A numerical method for fluid-structure interaction of a friction energy dissipation device controlling the flutter of long-span bridges

Abstract

The present application belongs to the technical field of bridge wind vibration control, and discloses a kind of fluid-structure coupling numerical calculation method for studying friction energy dissipation device control large-span bridge flutter, based on computational fluid dynamics software Fluent, secondary development program is embedded in solver calculation using dynamic mesh technology compiling user-defined function.The motion equation of the rigid main beam-friction energy dissipation device coupling system in the wind field is established, and the fluid-structure coupling solution is realized by adopting the alternating solution mode of rigid main beam motion and flow field motion, to obtain the vertical and torsional motion response of the controlled main beam.Compared with the wind tunnel test method, the present application can accurately set various parameters and stress modes of the rigid main beam and the friction energy dissipation device, and can realize full-scale simulation, to conveniently and safely obtain rich information such as motion time history data of the main beam and the flow field near the main beam under various parameter conditions, facilitate the analysis of vibration suppression mechanism, and greatly reduce the research difficulty, cost and risk.

Description

Technical Field

[0001] This invention belongs to the field of bridge wind vibration control technology, and relates to a fluid-structure interaction numerical calculation method for studying the control of flutter in long-span bridges by friction energy dissipation devices. Background Technology

[0002] With the increasing span of modern bridges, the bridge structure will experience various vibrations under wind loads. Flutter, as a divergent aeroelastic instability phenomenon, is one of the most threatening forms of vibration to bridge safety and must be strictly prevented.

[0003] To improve the wind resistance performance of long-span bridges, an effective technical approach is to introduce cost-effective and efficient friction energy dissipation devices to increase system damping and reduce amplitude. The applicant has been granted an invention patent (a friction energy dissipation device for controlling flutter in long-span bridges, CN119914639B) which discloses a friction energy dissipation device for temporarily controlling flutter in long-span bridges. This device provides a safe, reliable, economical, fast, efficient, and practical possible solution to the flutter control problem of long-span bridges.

[0004] To comprehensively and thoroughly study the control characteristics of this friction energy dissipation device on bridge flutter, three methods can be adopted: theoretical analysis, wind tunnel testing, and computational fluid dynamics (CFD). Each method has its relative advantages and disadvantages. Currently, no relevant literature reports the specific process of the three analysis methods and their effect on bridge flutter control.

[0005] This invention aims to develop a two-dimensional CFD numerical simulation technology to study the performance of a friction energy dissipation device in controlling the flutter of a full-scale rigid main beam of a bridge, and to provide a basis for the optimization design of its control scheme and parameters. Summary of the Invention

[0006] This invention proposes a fluid-structure interaction numerical calculation method for studying the flutter performance of a full-scale bridge rigid main beam controlled by a friction energy dissipation device. Compared with the physical model test of a rigid model, this method allows for full-scale parameter settings, can simulate various resistance modes, and can safely and efficiently simulate full-scale or arbitrarily scaled models. It can also conveniently obtain refined dynamic response data of the main beam and its surrounding flow field, thus providing a complete data foundation for revealing the energy dissipation mechanism and optimizing the performance of the device.

[0007] The technical solution of the present invention:

[0008] A fluid-structure interaction numerical calculation method for studying the control of flutter in long-span bridges by friction energy dissipation devices includes the following steps:

[0009] Step 1: Determine the mechanical model and parameters of the rigid main beam-friction energy dissipation device coupled system, and establish the motion equation of the rigid main beam under the action of the friction energy dissipation device in the wind field; wherein, the friction energy dissipation device is a friction energy dissipation device for controlling flutter of long-span bridges as described in patent CN119914639B.

[0010] The mechanical model of the rigid main beam-friction energy dissipation device coupling system that needs to be determined consists of a rigid main beam, a friction energy dissipation device, anchor cables, a conveyor belt, and a heavy block. Two identical friction energy dissipation devices are symmetrically arranged on both sides of the bottom of the rigid main beam along the longitudinal axis of the rigid main beam. One side of each friction energy dissipation device is anchored to the ground by an anchor cable, and the other side is suspended by a heavy block by a conveyor belt.

