A method for rapid evaluation of box girder flutter performance based on potential flow theory
By combining potential flow theory and neural network models, the high cost and high resource consumption problems of aerodynamic calculation and flutter performance evaluation of streamlined box girders are solved, and a fast and accurate flutter performance evaluation method is provided, which is suitable for multi-scheme comparison in the bridge design stage.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2024-11-20
- Publication Date
- 2026-04-07
AI Technical Summary
Existing technologies suffer from high costs and high computational resource consumption in the aerodynamic calculation and flutter performance evaluation of streamlined box girders. How to achieve efficient prediction of the flutter performance of streamlined box girders has become a key issue that urgently needs to be addressed.
Based on potential flow theory, the potential flow solution of unsteady aerodynamic forces for streamlined box girders is derived. By establishing the relationship between the aerodynamic potential flow solution and the viscous flow solution, a correction coefficient is established using a neural network model to correct the aerodynamic forces. Finally, a fast prediction method is proposed, which includes solving the complex potential function, the flow field pressure equation, the unsteady aerodynamic forces, the aerodynamic force correction, and the flutter derivative calculation.
It achieves rapid and accurate assessment of box girder flutter performance, reduces computational costs, saves numerical simulation resources, and the aerodynamic potential flow solution, after correction, matches well with the viscous flow solution, thus improving the assessment accuracy.
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Figure CN119623330B_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of structural wind resistance theory and design technology, specifically a rapid evaluation method for the flutter performance of box girders based on potential flow theory. Background Technology
[0002] Vibration risk of bridge structures under wind load is a key issue in long-span bridge engineering. With the increase in bridge span, especially the widespread application of flexible structures such as streamlined box girders, further research and innovation in wind load calculation methods are particularly important.
[0003] The classic Scanlan aerodynamic model is a linear function of the structural motion state, and the aerodynamic frequency is consistent with the coupled vibration frequency. However, in reality, under a single coupled vibration frequency, the aerodynamic force still has higher-order components, which are beyond the explanatory scope of the traditional model. Currently, nonlinear aerodynamic models that consider higher-order terms have been proposed, but the mechanism of the generation of higher-order terms has not been studied in depth. Potential flow theory, as the basic theory of fluid mechanics, can describe the motion law of fluids and provide tools for understanding and discovering the laws and trends of problems. However, the advancement of potential flow related technologies under streamlined box girders is not yet in-depth.
[0004] For a long time, using flutter derivatives to derive the aerodynamic forces of the main girder has been the most common method, usually obtained through wind tunnel tests or numerical simulations. However, these methods are costly and consume huge computational resources. In recent years, neural network models have been widely used in the field of bridge wind engineering due to their powerful nonlinear capabilities. By training neural network models, the flutter performance of bridges can be predicted quickly and accurately.
[0005] In summary, existing technologies have achieved significant results in the aerodynamic calculation and flutter performance evaluation of streamlined box girders. However, there are still problems in aerodynamic theory and other aspects that need to be further explored. How to efficiently predict the flutter performance of streamlined box girders and achieve rapid comparison of box girder design schemes has become an urgent problem to be solved by those skilled in the art. Summary of the Invention
[0006] (a) Technical problems to be solved
[0007] To address the shortcomings of existing technologies, this invention provides a rapid evaluation method for the flutter performance of box girders based on potential flow theory.
[0008] (II) Technical Solution
[0009] To achieve the above objectives, this invention provides the following technical solution: a rapid evaluation method for the flutter performance of box girders based on potential flow theory. This invention derives the potential flow solution for the unsteady aerodynamic forces of streamlined box girders based on potential flow theory. While the aerodynamic potential flow solution has a clear expression and high computational efficiency, its accuracy still needs improvement due to the neglect of viscous effects. Therefore, this method compares and analyzes the differences between the potential flow solution and the viscous flow solution, establishes a neural network model for calculating the correction coefficients of the potential flow aerodynamic forces, conducts research on the flutter performance prediction of streamlined box girders, and finally proposes a rapid prediction method, including the following steps:
[0010] (1) Solve for the complex potential function of the box girder motion;
[0011] (2) Solve the pressure equation for the flow field;
[0012] (3) Solve the unsteady aerodynamic forces of the box girder based on the potential flow solution, namely aerodynamic drag, aerodynamic lift and aerodynamic torque;
[0013] (4) Compare the aerodynamic potential flow solution and the viscous flow solution to establish the relationship between the potential flow solution and the viscous flow solution;
[0014] (5) Correction of aerodynamic potential flow solution;
[0015] (6) Calculate the flutter derivative and the flutter critical wind speed.
