A fluid-structure interaction numerical method for controlling flutter of long-span bridges by water-soaked vertical plate

Abstract

The application belongs to the technical field of vibration control, and provides a fluid-structure coupling numerical calculation method for controlling large-span bridge flutter by using a water immersed heaving plate. The method is based on computational fluid dynamics software Fluent, uses dynamic mesh technology, and compiles a UDF secondary development program to embed the solver for calculation. The motion control equation of the rigid main beam-cable-water heaving plate coupling system in the wind field is established, the user-defined function is used to embed the system motion solving process into the Fluent software, the fluid-structure coupling solving of the system is realized by adopting the alternating solving of the rigid main beam and the wind field calculation domain and the simultaneous solving of the heaving plate and the water body calculation domain, and the vertical and torsional motion responses of the controlled main beam are obtained. Compared with physical experiments, the motion time history data of the main beam, the heaving plate and the nearby flow field under various size conditions and other rich information can be conveniently and safely obtained, the vibration suppression mechanism analysis is facilitated, and the research difficulty, cost and risk are greatly reduced.

Description

Technical Field

[0001] This invention belongs to the field of bridge wind vibration control technology, and involves calculation methods for fluid-structure interaction between the main beam and the wind field, fluid-structure interaction between the sway plate and the water, and coupled motion of the main beam-suspension cable-sway plate system. In particular, it relates to a numerical calculation method for fluid-structure interaction of a sway plate controlled by a water-immersed sway plate for flutter control of long-span bridges. Background Technology

[0002] With the increasing span of modern bridges, the bridge structure will experience various vibrations under wind loads, among which flutter is one of the most dangerous forms of vibration and should be prevented from occurring.

[0003] For many long-span bridges crossing rivers or seas, the damping and wind resistance performance of the submerged sway plate system can be improved. The sway plate is suspended in the water below the bridge by flexible cables. When the bridge undergoes vertical bending or torsional motion, the sway plate moves up and down in the water, thereby consuming the mechanical energy of the structure and controlling structural vibration. This provides a means of controlling flutter in long-span bridges.

[0004] The improvement of flutter performance of long-span bridges by heave plates can be achieved through wind tunnel and water tank tests and computational fluid dynamics (CFD). Li Youwei et al., in their study "Wind Tunnel Test Research on a Novel Wind-Resistant Underwater Damping System," investigated bridge flutter control using heave plates based on scaled-down model tests. However, the limited size of their water tank made it impossible to avoid the influence of the water tank boundary effect on the control effect. The experimental method also has the following limitations: ① It requires stringent conditions, necessitating simultaneous wind tunnel and water tank testing; ② It can only be used for small-scale scaled models, making it impossible to avoid the influence of Reynolds number effects on the test results; ③ When using experimental methods, it is difficult to simultaneously monitor the motion process of the main beam and the heave plate in the water, and the flow field changes are unknown, making it difficult to deeply study the energy dissipation process and characteristics of the heave plate, which is detrimental to the optimization and widespread application of this device; ④ It carries a high degree of risk. In contrast, the CFD method can conveniently calculate the wind field and the water body computational domain simultaneously, and can be carried out conveniently and safely under full-scale conditions. Furthermore, CFD methods can yield richer data, such as the motion time histories of the main beam and the heave plate, as well as the changes in the flow field near them. This facilitates in-depth analysis of the energy dissipation process and characteristics of the heave plate on bridge flutter. Therefore, developing a CFD numerical calculation method is the best choice for studying the flutter characteristics of bridges controlled by submerged heave plates, providing important technical support for the optimized design of its control scheme. Summary of the Invention

[0005] This invention proposes a fluid-structure interaction numerical calculation method for studying the flutter performance of long-span bridges controlled by a submerged heave plate. Compared with physical experiments, this method can conveniently and safely obtain motion time history data of the main beam, heave plate, and surrounding flow field under various size conditions.