[0011] The parameters that need to be determined for the rigid main beam include its mass, moment of inertia, vertical motion damping coefficient, torsional motion damping coefficient, vertical motion stiffness, and torsional motion stiffness; the parameters that need to be determined for the friction energy dissipation device are the friction force threshold; and the parameters that need to be determined for the anchor cable include the elastic modulus, cross-sectional area, and length of the anchor cable.

[0012] The equations of motion for a rigid main beam in a wind farm under the action of a friction energy dissipation device are divided into vertical motion equations and torsional motion equations:

[0013] (1)

[0014] (2)

[0015] In the formula, y b , and These represent the displacement, velocity, and acceleration of the rigid main beam's vertical motion, respectively. α b , and These represent the torsional displacement, torsional velocity, and torsional acceleration of the rigid main beam about its longitudinal axis, respectively. m b and J b These are the mass and moment of inertia per unit length of the rigid main beam, respectively. C bh and C bα These are the vertical motion damping coefficient and torsional motion damping coefficient of the rigid main beam, respectively. K bh and K bα These are the vertical motion stiffness and torsional motion stiffness of the rigid main beam, respectively. F w (t )and M w ( t These represent the aerodynamic lift and aerodynamic torque per unit length of the rigid main beam, respectively. F c ( t )and M c ( t The vertical load and torque applied per unit length of rigid main beam by the friction energy dissipation device are respectively expressed as: , M c ( t )=[ F c1 ( t )- F c2 ( t )]× d s / 2, i This represents the serial number of the friction energy dissipation device. i =1, 2, where 1 is the number of the friction energy dissipation device on the left and 2 is the number of the friction energy dissipation device on the right. F ci ( t )for i The control force acting on the rigid main beam by the friction energy dissipation device No. 1 d s The spacing of the friction energy dissipation devices symmetrically arranged on both sides of the rigid main beam section; wherein, F c1 ( t )and F c2 ( t They are represented as follows:

[0016] (3)

[0017] (4)

[0018] In the formula, y c1 and Representing the displacement and velocity at the connection point between the No. 1 friction energy dissipation device and the rigid main beam, respectively, are expressed as follows: y c1 = y b -0.5 d s sin( α b )and , y c2 and Representing the displacement and velocity at the connection point between the No. 2 friction energy dissipation device and the rigid main beam, respectively, they are expressed as follows: y c2 = y b +0.5 d s sin( α b )and ; y cbi and y cti They represent the current calculation time, respectively. t nearest i The minimum and maximum displacement values ​​at the connection point between the friction energy dissipation device and the rigid main beam are obtained through the adjacent time period. y ci Historical data was identified; F s1 and F s2 The friction force thresholds set for friction energy dissipation devices No. 1 and No. 2 are adjusted to the required values ​​by adjusting the physical materials of the friction energy dissipation devices. K c1 and K c2 The tensile stiffnesses of anchor cables No. 1 and No. 2 are respectively expressed as... K c1 = E 1 A 1 / l 1 and K c2 = E 2 A 2 / l 2, E 1. A 1 and l 1 represents the elastic modulus, cross-sectional area, and length of anchor cable No. 1, respectively. E 2. A 2 and l 2 represents the elastic modulus, cross-sectional area, and length of anchor cable No. 2, respectively.

[0019] Step 2: Construct the state equations for the motion of the rigid main beam in the wind field based on the equations of motion, thereby reducing the order of the equations of motion;

[0020] Rearranging equations (1) and (2) yields:

[0021] (5)

[0022] (6)

[0023] Let X( t )=[ y b ( t ), α b ( t ), , ] T By rearranging equations (5) and (6) into the form of the following first-order differential equations, the order of equations (1) and (2) can be reduced:

[0024] (7)

[0025] Equation (7) 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 force and aerodynamic torque of the wind load acting on the rigid main beam at each moment, as well as the control force and control torque of the friction energy dissipation device acting on the rigid main beam, are obtained, the fourth-order Runge-Kutta numerical calculation method is used to advance Equation (7) in the time domain to obtain the displacement and velocity response of the rigid main beam. y b ( t ), α b ( t ), , .

