subjected to Fourier transformation to obtain the acceleration response spectrum of each node and the corresponding dominant frequency. The dominant frequency is the controlled frequency. According to this frequency, the natural frequency of the tuned mass damper is adjusted to be close to it, and then the acceleration response control analysis and research are carried out, and then the following specific schemes are selected for control: When the dominant frequency of the bridge girder is unique and the mass of a single tuned mass damper meets the actual installation requirements, a single tuned mass damper control scheme is adopted and the tuned mass damper is arranged in the mid-span of the bridge girder to achieve effective vibration reduction; When the dominant frequency of the bridge main beam is unique but the mass of a single tuned mass damper cannot meet the actual installation requirements, a control scheme of multiple tuned mass dampers with the same parameters is adopted. The control task is shared by reasonably arranging multiple small mass dampers. The arrangement method is usually determined according to the controlled modal shape. The specific steps are as follows: based on the construction of the linear full-scale anchored floating bridge structure numerical model, modal analysis is carried out to obtain the modal frequencies and corresponding modal shapes of each order of the anchored floating bridge, find a modal frequency closest to the dominant frequency of the bridge main beam, determine the modal shape corresponding to the modal frequency as the controlled modal shape, and select the bridge main beam section with a larger amplitude as the arrangement position of the tuned mass damper according to the amplitude distribution of the controlled modal shape; For bridge girders with multiple dominant frequencies, multiple tuned mass dampers are used, including multiple tuned mass dampers with different dynamic characteristics. Their layout positions are determined according to the controlled modal shape. The specific steps are similar to the control scheme using multiple tuned mass dampers with the same parameters. The difference is that it is necessary to find the multi-order modal frequencies closest to the dominant frequencies of the bridge girders and determine multiple controlled modal shapes, thereby achieving efficient control of multi-modal vibrations.

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