[0006] The technical solution of the present invention:

[0007] A fluid-structure interaction numerical calculation method for controlling flutter in long-span bridges using a water-immersed heave plate is presented, with the following steps:

[0008] Step 1: Determine the dynamic parameters of the rigid main beam and the heave plate, and establish the motion control equations of the rigid main beam-suspension cable-heave plate coupled system in the wind field;

[0009] The governing equations of motion for the rigid main beam-suspension cable-slab coupled system in a wind farm are as follows:

[0010] (1)

[0011] (2)

[0012] (3)

[0013] In the formula, These represent the displacement, velocity, and acceleration of the rigid main beam's vertical motion, respectively. , and These represent the torsional displacement, torsional velocity, and torsional acceleration of the rigid main beam about its longitudinal axis, respectively. and These are the total mass and total mass moment of inertia of the rigid main beam, respectively. and These are the vertical motion damping coefficient and torsional motion damping coefficient of the rigid main beam, respectively. and These are the vertical motion stiffness and torsional motion stiffness of the rigid main beam, respectively. and These represent the aerodynamic lift and aerodynamic torque acting on the rigid main beam, respectively. and Let be the vertical load and torque applied to the rigid main beam by the suspenders, respectively, and expressed as . , , The serial number representing the heave plate. =1, 2, as shown Figure 2 As shown, 1 is the number of the left heave plate, and 2 is the number of the right heave plate. The center-to-center spacing of the sway plates symmetrically arranged on both sides of the rigid main beam section, For the force of the slings; for The quality of the No. 1 heave plate for The vertical acceleration of the heave plate. for The vertical displacement of the heave plate. for The hydrodynamic forces acting on the vertical motion of the heave plate The gravity of the helical plate can be expressed as: , Let gravitational acceleration be the acceleration due to gravity; where the force of the sling is the force of the sling. and Represented as:

[0014] (4)

[0015] (5)

[0016] In the formula, and The forces of slings No. 1 and No. 2 are respectively. and The displacement and velocity of the upper end of sling No. 1 are represented as follows: and , and The displacement and velocity of the upper end of sling #2 are represented as follows: and , and The tensile stiffnesses of slings 1 and 2 are respectively expressed as... and , , and These represent the elastic modulus, cross-sectional area, and length of sling #1, respectively. , and These represent the elastic modulus, cross-sectional area, and length of sling #2, respectively. and These are the cable tension damping ratios;

[0017] Step 2: Construct state equations based on the motion control equations of the rigid main beam-suspension cable-sway plate coupled system, thereby reducing the order of the rigid main beam's motion equations;

[0018] Rearranging equations (1) and (2) yields:

[0019] (6)

[0020] (7)

[0021] make By rearranging equations (6) and (7) into the form of the following first-order differential equations, the order of equations (1) and (2) can be reduced:

[0022] (8)

[0023] Equation (8) is the state equation for the motion of the rigid main beam in the wind field. In the numerical simulation, as long as the aerodynamic forces, aerodynamic torques, and cable forces acting on the rigid main beam at each moment are obtained, that is, the fourth-order Runge-Kutta numerical calculation method is used to advance Equation (8) in the time domain, and then the displacement and velocity response of the rigid main beam can be obtained. ;

[0024] Step 3: Establish the geometric model of the rigid main beam and the heave plate, determine the computational domain and boundary conditions of the three-dimensional flow field, and divide the flow field mesh;

[0025] The computational domain of the three-dimensional flow field is divided into two parts: a cuboid wind field computational domain surrounding the rigid main beam, and a cuboid water field computational domain surrounding two horizontally placed helical plates. The left side of the wind field computational domain belonging to the rigid main beam is the velocity inlet boundary, and the right side is the pressure outlet boundary. The front, rear, top, and bottom sides of the three-dimensional flow field computational domain are symmetrical boundaries, and the surface of the rigid main beam is a no-slip wall boundary. The left and right boundaries of the wind field computational domain are 100 and 200 times the height of the rigid main beam, respectively, from the center of the rigid main beam, while the top and bottom boundaries are both 100 times the height of the rigid main beam. The center-to-center distance between the helical plates symmetrically arranged on both sides of the rigid main beam cross-section is... Set to 5 , This represents the length of the longer side of the rectangular heave plate; the front, back, top, bottom, left, and right boundaries of the computational domain to which the heave plate belongs are all set as symmetrical boundaries, and the center distance between all boundaries of this computational domain and the nearest heave plate is 15. The above parameters are not fixed and may be adjusted as needed.