[0016] Preferably, the complex potential function for the box girder motion is solved as follows:
[0017] Box girder as Figure 1 As shown in the motion diagram, since the gas satisfies the non-penetration condition on the surface of the box girder, the normal velocity of the air flowing through point P is equal to the normal velocity of the box girder at point P.
[0018] Let θ be the angle of inclination between the boundary containing point P and the positive x-axis. The normal velocity of point P can then be calculated as: u pn =(u x +ωy p )sinθ-(u y -ωx p cosθ
[0019] The condition of no penetration can be written as:
[0020] Where c represents the box girder boundary, substituting the former equation into the latter and integrating along the box girder boundary, we obtain the stream function as follows:
[0021] In the formula, Const represents a constant.
[0022] Let z = x + iy, u = u x +iu y Define the following functions:
[0023] This formula represents the complex potential function at the boundary of the box girder, i.e.
[0024] To obtain the complex potential function of the box girder during motion, the following transformation is required.
[0025] Let z = f(ζ) be the conformal mapping function from the unit circle in the ζ-plane to the box girder in the z-plane. Let ζ u =e iθ Let B(ζu) be the boundary function of the box girder, located on the unit circle boundary. The relationship between the complex potential function on the circumference and the boundary conditions is established as follows:
[0026] Cauchy's integral formula can establish a connection between the solutions on the boundary and the solutions at the internal and external points. Using Cauchy's integral formula, the complex potential function expression of the outer domain of the box girder can be obtained as: w(ζ)=B1(ζ).
[0027] The conformal mapping function from the unit circle in the ζ-plane to the box girder in the z-plane can be written as:
[0028] Among them, c k =a k +ib k a k b k For the coefficients to be determined, substitute this formula into the complex potential function of the box girder boundary. Extracting the negative exponent terms, we can obtain the complex potential function of the box girder during motion as follows:
[0029] Preferably, the pressure equation for the flow field is solved as follows:
[0030] According to the unsteady Bernoulli equation, the pressure equation in an ideal incompressible flow field can be written as: Where p is pressure, ρ represents air density, and V = (u x u y ) represents the incoming flow velocity vector, and Const(t) is a constant.
[0031] like Figure 2 As shown, the reference frame undergoes both translational and rotational motions along with the box girder. Let this reference frame be x. * O * y * If the angle between p and the absolutely stationary frame is α, then p and V are consistent with the absolutely stationary frame. Let p be an angle of α. * and V * The velocity components are represented by u. * x and u * yLet the incoming flow velocity be V0, then we have:
[0032] The velocities between a stationary frame of reference and a moving frame of reference satisfy the following relationship: V = ▽φ = V0 + u rx e x +u ry e y , where u r =u rx +iu ry For relative velocity, the following condition must be met:
[0033] Substituting all the above equations into the unsteady Bernoulli equation:
[0034] The pressure equation can be obtained as follows:
[0035] Preferably, the unsteady aerodynamic forces of the box girder based on the potential flow solution, namely aerodynamic drag, aerodynamic lift, and aerodynamic torque, are solved as follows:
[0036] To determine the aerodynamic forces acting on the box girder during its motion, it is necessary to integrate the pressure equation obtained in step two of the equation.
[0037] According to complex function theory
[0038] Then the aerodynamic drag F x and aerodynamic lift F y It can be written as:
[0039] Substituting the first equation into the second equation, we get:
[0040]
[0041] Solving for each integral separately, the final expressions for aerodynamic drag and aerodynamic lift are:
[0042] Where A is the area of the box girder, Re represents the real part, Im represents the imaginary part, and F is expressed as:
[0043]
[0044] By integrating the pressure torque on the box girder surface, the aerodynamic torque can be expressed as:
[0045]
[0046] Substituting the pressure equation into this expression and solving the integral, we obtain the expression for the aerodynamic torque as follows:
[0047]
[0048] in:
[0049] dyn = min{n, n-l+k}
[0050] dyx = max{3, l + kn}.
