CFD numerical simulation-based TMDI control bridge rigid girder low-frequency vertical vortex vibration research method

Abstract

The invention belongs to the technical field of vibration control, and provides a CFD numerical simulation-based TMDI control bridge rigid main beam low-frequency vertical vortex vibration research method, which comprises the following steps of: establishing a rigid main beam-TMDI vertical coupling vibration equation in a wind field, carrying out order reduction processing on the coupling vibration equation by constructing a state equation, embedding a solving process into Fluent software by utilizing a user-defined function, and carrying out low-frequency vertical vortex vibration research on a rigid main beam-TMDI control bridge rigid main beam. And the vertical vortex-induced vibration response of the controlled main beam is obtained by alternately solving the flow field domain and the structural domain. Compared with a theoretical method, the fluid-solid coupling effect can be directly simulated, a vortex-induced force model does not need to be assumed, and the result is more reliable; compared with a wind tunnel test method, various parameters of the structure and the TMDI can be accurately set, physical space constraint is avoided, machining errors do not exist, the method is not limited to low wind speed, and the vibration suppression effect can be verified more conveniently; compared with an on-site actual measurement method, the method does not need to passively wait for vertical vortex vibration of a real bridge for a long time, can obtain richer information, facilitates the development of vibration suppression mechanism analysis, and greatly reduces the research difficulty and cost.

Description

Technical Field

[0001] The invention belongs to the technical field of vibration control, and relates to a method for studying the low-frequency vertical vortex vibration performance of a rigid main beam of a bridge by using a Tuned Mass Damper Inerter (TMDI) numerical simulation using computational fluid dynamics (CFD). Background Art

[0002] Due to the low frequency and damping of large-span bridges, large vertical vortex vibrations may occur under common wind speeds, which not only threatens driving safety, but also causes social panic and adverse effects.

[0003] Tuned Mass Damper (TMD) can be used to control vertical vortex-induced vibration of bridges, but the vertical vortex-induced vibration frequency of long-span bridges may be as low as 0.2 Hz or even lower than 0.1 Hz. Accordingly, the static deformation of the spring required by traditional TMD will exceed 6 m or even reach 25 m, far exceeding the available installation space in the bridge main beam box.

[0004] TMDI incorporates a rotor with a large rotational mass moment of inertia into the original TMD system. It can significantly reduce the static and dynamic displacements of the TMD spring while ensuring a large equivalent mass, thereby achieving a lower vibration frequency. Therefore, it can provide a means for controlling low-frequency vertical vortex-vibration on super-long span bridges.

[0005] The inventor has not seen any relevant literature that uses CFD numerical simulation to study the method of using TMDI to control the low-frequency vertical vortex-vibration performance of rigid bridges. Therefore, the present invention proposes to use CFD numerical simulation methods to directly solve the vertical vortex-vibration response of the rigid main beam-TMDI coupled vibration system in the wind field. This method can directly simulate the wind load on the main beam, taking into account the fluid-solid coupling effect, without the need to introduce an empirical vortex-excitation model, and the various parameters of the TMDI system such as physical mass, equivalent mass, frequency, and damping ratio can be accurately set as needed, which is convenient for analyzing the vortex-vibration control effect under different parameter combination conditions. The numerical simulation method is used to verify the reliability of the theoretical method, which has obvious advantages over the wind tunnel test method and the on-site measurement method. Therefore, this method can provide important technical support for the optimization design of low-frequency vertical vortex-vibration control of large-span bridges using TMDI. Summary of the invention

[0006] The present invention provides a CFD numerical simulation method for controlling low-frequency vertical vortex vibration of a bridge by using TMDI, which can directly solve the vertical vortex vibration response of the rigid main beam of the bridge under the action of wind and TMDI, and is used for controlling and optimizing the vertical vortex vibration of the bridge.