[0026] Flow field mesh generation: A structured boundary layer mesh is set in the region near the rigid main beam surface or the heave plate surface, while a structured or unstructured mesh with gradually increasing size is set in the region away from the rigid main beam and the heave plate wall. The structured boundary layer mesh near the rigid main beam surface should have at least 10 layers, ensuring dimensionless height. The grid size gradually increases outwards, and the height ratio of adjacent grids does not exceed 1.2;

[0027] Step 4: Import the flow field mesh generated in Step 3 into Fluent software, and use user-defined functions (UserDefined) to... The Functions, or UDFs, compile the solution process of the motion control equations of the rigid main beam-suspension cable-heavy plate coupled system in a wind field into the Fluent software. It achieves fluid-structure interaction (FSI) solution of the system by alternately solving the rigid main beam and wind field computational domains, and simultaneously solving the heaving plate and water computational domains. At the beginning of each time step, the suspension cable force is calculated based on the relative positions between the rigid main beam and the heaving plate. This force is then read into the six-DOF solver embedded in Fluent software to solve for the position of the heaving plate at the end of the corresponding time step and automatically update the mesh of the water computational domain. At the end of each time step, the suspension cable force is calculated based on the relative positions between the rigid main beam and the heaving plate. The state equations are then advanced in the time domain using the fourth-order Runge-Kutta method based on the vertical and torsional aerodynamic forces acting on the rigid main beam and the suspension cable force. Finally, the mesh of the wind field computational domain is updated based on the latest position of the rigid main beam.

[0028] The mesh update of the wind field computational domain adopts a smoothing method based on the diffusion equation, and the displacement of the mesh point is inversely proportional to the 1.5th power of its nearest distance to the main beam surface;

[0029] Step 5: Apply an initial torsional displacement excitation to the rigid main beam, solve the time history of the coupled motion response of the main beam and the heave plate after excitation, and then evaluate the control effect of the heave plate on the flutter of the rigid main beam.

[0030] The beneficial effects of this invention are as follows: Compared with experimental methods: ① It does not require the conditions for wind tunnel and water tank combined testing; ② It is not affected by physical space and model processing accuracy, and various parameters of the main beam and heave plate can be accurately set as needed; ③ It can be conveniently and safely carried out under various size conditions, and the flutter control effect and characteristics of the heave plate on the main beam under full-scale conditions can be studied; ④ It can simultaneously monitor the motion or change process of the main beam, the heave plate in water and the flow field near both, and can conveniently and deeply study the energy consumption process and characteristics of the heave plate. Attached Figure Description

[0031] Figure 1 This is a flowchart of a method according to an embodiment of the present invention.

[0032] Figure 2 This is a mechanical model of the rigid main beam-suspension cable-underwater swaying plate system in an embodiment of the present invention.

[0033] Figure 3 This describes the wind field calculation domain and boundary conditions in an embodiment of the present invention.

[0034] Figure 4 This refers to the water body calculation domain and boundary conditions in an embodiment of the present invention.

[0035] Figure 5 The wind field calculation domain flow field grid is shown in the embodiment of the present invention; wherein, (a) is a two-dimensional cross-section of the overall region; (b) is a three-dimensional local region; (c) is a two-dimensional cross-section of the region near the main beam; and (d) is a two-dimensional cross-section of the region near the wall of the main beam.

[0036] Figure 6 The flow field grid for the water computation domain in this embodiment of the invention is shown below; where (a) is a two-dimensional cross-section of the region near the heave plate; (b) is a three-dimensional local region near the wall of the heave plate; and (c) is a two-dimensional cross-section of the local region near the wall of the heave plate.

[0037] Figure 7 Time history of flutter displacement of main beam after installation of heave plate ; where (a) is (b) is .

[0038] Figure 8 Displacement time history of the upper ends of the suspenders on both sides and the sway plate ; where (a) is and (b) is and .

[0039] Figure 9 Time history of flutter displacement of main beam without control measures ; where (a) is (b) is . Detailed Implementation

[0040] The specific embodiments of the present invention will be further described below with reference to the accompanying drawings and technical solutions.

[0041] In this embodiment, a rectangular cross-section main beam and a square heave plate are used. The three-dimensional model parameters are as follows: , , , , , , , , , , , , , The area of ​​both the ① and ② heave plates is 0.04m². 2 Both heave plates ① and ② have a mass of 0.40 kg. Using the method of this invention, the rigid main beam under wind speed conditions during the installation of the heave plates is obtained. 10.00 m / s (dimensionless reduced wind speed)

[0042] The vertical and torsional motion responses of the main beam under these conditions are illustrated in the flowchart below. Figure 1 The specific operating steps are as follows:

[0043] Step 1: Determine the mechanical model of the rigid main beam-suspender-slab coupled system in the wind farm, such as... Figure 2 As shown, the system's coupled motion control equations are established.