[0051] Preferably, the aerodynamic potential flow solution and the viscous flow solution are compared to establish the relationship between the potential flow solution and the viscous flow solution, as follows:
[0052] The unsteady aerodynamic drag, lift, and torque of a box girder under potential flow are functions of its motion states ux, uy, ω, and shape parameter c. For a box girder with known motion, the above aerodynamic calculation method can quickly and conveniently calculate the aerodynamic forces it experiences. However, the airflow field in reality is viscous, therefore a comparative study of the potential flow solution and the viscous flow solution is needed. The aerodynamic forces of the box girder under viscous flow were calculated using Fluent software, and the differences between the viscous aerodynamic force results for different box girders at different wind attack angles and the potential flow results calculated by the above formulas were analyzed. This method uses the Dadaidong Bridge as the analysis object, and the reliability of the Fluent numerical model has been verified by comparing the numerical solution of flutter performance with wind tunnel test values.
[0053] The external dimensions of the box girder, the computational domain of the numerical model, and the mesh generation are as follows: Figure 3 This method compares the differences between the potential flow solution and the viscous flow solution of unsteady aerodynamic forces for five box girder sections. The five box girder sections are shown below. Figure 4 As shown, different aspect ratios represent different degrees of streamline, with B3 representing the box girder section of the Dadaidong Bridge. Aerodynamic forces are expressed using aerodynamic coefficients.
[0054] Taking section B3 as an example, Figure 5 The aerodynamic time histories of the box girder section at different angles of attack are compared. It can be seen that at any angle of attack, the first-order component of drag contributes more than the second-order component, consistent with the phenomenon observed in the potential flow solution. The potential flow solution for lift agrees well with the viscous flow solution, while the torque shows little difference in amplitude but exhibits a certain phase lag, consistent with the case at 0° angle of attack. Therefore, the aerodynamic potential flow solution and viscous flow solution proposed in this method show significant similarity in the magnitude and frequency of unsteady aerodynamic forces. The accuracy of the results can be improved by correcting the potential flow solution.
[0055] The preferred correction to the aerodynamic potential flow solution is as follows:
[0056] While aerodynamic potential flow solutions are computationally efficient due to their explicit expressions, their accuracy still needs improvement as they neglect viscous effects. This method, based on aerodynamic numerical simulations of 77 box girder sections, calculates correction coefficients for the amplitude and phase of the corresponding potential flow aerodynamic self-excited force. The numerical model settings are consistent with... Figure 3The results are consistent with those shown. By training a neural network model, the relationship between the box girder's shape parameters and correction coefficients is established, and relatively accurate aerodynamic forces are directly calculated based on the box girder's shape parameters and motion state.
[0057] Since there is a one-to-one correspondence between the box girder shape and the correction coefficient, there is a certain correlation between the two, which can be determined through regression analysis. After assuming multiple variables and conducting multiple rounds of linear regression on the correction coefficient, a highly complex nonlinear relationship was found, requiring a more reasonable mathematical model to effectively predict the correction coefficient.
[0058] To avoid overfitting, a fully connected neural network is used to fit the correction coefficients. Input features include... The meanings of each parameter are as follows: Figure 6 As shown, the output features consist of eight correction coefficients: Ccl, Ccm, Cclp, Ccmp, Ccd1, Ccd2, Ccd1p, and Cccd2p. cd, cl, and cm represent the drag, lift, and torque amplitude correction coefficients, respectively; the suffixes 1 and 2 represent the first-order and second-order components, respectively; and the suffix p represents the phase correction coefficient. The neural network model in this method is trained using the Levenberg-Marquardt algorithm, with the tansig activation function. A schematic diagram of a neural network structure is shown below. Figure 7 As shown, 70% of the 77 sets of sample data were used for training, 15% for overfitting validation, and 15% for model testing. That is, there were 53 sets of training data and 12 sets of validation and testing data.
[0059] Taking a box girder not included in the training library of the correction coefficient neural network model as an example, the model is scaled down to 1:50 and has a vibration frequency of 2Hz. The corrected potential flow aerodynamic time history and numerical simulation (CFD) results are compared. The comparison results are shown below. Figure 8 It can be seen that the corrected aerodynamic drag, lift, and torque potential flow solutions agree well with the viscous flow solutions, especially lift and torque, which almost overlap, indicating that the neural network model with the correction coefficients is reliable.