[0007] The technical solution of the present invention:

[0008] A research method for TMDI control of low-frequency vertical vortex vibration of rigid main beam of bridge based on CFD numerical simulation, the steps are as follows:

[0009] Step 1: Determine the dynamic parameters of the rigid main beam and TMDI, and establish the vertical vibration control equation of the rigid main beam-TMDI coupling system in the wind farm;

[0010] Step 2: construct the state equation based on the rigid main beam-TMDI coupled vibration equation, and then realize the order reduction processing of the coupled vibration equation;

[0011] Step 3: Establish a rigid main beam geometric model, determine the calculation domain and boundary conditions of the two-dimensional or three-dimensional flow field, and divide the flow field grid;

[0012] Step 4: Import the rigid main beam mesh model into Fluent software, use user-defined functions (UDF) to compile the solution process of the coupled vibration equation into Fluent, and use the flow field domain-structure domain alternating solution method to achieve fluid-solid coupling solution. At the end of each time step, the fourth-order Runge-Kutta method is used to advance the state equation in the time domain according to the vertical vortex excitation force on the main beam, and then the flow field mesh is updated according to the latest position of the rigid main beam;

[0013] Step 5: Apply an initial vertical displacement excitation to the rigid main beam, solve the vertical vibration response time history of the main beam and TMDI after excitation, and then evaluate the control effect of TMDI on the vertical vortex-induced vibration response of the rigid main beam.

[0014] As a further limitation of the present invention, the specific method of establishing the rigid main beam-TMDI coupling vibration equation in step 1 is:

[0015] The vertical vibration control equation of the rigid main beam-TMDI coupling system in the wind farm is:

[0016]

[0017] Among them, m1, m2 and m3 are the physical masses of the main beam, TMD and inertia respectively, and m 3e is the equivalent mass provided by the inertia capacity, c1 and c2 are the damping coefficients of the main beam and the TMDI system, k1 and k2 are the stiffnesses of the main beam and the TMDI system, F L is the vertical vortex force perpendicular to the flow direction on the rigid main beam, h1, are the vertical vibration displacement, velocity and acceleration of the rigid main beam, h2, are the vertical vibration displacement, velocity and acceleration of TMD respectively. For the convenience of design, the TMD mass ratio m is defined as * =m2 / m1, inertia equivalent mass magnification λ = m3e / m2, frequency ratio f * =ω2 / ω1, where ω1 = (k1 / m1) 1 / 2 is the vertical natural circular frequency of the rigid main beam, ω2=(k2 / (m2+m 3e )) 1 / 2 is the vertical natural circular frequency of the TMDI system, and the damping ratio ξ2=c2 / (2(m2+m 3e )ω2).

[0018] As a further limitation of the present invention, the specific order reduction method of the vertical vibration equation of the rigid main beam and TMDI coupling system in step 2 is:

[0019] Formula (1) can be rearranged as:

[0020]

[0021] Substitute equation (3) into equation (2) and rearrange it into:

[0022]

[0023] in: A custom coefficient.

[0024] Substitute equation (4) into equation (3):

[0025]

[0026] make is the state vector, and equations (4) and (5) are organized into the following first-order differential equation form to achieve the order reduction of equations (1) and (2):

[0027]

[0028] Among them: A3=A2(m1+m3) is the custom coefficient.

[0029] Formula (6) is the state equation of the vertical vibration of the rigid main beam and TMDI coupling system in the wind field. In the numerical simulation calculation, as long as the vertical vortex excitation force acting on the main beam at each moment is obtained, the fourth-order Runge-Kutta format can be used to advance Formula (6) in the time domain to obtain the vertical vibration displacement and velocity response h1, h2, h3 of the rigid main beam and TMDI.

[0030] As a further limitation of the present invention, the calculation domain in step three is a rectangular area (two-dimensional) or a cubic area (three-dimensional) surrounding the main beam, the left side of the calculation domain is the velocity inlet boundary, the right side is the pressure outlet boundary, the upper and lower sides are symmetrical boundaries, the main beam surface is a no-slip wall boundary, the front and back of the three-dimensional calculation domain are symmetrical boundaries, the left and right sides of the calculation domain are 50 times and 100 times the main beam height respectively from the center of the main beam, the upper and lower side boundaries are 50 times the main beam height from the center of the main beam, and the front and back of the three-dimensional calculation domain are 5 times the main beam height away. The above parameters are not fixed and can also be adjusted appropriately.

[0031] As a further limitation of the present invention, in step 3, a structured boundary layer grid is set in the area close to the main beam surface, and an unstructured grid with gradually increasing size is set in the area away from the wall. It is recommended that the structured grid close to the main beam surface is not less than 10 layers, and the first layer grid should ensure the dimensionless height y + ≤1, the grid size gradually increases outwards, but the ratio of adjacent grid heights should not exceed 1.2.

[0032] As a further limitation of the present invention, in step 4, it is recommended to adopt a smoothing method based on the diffusion equation for the grid update, and the displacement of the grid point is inversely proportional to the 1.5th power of the closest distance to the main beam surface.