[0044] Step 2: Construct state equations based on the motion equations of the rigid main beam, thereby reducing the order of the motion equations of the main beam;

[0045] Step 3: Establish the geometric model of the rigid main beam and the heave plate, determine the computational domain and boundary conditions of the three-dimensional wind field and water body, and divide the flow field mesh. The left side of the wind field computational domain to which the main beam belongs is the velocity inlet boundary, the right side is the pressure outlet boundary, and the upper, lower, front, and rear sides are symmetrical boundaries. The surface of the main beam is a no-slip wall boundary. The left and right boundaries of this computational domain are 100 and 200 times the height of the main beam, respectively, from the center of the main beam. The upper and lower boundaries are both 100 times the height of the main beam from the center of the main beam. Figure 3 As shown. The horizontal distance between the two heave plates is The front, back, top, bottom, left, and right boundaries of the computational domain of the water body to which the heave plate belongs are all set as symmetrical boundaries. The center distance between all boundaries of this computational domain and the nearest heave plate is 1. ,like Figure 4 As shown. The grids for the wind field and water body computational domains are shown in the figure. Figure 5 and Figure 6 .

[0046] Step 4: Import the flow field mesh generated in Step 3 into Fluent software. Use user-defined functions (UDFs) to compile the solution process of the coupled system's motion equations into Fluent. The fluid-structure interaction solution of the system is achieved by alternately solving the main beam and wind field computational domains and simultaneously solving the heave plate and water body computational domains. At the beginning of each time step, the displacement and velocity of the main beam and the heave plate are substituted into equations (4) and (5) to calculate the cable force. The cable force is read into the six-degree-of-freedom solver embedded in Fluent to solve the position of the heave plate at the end of the corresponding time step and automatically update the grid of the water computation domain. At the end of each time step, the cable force is calculated based on the relative position between the main beam and the heave plate. The state equation is advanced in the time domain using the fourth-order Runge-Kutta method based on the aerodynamic forces in the vertical and torsional directions and the cable force on the main beam. Then, the grid of the wind field computation domain is updated based on the latest position of the rigid main beam. The grid update adopts the smoothing method based on the diffusion equation. The displacement of the grid point is inversely proportional to the 1.5th power of its nearest distance to the structure surface.

[0047] Step 5: Apply initial vertical and torsional displacement excitation to the rigid main beam (e.g., vertical displacement 1cm, torsional displacement 1°), and solve for the time history of the coupled motion response of the main beam and the heave plate after excitation to obtain the displacement time history of the main beam and the heave plate (see [link to relevant documentation]). Figure 7 and Figure 8 ), and the flutter displacement of the main beam when the sway bar is not installed ( Figure 9 By comparison, the control effect of the heave plate on the flutter of the rigid main beam can be evaluated.

[0048] This invention is not limited to the above embodiments. Based on the technical solutions disclosed in this invention, those skilled in the art can make some substitutions and modifications to some of the technical features without creative effort, and all such substitutions and modifications are within the protection scope of this invention.