[0026] Step 3: Establish a two-dimensional or three-dimensional geometric model of the rigid main beam, determine the computational domain and boundary conditions of the wind field in its vicinity, and divide the flow field mesh;

[0027] The computational domain is a rectangular or cuboid region enclosing the rigid main beam. The left side of the computational domain is the velocity inlet boundary, the right side is the pressure outlet boundary, the upper and lower sides of the computational domain are symmetrical boundaries, the surface of the rigid main beam is a non-slip wall boundary, and the front and back of the cuboid region are symmetrical boundaries. The left and right sides of the computational domain are 5 times and 15 times the width of the rigid main beam, respectively, from the center of the rigid main beam. The upper and lower sides of the computational domain are both 5 times the width of the rigid main beam from the center of the rigid main beam. The distance between the front and back of the computational domain is the same as the width of the rigid main beam.

[0028] In step three, a structured boundary layer mesh is set in the region near the surface of the rigid main beam, and a structured boundary layer mesh or unstructured boundary layer mesh with gradually increasing size is set in the region away from the rigid main beam wall. The structured boundary layer mesh in the region near the surface of the rigid main beam has no less than 10 layers, and the first layer of mesh ensures the dimensionless height y. +≤1, the boundary layer mesh size gradually increases outward, the height ratio of adjacent boundary layer meshes does not exceed 1.2, the unstructured boundary layer mesh in the region far from the rigid main beam wall meets the principle of changing from dense to sparse, and the growth ratio between adjacent mesh cell sizes does not exceed 1.2.

[0029] Step 4: Import the flow field mesh generated in Step 3 into Fluent software. Compile the solution process of the state equation constructed in Step 2 using a user-defined function (UDF). Implement fluid-structure interaction solution by alternately solving the flow field motion and the main beam motion. After the flow field solution is completed at each time step, obtain the aerodynamic lift and aerodynamic torque of the rigid main beam. Calculate the control force and control torque provided by the friction energy dissipation device based on the motion displacement and velocity of the main beam. Based on the aerodynamic lift, aerodynamic torque, control force, and control torque on the rigid main beam, use the fourth-order Runge-Kutta method to solve for the vertical and torsional motion displacement of the rigid main beam in the next time step. Then update the flow field mesh based on this displacement.

[0030] Step 5: Apply an initial displacement excitation to the rigid main beam, solve the motion response time history of the main beam under the action of the friction energy dissipation device after excitation, and then evaluate the control effect of the control device on the flutter of the rigid main beam.

[0031] The beneficial effects of this invention are:

[0032] ① It allows for convenient and safe study of the effect and characteristics of friction energy dissipation devices on the flutter control of the main beam under various size and scale conditions; ② It is not affected by physical space and model processing accuracy, and allows for precise setting of various parameters and force modes of the main beam and friction energy dissipation devices as needed; ③ It simultaneously monitors the time history of the mechanical force acting on the main beam during vibration and the motion or change process of the nearby flow field, enabling convenient and in-depth study of the energy dissipation process and characteristics of the friction energy dissipation device. Attached Figure Description

[0033] Figure 1 This is a mechanical model diagram of the rigid main beam-friction energy dissipation device system according to an embodiment of the present invention.

[0034] Figure 2 This is a flowchart of a method according to an embodiment of the present invention.

[0035] Figure 3 This is a cross-sectional outline of the main beam according to an embodiment of the present invention.

[0036] Figure 4 This describes the wind field calculation domain and boundary conditions in an embodiment of the present invention.

[0037] Figure 5 The flow field grid for the wind field calculation domain in this embodiment of the invention is as follows: (a) is the overall region; (b) is a local region near the main beam; (c) is a local region near the wall of the main beam; (d) is a local region near the wall of the main beam.

[0038] Figure 6 Time history of flutter displacement of main beam under uncontrolled conditions ( U =9m / s): (a) is y b (b) is α b .

[0039] Figure 7 Time history of flutter displacement of main beam after installation of friction energy dissipation device ( U =20m / s, K c =9331N / m, F s =466.6N): (a) is y b (b) is α b .

[0040] Figure 8 Time history of flutter displacement of main beam after installation of friction energy dissipation device ( U =25m / s, K c =16966N / m, F s =848.3N): (a) is y b (b) is α b .