[0033] Beneficial effects of the present invention:

[0034] (1) Compared with the theoretical analysis method, this method does not require the use of empirical vertical vortex-induced force models or assumed vibration forms. By directly solving the flow field-rigid main beam-TMDI coupling problem, the vertical vortex-induced vibration response of the rigid main beam in the uncontrolled state or TMDI control state is obtained, so the calculation results are more accurate. According to the theoretical method, a dimensionless analysis can be performed, and the rationality and accuracy of the results can be verified by this numerical simulation method.

[0035] (2) Compared with the wind tunnel test research method, this method is not constrained by physical space and model processing accuracy. It can accurately set various parameters of the structure and TMDI according to needs. In particular, it is difficult for the wind tunnel test model to accurately simulate the damping characteristics of the inertial capacity system. It can also avoid problems such as low vortex-induced wind speed and unsatisfactory wind field conditions in wind tunnel tests. Therefore, it is more conducive to direct numerical verification of the vibration suppression effect.

[0036] (3) Compared with the on-site measurement research method, this method does not require long-term passive waiting for the vertical vortex vibration of the actual bridge. It can easily create large-scale vortex vibration conditions and obtain rich vibration and flow field data. It has low cost and low risk, and is therefore more conducive to the development of vibration suppression mechanism and parameter optimization analysis. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] Figure 1 It is a flow chart of a method according to an embodiment of the present invention.

[0038] Figure 2 It is the mechanical model of the rigid main beam-TMDI coupling system of the embodiment of the present invention.

[0039] Figure 3 It is the calculation domain and boundary conditions of the rigid main beam flow field of the embodiment of the present invention.

[0040] Figure 4 This is the near-wall flow field grid of the rigid main beam of an embodiment of the present invention: (a) the entire area around the main beam; (b) the local area around the railing; (c) the local area around the wind nozzle.

[0041] Figure 5 It is the vertical vortex-induced vibration time history of the rigid main beam in an uncontrolled state and a controlled state according to an embodiment of the present invention.

[0042] Figure 6 The vertical vibration time history of the rigid main beam of the embodiment of the present invention under λ=4: (a) ξ2=0.020, different f * ; (b) f * =0.990, different ξ2.

[0043] Figure 7 The vertical vibration time history of the rigid main beam of the embodiment of the present invention under λ=6: (a) ξ2=0.020, different f * ; (b) f * =0.990, different ξ2.

[0044] Figure 8 The vertical vibration time history of the rigid main beam of the embodiment of the present invention under λ=8: (a) ξ2=0.020, different f * ; (b) f * =0.990, different ξ2. DETAILED DESCRIPTION

[0045] The specific implementation of the present invention is described in detail below in conjunction with the accompanying drawings and technical solutions.

[0046] This embodiment uses the main beam of the Great Belt Bridge, which has experienced large vertical vortex vibration, as the object and uses the method proposed in the present invention to simulate. It should be pointed out that the present invention has no special requirements on the cross-sectional form. In addition to being applicable to the vertical vortex vibration control of the rigid main beam of the bridge, it can also be applied to other structures with low-frequency vertical vortex vibration problems.

[0047] The rigid main beam in the CFD numerical model of the present invention can adopt a two-dimensional rigid model and a three-dimensional rigid model, wherein the three-dimensional model has higher flow field simulation accuracy, but the amount of calculation is larger, so this embodiment is described with a two-dimensional model. In the specific implementation process, except that the mesh of the three-dimensional model in step 3 needs to be obtained by stretching the mesh of the two-dimensional model along the span direction, the remaining steps are the same.

[0048] The geometric scale ratio of the rigid main beam model in this embodiment is 1:25, the two-dimensional model parameters are m1=36.320kg, k1=605.804N / m, c1=0.913N·s / m, D=0.179m, B=1.240m, f1=0.650Hz, and the TMDI parameters are m2=0.1816kg, k2=14.994N / m, c2=0.1476N·s / m, f2=0.64675Hz, m3=0.01816kg, m 3e =1.816kg, corresponding to the system mass ratio m * =0.005, amplification factor λ=4, frequency ratio f * =0.995, damping ratio ξ2 =0.02, the method of the present invention is used to obtain the rigid main beam at the reduced wind speed (U r =U / f1D, where U is the physical wind speed) is 8.59, the vertical vortex-induced vibration response under the action of TMDI is realized as shown in the flow chart. Figure 1 The specific steps are as follows:

[0049] Step 1: Determine the mechanical model of the rigid main beam and TMDI system, such as Figure 2 As shown, the vertical vibration control equation of the rigid main beam-TMDI coupling system in the wind farm is established.