Claims

1. A fluid-structure interaction numerical calculation method for controlling flutter in long-span bridges using a water-immersed sway plate, characterized in that... The steps are as follows: Step 1: Determine the dynamic parameters of the rigid main beam and the heave plate, and establish the motion control equations of the rigid main beam-suspension cable-heave plate coupled system in the wind field; Step 2: Based on the motion control equations of the rigid main beam-suspension cable-slab coupled system in the wind field, construct the state equations to achieve order reduction of the state equations for the rigid main beam motion; Step 3: Establish the geometric model of the rigid main beam and the heave plate, determine the computational domain and boundary conditions of the three-dimensional flow field, and divide the flow field mesh; Step 4: Import the flow field mesh generated in Step 3 into Fluent software. Compile the solution process of the motion control equations of the rigid main beam-suspension cable-heavy plate coupled system in the wind field into Fluent software using a user-defined function. The fluid-structure interaction solution of the rigid main beam-suspension cable-heavy plate coupled system in the wind field is achieved by alternately solving the rigid main beam and wind field computational domains and simultaneously solving the heaving plate and water computational domains. At the beginning of each time step, the suspension cable force is calculated based on the relative position between the rigid main beam and the heaving plate. The suspension cable force is read into the six-degree-of-freedom solver embedded in Fluent software to solve for the position of the heaving plate at the end of the corresponding time step and automatically update the mesh of the water computational domain. At the end of each time step, the suspension cable force is calculated based on the relative position between the rigid main beam and the heaving plate. The state equations are advanced in the time domain using the fourth-order Runge-Kutta method based on the vertical and torsional aerodynamic forces on the rigid main beam and the suspension cable force. Then, the mesh of the wind field computational domain is updated based on the latest position of the rigid main beam. Step 5: Apply an initial torsional displacement excitation to the rigid main beam, solve the time history of the coupled motion response of the main beam and the heave plate after excitation, and then evaluate the control effect of the heave plate on the flutter of the rigid main beam. Its characteristic is that the motion control equation of the rigid main beam-suspender-heavy plate coupled system in the wind field is: (1) ； (2) ； (3) ； In the formula, , and These represent the displacement, velocity, and acceleration of the rigid main beam's vertical motion, respectively. , and These represent the torsional displacement, torsional velocity, and torsional acceleration of the rigid main beam about its longitudinal axis, respectively. and These are the total mass and total mass moment of inertia of the rigid main beam, respectively. and These are the vertical motion damping coefficient and torsional motion damping coefficient of the rigid main beam, respectively. and These are the vertical motion stiffness and torsional motion stiffness of the rigid main beam, respectively. and These represent the aerodynamic lift and aerodynamic torque acting on the rigid main beam, respectively. and Let be the vertical load and torque applied to the rigid main beam by the suspenders, respectively, and expressed as . , , The serial number representing the heave plate. The center-to-center spacing of the sway plates symmetrically arranged on both sides of the rigid main beam section, For the force of the slings; for The quality of the No. 1 heave plate for The vertical acceleration of the heave plate. for The hydrodynamic forces acting on the vertical motion of the heave plate; Let g be the weight of the helical plate, expressed as , Let gravitational acceleration be the acceleration due to gravity; where the sling force is the force of the cable. and Represented as: (4) (5) In the formula, and The forces of slings No. 1 and No. 2 are respectively. and The displacement and velocity of the upper end of sling No. 1 are represented as follows: and , and The displacement and velocity of the upper end of sling #2 are represented as follows: and , and The tensile stiffnesses of slings 1 and 2 are respectively expressed as... and , , and These represent the elastic modulus, cross-sectional area, and length of sling #1, respectively. , and These represent the elastic modulus, cross-sectional area, and length of sling #2, respectively. and These are the cable tension damping ratios; This represents the vertical displacement of the first heave plate. This represents the vertical displacement of the No. 2 heave plate; Its features are, Rearranging equations (1) and (2) yields: (6) ； (7) ； make By rearranging equations (6) and (7) into the form of the following first-order differential equations, the order of equations (1) and (2) can be reduced: (8) Equation (8) is the state equation for the motion of the rigid main beam in the wind field. In the numerical simulation, as long as the aerodynamic forces, aerodynamic torques, and cable forces acting on the rigid main beam at each moment are obtained, the fourth-order Runge-Kutta numerical calculation method is used to advance Equation (8) in the time domain, and then the displacement and velocity response of the rigid main beam can be obtained. .

2. The fluid-structure interaction numerical calculation method for controlling flutter of long-span bridges using a water-immersed swaying plate according to claim 1, characterized in that, The computational domain of the three-dimensional flow field is divided into two parts: a cuboid wind field computational domain surrounding the rigid main beam, and a cuboid water field computational domain surrounding two horizontally placed helical plates. The left side of the wind field computational domain belonging to the rigid main beam is the velocity inlet boundary, and the right side is the pressure outlet boundary. The front, back, top, and bottom sides of the three-dimensional flow field computational domain are all symmetrical boundaries, and the surface of the rigid main beam is a no-slip wall boundary. The left and right boundaries of the wind field computational domain are 100 and 200 times the height of the rigid main beam, respectively, from the center of the rigid main beam, while the top and bottom boundaries are both 100 times the height of the rigid main beam. The center-to-center distance between the helical plates symmetrically arranged on both sides of the rigid main beam cross-section is... Set as , This represents the length of the longer side of the rectangular heave plate; the front, back, top, bottom, left, and right boundaries of the computational domain to which the heave plate belongs are all set as symmetrical boundaries, and the center distance between all boundaries of this computational domain and the nearest heave plate is 1. ; Flow field mesh generation: Structured boundary layer meshes are set in regions near the rigid main beam surface or the heave plate surface; structured or unstructured meshes with gradually increasing sizes are set in regions far from the rigid main beam and the heave plate wall. The structured boundary layer meshes near the rigid main beam surface should have at least 10 layers, ensuring dimensionless height. The grid size gradually increases outwards, and the height ratio of adjacent grids does not exceed 1.2.

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