[0041] Figure 9 Time history of flutter displacement of main beam after installation of friction energy dissipation device ( U =30m / s, K c =23752N / m, F s =1187.6N): (a) is y b (b) is α b . Detailed Implementation

[0042] The specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings and technical solutions.

[0043] This embodiment uses the flutter of the rigid main girder of the old Tacoma Narrows Bridge in the United States as the controlled object and simulates it using the method proposed in this invention. It should be noted that this invention has no special requirements on the cross-sectional shape and dimensions of the main girder and can be applied to any cross-sectional shape.

[0044] In the CFD numerical model of this invention, the rigid main beam can be modeled using either a two-dimensional or a three-dimensional geometric model. The three-dimensional model has significantly higher accuracy and computational complexity in flow field simulation than the two-dimensional model, but the results are very close. Therefore, this embodiment uses a two-dimensional geometric model for illustration. In the specific implementation process, except for step three where the mesh of the three-dimensional model needs to be obtained by stretching the mesh of the two-dimensional geometric model along the spanwise direction, all other steps are the same.

[0045] In this embodiment, the controlled object is a full-scale rigid main beam per unit length. The relevant structural parameters are referenced in the literature (Experimental Investigations on Nonlinear Flutter Performance of the Old Tacoma NarrowsBridge Deck under Skew Winds. Journal of Structural Engineering, 2025, 151(7): 04025070). The two-dimensional geometric model parameters are: main beam length... L b =1m, m b =8483kg, J b =176824 kg·m 2 , f h =0.145Hz, f α =0.2Hz, C bh =154.6kg rad / s, C bα =4444.1kg m 2 rad / s, K bh =7041.1 N / m, K bα =279229.3N m / rad B =11.887m, D =2.5m, d s =11.875m, K c1 =9331N / m, K c2 =9331N / m, F s1 =466.6N, F s2=466.6N. The friction energy dissipation devices on both sides use the same design parameters. Using the method of this invention, the rigid main beam was obtained under different wind speeds when the friction energy dissipation devices were installed. U The vertical and torsional motion responses of the main beam under certain conditions are illustrated in the flowchart below. Figure 2 The specific operating steps are as follows:

[0046] Step 1: Determine the mechanical model of the rigid main beam-friction energy dissipation device coupled system (see...) Figure 1 Based on the parameters, establish the motion equation of the rigid main beam in the wind field under the action of the friction energy dissipation device;

[0047] Step 2: Construct state equations based on the equations of motion, thereby reducing the order of the equations of motion;

[0048] Step 3: Establish a two-dimensional geometric model of the rigid main beam; its cross-sectional profile is shown in the figure. Figure 3 The computational domain and boundary conditions of the two-dimensional wind field were determined, and the flow field mesh was generated. The computational domain is a rectangular region enclosing the rigid main beam. The left side of the computational domain is the velocity inlet boundary, the right side is the pressure outlet boundary, and the upper and lower sides are symmetrical boundaries. The surface of the rigid main beam is a no-slip wall boundary. The distances from the upper, lower, left, and right boundaries of the computational domain to the center of the main beam are 5, 5, 5, and 15 times the width of the main beam, respectively. Figure 4 As shown. The grid of the wind field computational domain is shown in [image / reference]. Figure 5 .

[0049] Step 4: Import the flow field mesh generated in Step 3 into Fluent software. Compile the solution process of the state equations constructed in Step 2 using user-defined functions (UDFs). Implement fluid-structure interaction solution by alternately solving the flow field motion and the main beam motion. After the flow field solution is completed at each time step, obtain the aerodynamic lift and aerodynamic torque of the rigid main beam. Calculate the control force and control torque provided by the friction energy dissipation device based on the motion displacement and velocity of the main beam. Based on the aerodynamic lift, aerodynamic torque, control force, and control torque acting on the rigid main beam, use the fourth-order Runge-Kutta method to solve for the vertical and torsional displacements of the rigid main beam in the next time step. Then update the flow field mesh based on this displacement. The mesh update of the computational domain adopts a smoothing method based on the diffusion equation. The displacement of a mesh point is inversely proportional to the 1.5th power of its nearest distance to the surface of the main beam.