[0050] Step 2: Construct the state equation based on the rigid main beam-TMDI coupled vibration equation, and then realize the order reduction processing of the coupled vibration equation.

[0051] Step 3: Establish a rigid main beam geometric model, determine the computational domain and boundary conditions of the two-dimensional flow field, and divide the flow field grid. The computational domain is a rectangular area surrounding the main beam. The left side is the velocity inlet boundary, the right side is the pressure outlet boundary, the upper and lower sides are symmetrical boundaries, and the main beam surface is a no-slip wall boundary. The left and right boundaries of the computational domain are 50 and 100 times the main beam height from the center of the main beam, respectively, and the upper and lower side boundaries are 50 times the structure height from the center of the main beam, such as Figure 3 12 layers of structured boundary layer grids are set near the main beam surface. The height of the first layer grid is 0.25 mm. The grid size gradually increases outwards. The ratio of adjacent grid heights is about 1.1. The grid of the flow field near the wall of the rigid main beam is as follows: Figure 4 shown.

[0052] Step 4: Import the rigid main beam mesh model into Fluent software, and use the user-defined function (UDF) to compile the solution process of the coupled vibration equation into Fluent. The fluid-solid coupling solution is achieved by alternating the flow field domain and the structure domain. At the end of each time step, the state equation is advanced in the time domain using the fourth-order Runge-Kutta method according to the vertical vortex force on the main beam. Then, the flow field mesh is updated according to the latest position of the rigid main beam. The mesh update adopts the smoothing method based on the diffusion equation, and the displacement of the mesh point is inversely proportional to the 1.5th power of the closest distance to the structure surface.

[0053] Step 5: To save calculation time, an initial vertical displacement excitation (10 mm) is applied to the rigid main beam according to the vertical vortex-vibration amplitude of the uncontrolled structure (about 11 mm). Then, the fluid-solid coupling solution is enabled to obtain the vertical vibration response time history of the rigid main beam and TMDI after the initial excitation is applied. By comparing it with the vertical vibration response of the uncontrolled structure, the control effect of TMDI on the vertical vortex-vibration response of the rigid main beam can be evaluated. Figure 5 In addition, by modifying m * ,λ,f * , ξ2, we can study the effect of different TMDI parameter combinations on the vertical vortex-vibration suppression of the rigid main beam and obtain the optimal parameters for design reference. Figure 6-8 Shown is m * =0.005, using different λ (4, 6, 8), different f * The vertical vibration displacement time history of the rigid main beam under the action of TMDI at different ξ2 (0.980, 0.985, 0.990, 0.995) and different ξ2 (0.010, 0.020, 0.030, 0.040). It can be seen that within the above parameter range, TMDI can effectively suppress the occurrence of vertical vortex vibration of the main beam, and the vibration suppression efficiency gradually decreases with the increase of λ. Under each λ, the optimal f * and ξ2 are basically unchanged, around 0.985 and 0.02 respectively.

[0054] The present invention is not limited to the above-mentioned embodiments. On the basis of the technical solution disclosed in the present invention, technicians in this field can make some substitutions and deformations to some technical features therein according to the disclosed technical content without creative labor, and these substitutions and deformations are all within the protection scope of the present invention.

Claims

1. A research method for TMDI control of low-frequency vertical vortex vibration of rigid main beam of bridge based on CFD numerical simulation, characterized in that: The following steps are involved: Step 1: Determine the dynamic parameters of the rigid main beam and TMDI, and establish the vertical vibration control equation of the rigid main beam-TMDI coupling system in the wind farm; Step 2: Construct the state equation based on the vertical vibration control equation of the rigid main beam-TMDI coupling system, and then realize the order reduction processing of the coupling vibration equation; Step 3: Establish a rigid main beam geometric model, determine the calculation domain and boundary conditions of the two-dimensional or three-dimensional flow field, and divide the flow field grid; Step 4: Import the rigid main beam geometric model into Fluent software, use the user-defined function UDF to compile the solution process of the vertical vibration control equation of the rigid main beam-TMDI coupling system into Fluent, and use the flow field domain-structure domain alternating solution method to achieve fluid-solid coupling solution. At the end of each time step, the fourth-order Runge-Kutta method is used to advance the state equation in the time domain according to the vertical vortex excitation force on the rigid main beam, and then the flow field grid is updated according to the latest position of the rigid main beam; Step 5: Apply an initial vertical displacement excitation to the rigid main beam, solve the vertical vibration response time history of the main beam and TMDI coupling system after excitation, and then evaluate the control effect of TMDI on the vertical vortex-induced vibration response of the rigid main beam.

2. The research method of TMDI control of low-frequency vertical vortex vibration of bridge rigid main beam based on CFD numerical simulation according to claim 1 is characterized in that: The vertical vibration control equation of the rigid main beam-TMDI coupling system in the wind farm in step 1 is: Among them, m1, m2 and m3 are the physical masses of the rigid main beam, TMD and inertia capacity respectively, and m 3e is the equivalent mass provided by the inertia capacity, c1 and c2 are the damping coefficients of the rigid main beam and the TMDI coupling system, k1 and k2 are the stiffness of the rigid main beam and the TMDI coupling system, F L is the vortex force perpendicular to the flow direction on the rigid main beam, h1, are the vibration displacement, velocity and acceleration of the rigid main beam, h2, are the vibration displacement, velocity and acceleration of TMD respectively; define the TMD mass ratio m * =m2 / m1, inertia equivalent mass magnification λ = m 3e / m2, frequency ratio f * =ω2 / ω1, where ω1 = (k1 / m1) 1 / 2 is the natural circular frequency of the rigid main beam, ω2=(k2 / (m2+m 3e )) 1 / 2 is the natural circular frequency of the TMDI coupling system, and the damping ratio ξ2=c2 / (2(m2+m 3e )ω2).

3. The research method of TMDI control of low-frequency vertical vortex vibration of bridge rigid main beam based on CFD numerical simulation according to claim 2 is characterized in that: The specific method for reducing the vertical vibration control equation of the rigid main beam-TMDI coupling system in step 2 is: Equation (1) is rearranged as: Substitute equation (3) into equation (2) and rearrange it into: in: is a custom coefficient; Substitute equation (4) into equation (3): make is the state vector, and equations (4) and (5) are organized into the following first-order differential equation form to achieve the order reduction of equations (1) and (2): Among them: A3=A2(m1+m3) is the custom coefficient; Formula (6) is the state equation of the vertical vibration of the rigid main beam and TMDI coupling system in the wind field. In the numerical simulation calculation, as long as the vertical vortex excitation force acting on the main beam at each moment is obtained, the fourth-order Runge-Kutta format can be used to advance Formula (6) in the time domain, that is, the vertical vibration displacement and velocity response h1, h2, h3 of the rigid main beam and TMDI coupling system can be obtained.

4. The research method of TMDI control of low-frequency vertical vortex vibration of bridge rigid main beam based on CFD numerical simulation according to claim 1 is characterized in that: In step three, the computational domain is a two-dimensional rectangular area or a three-dimensional cubic area surrounding 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 symmetric boundaries; the surface of the rigid main beam is the no-slip wall boundary; the front and back of the three-dimensional computational domain are symmetric boundaries.

5. The research method of TMDI control of low-frequency vertical vortex vibration of rigid main beam of bridge based on CFD numerical simulation according to claim 4 is characterized in that: The left and right side boundaries of the calculation domain are 50 and 100 times the rigid main beam height from the center of the rigid main beam respectively, the upper and lower side boundaries of the calculation domain are both 50 times the rigid main beam height from the center of the main beam, and the front and back faces of the three-dimensional calculation domain are 5 times the rigid main beam height.

6. The research method of TMDI controlling low-frequency vertical vortex vibration of rigid main beam of bridge based on CFD numerical simulation according to claim 4 is characterized in that: In step 3, a structured boundary layer grid is set in the area close to the main beam surface, and an unstructured grid with gradually increasing size is set in the area far from the wall. It is recommended that the structured grid should be no less than 10 layers, and the first layer grid should ensure the dimensionless height y + ≤1, the grid size gradually increases outwards, but the ratio of adjacent grid heights should not exceed 1.

2.

7. The research method of TMDI controlling low-frequency vertical vortex vibration of rigid main beam of bridge based on CFD numerical simulation according to claim 1 is characterized in that: In step 4, the grid update adopts a smoothing method based on the diffusion equation, and the displacement of the grid point is inversely proportional to the 1.5th power of its closest distance to the rigid main beam surface.

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