[0050] Step 5: Apply an initial vertical or torsional displacement excitation (e.g., a torsional displacement of 2°) to the rigid main beam. Solve the motion response time history of the rigid main beam under the action of the friction energy dissipation device after excitation. Compare this with the flutter response of the uncontrolled structure to evaluate the control effect on the flutter of the rigid main beam. The time histories of the vertical and torsional displacements of the main beam under different wind speeds and friction energy dissipation device parameters in both uncontrolled and controlled states are shown below. Figure 6-9Therefore, the numerical simulation method of this invention can be used to study the effect of friction energy dissipation devices on controlling bridge flutter, and the results show that the vibration control is highly efficient.

[0051] 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 studying the control of flutter in long-span bridges by friction energy dissipation devices, characterized in that, Includes the following steps: Step 1: Determine the mechanical model and parameters of the rigid main beam-friction energy dissipation device coupled system, and establish the motion equation of the rigid main beam under the action of the friction energy dissipation device in the wind field; In step one, the equations of motion for the rigid main beam in the wind field under the action of the friction energy dissipation device are divided into vertical motion equations and torsional motion equations: (1) (2) In the formula, y b , and These represent the displacement, velocity, and acceleration of the rigid main beam's vertical motion, respectively. α b , and These represent the torsional displacement, torsional velocity, and torsional acceleration of the rigid main beam about its longitudinal axis, respectively. m b and J b These are the mass and moment of inertia per unit length of the rigid main beam, respectively. C bh and C bα These are the vertical motion damping coefficient and torsional motion damping coefficient of the rigid main beam, respectively. K bh and K bα These are the vertical motion stiffness and torsional motion stiffness of the rigid main beam, respectively. F w ( t )and M w ( t These represent the aerodynamic lift and aerodynamic torque per unit length of the rigid main beam, respectively. F c ( t )and M c ( t The vertical load and torque applied per unit length of rigid main beam by the friction energy dissipation device are respectively expressed as: , M c ( t )=[ F c1 ( t )- F c2 ( t )]× d s / 2, i This represents the serial number of the friction energy dissipation device. i =1, 2, where 1 is the number of the friction energy dissipation device on the left and 2 is the number of the friction energy dissipation device on the right. F ci ( t )for i The control force acting on the rigid main beam by the friction energy dissipation device No. 1 d s The spacing of the friction energy dissipation devices symmetrically arranged on both sides of the rigid main beam section; wherein, F c1 ( t )and F c2 ( t They are represented as follows: (3) (4) In the formula, y c1 and Representing the displacement and velocity at the connection point between the No. 1 friction energy dissipation device and the rigid main beam, respectively, are expressed as follows: y c1 = y b -0.5 d s sin( α b )and , y c2 and Representing the displacement and velocity at the connection point between the No. 2 friction energy dissipation device and the rigid main beam, respectively, they are expressed as follows: y c2 = y b +0.5 d s sin( α b )and ; y cbi and y cti They represent the current calculation time, respectively. t nearest i The minimum and maximum displacement values ​​at the connection point between the friction energy dissipation device and the rigid main beam are obtained through the adjacent time period. y ci Historical data was identified; F s1 and F s2 The friction force thresholds set for friction energy dissipation devices No. 1 and No. 2 are adjusted to the required values ​​by adjusting the physical materials of the friction energy dissipation devices. K c1 and K c2 The tensile stiffnesses of anchor cables No. 1 and No. 2 are respectively expressed as... K c1 = E 1 A 1 / l 1 and K c2 = E 2 A 2 / l 2, E 1. A 1 and l 1 represents the elastic modulus, cross-sectional area, and length of anchor cable No. 1, respectively. E 2. A 2 and l 2 represents the elastic modulus, cross-sectional area, and length of anchor cable No. 2, respectively; Step 2: Construct the state equations for the motion of the rigid main beam in the wind field based on the equations of motion, thereby reducing the order of the equations of motion; Step 3: Establish a two-dimensional or three-dimensional geometric model of the rigid main beam, determine the computational domain and boundary conditions of the wind field in its vicinity, 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 state equations constructed in Step 2 using a custom function. Implement fluid-structure interaction solution by alternately solving the flow field motion and the main beam motion. After the flow field solution is completed at each time step, obtain the aerodynamic lift and aerodynamic torque of the rigid main beam. Calculate the control force and control torque provided by the friction energy dissipation device based on the motion displacement and velocity of the rigid main beam. Based on the aerodynamic lift, aerodynamic torque, control force, and control torque on the rigid main beam, use the fourth-order Runge-Kutta method to solve for the vertical and torsional motion displacement of the rigid main beam in the next time step. Then update the flow field mesh based on this displacement.

2. The fluid-structure interaction numerical calculation method for controlling flutter of long-span bridges using friction energy dissipation devices according to claim 1, characterized in that, The mechanical model of the rigid main beam-friction energy dissipation device coupled system to be determined in step one consists of a rigid main beam, a friction energy dissipation device, anchor cables, a conveyor belt, and a weight block. Two identical friction energy dissipation devices are symmetrically arranged on both sides of the bottom of the rigid main beam along the longitudinal axis of the rigid main beam. One side of each friction energy dissipation device is anchored to the ground by an anchor cable, and the other side is suspended by a weight block by a conveyor belt.

3. The fluid-structure interaction numerical calculation method for controlling flutter in long-span bridges using a friction energy dissipation device, as described in claim 2, is characterized in that... The parameters of the rigid main beam that need to be determined in step one include the mass, moment of inertia, vertical motion damping coefficient, torsional motion damping coefficient, vertical motion stiffness, and torsional motion stiffness of the rigid main beam; the parameters of the friction energy dissipation device that need to be determined are the friction force threshold; the parameters of the anchor cable that need to be determined include the elastic modulus, cross-sectional area, and length of the anchor cable.

4. The fluid-structure interaction numerical calculation method for controlling flutter of long-span bridges using a friction energy dissipation device, as described in claim 3, is characterized in that... The reduction of the order of the equations of motion in step two is as follows: Rearranging equations (1) and (2) yields: (5) (6) Let X( t )=[ y b ( t ), α b ( t ), , ] T By rearranging equations (5) and (6) into the form of the following first-order differential equations, the order of equations (1) and (2) can be reduced: (7) Equation (7) 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 force and aerodynamic torque of the wind load acting on the rigid main beam at each moment, as well as the control force and control torque of the friction energy dissipation device acting on the rigid main beam, are obtained, the fourth-order Runge-Kutta numerical calculation method is used to advance Equation (7) in the time domain to obtain the displacement and velocity response of the rigid main beam. y b ( t ), α b ( t ), , .

5. The fluid-structure interaction numerical calculation method for controlling flutter of long-span bridges using a friction energy dissipation device according to claim 4, characterized in that, In step three, the computational domain is a rectangular or cuboid region enclosing the rigid main beam. The left side of the computational domain is the velocity inlet boundary, the right side is the pressure outlet boundary, the upper and lower sides of the computational domain are symmetrical boundaries, the surface of the rigid main beam is a non-slip wall boundary, and the front and back of the cuboid region are symmetrical boundaries. The left and right sides of the computational domain are 5 times and 15 times the width of the rigid main beam, respectively, from the center of the rigid main beam. The upper and lower sides of the computational domain are both 5 times the width of the rigid main beam from the center of the rigid main beam. The distance between the front and back of the computational domain is the same as the width of the rigid main beam.

6. The fluid-structure interaction numerical calculation method for controlling flutter of long-span bridges using a friction energy dissipation device according to claim 5, characterized in that, The flow field mesh generation method in step three is as follows: A structured boundary layer mesh is set in the region near the rigid main beam surface, and a structured boundary layer mesh or unstructured boundary layer mesh with gradually increasing size is set in the region away from the rigid main beam wall. The structured boundary layer mesh near the rigid main beam surface should have no fewer than 10 layers, and the first layer mesh should ensure a dimensionless height y. + ≤1, the boundary layer mesh size gradually increases outward, the height ratio of adjacent boundary layer meshes does not exceed 1.2, the unstructured boundary layer mesh in the region far from the rigid main beam wall meets the principle of changing from dense to sparse, and the growth ratio between adjacent mesh cell sizes does not exceed 1.2.

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