[0060] Preferably, the flutter derivative and the flutter critical wind speed are calculated as follows:
[0061] Since each equation in the multivariate linear equation system of flutter derivative and aerodynamic self-excited force contains three flutter derivatives to be calculated, it is necessary to increase the number of equations by changing the amplitude twice. To simplify the calculation, the amplitudes of the second and third vertical bending and torsional movements can be set to be twice the amplitude of the first movement, resulting in the following formula. The flutter derivative can then be calculated from the aerodynamic self-excited force using the following formula.
[0062] Three-dimensional flutter derivative:
[0063]
[0064]
[0065]
[0066]
[0067]
[0068]
[0069] Two-dimensional flutter derivative:
[0070]
[0071]
[0072]
[0073]
[0074] The slanted stroke ' represents the amplitude and phase of the self-excited force obtained from the second vibration, " represents the amplitude and phase of the self-excited force obtained from the third vibration, D0, L0, and M0 represent drag, lift, and torque, respectively, and λ, β, and γ represent the phases corresponding to drag, lift, and torque, respectively.
[0075] (III) Beneficial Effects
[0076] Compared with existing technologies, this invention provides a rapid evaluation method for the flutter performance of box girders based on potential flow theory, which has the following advantages:
[0077] 1. This rapid evaluation method for box girder flutter performance based on potential flow theory utilizes the powerful nonlinear capabilities of neural network models. After the model is trained, the target result can be quickly calculated based on the input parameters. Subsequently, a neural network model is established based on the corrected potential flow solution data. This eliminates the need for wind tunnel testing equipment and saves computational resources for numerical simulation. Finally, the corrected aerodynamic potential flow solution shows good agreement with the viscous flow solution, demonstrating excellent performance in flutter performance prediction. Attached Figure Description
[0078] Figure 1 This is a schematic diagram of the box girder movement according to the present invention;
[0079] Figure 2 This is a schematic diagram of the absolutely stationary position and the box girder reference system of the present invention;
[0080] Figure 3 This is a schematic diagram of the mesh generation for the numerical network model of the present invention;
[0081] Figure 4These are schematic diagrams of different box girder cross sections of the present invention;
[0082] Figure 5 This is a schematic diagram comparing the aerodynamic time histories of the box girder of the present invention under wind angles of attack of -3°, 0°, and +3°;
[0083] Figure 6 This is a schematic diagram of the box girder parameter settings for the present invention;
[0084] Figure 7 This is a schematic diagram of the neural network structure of the present invention;
[0085] Figure 8 This is a schematic diagram comparing the modified aerodynamic potential flow solution and viscous flow solution of the present invention;
[0086] Figure 9 This is a schematic diagram of the calculation process for the critical wind speed of flutter in the streamlined box girder of the present invention;
[0087] Figure 10 This is a schematic diagram of the flutter critical wind speed prediction results of the present invention. Detailed Implementation
[0088] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.
[0089] Please see Figures 1-10 This invention provides a technical solution: a rapid evaluation method for the flutter performance of box girders based on potential flow theory. This invention derives the potential flow solution for the unsteady aerodynamic forces of streamlined box girders based on potential flow theory. While the aerodynamic potential flow solution has a clear expression and high computational efficiency, its accuracy still needs improvement due to the neglect of viscous effects. Therefore, this method compares and analyzes the differences between the potential flow solution and the viscous flow solution, establishes a neural network model for calculating the correction coefficients of the potential flow aerodynamic forces, conducts research on the flutter performance prediction of streamlined box girders, and finally proposes a rapid prediction method, including the following steps:
[0090] (1) Solve for the complex potential function of the box girder motion;
[0091] (2) Solve the pressure equation for the flow field;
[0092] (3) Solve the unsteady aerodynamic forces of the box girder based on the potential flow solution, namely aerodynamic drag, aerodynamic lift and aerodynamic torque;
[0093] (4) Compare the aerodynamic potential flow solution and the viscous flow solution to establish the relationship between the potential flow solution and the viscous flow solution;
[0094] (5) Correction of aerodynamic potential flow solution;
[0095] (6) Calculate the flutter derivative and the flutter critical wind speed.
[0096] In this invention, in order to solve for the complex potential function of the box girder motion, therefore:
[0097] Box girder as Figure 1 As shown in the motion diagram, since the gas satisfies the non-penetration condition on the surface of the box girder, the normal velocity of the air flowing through point P is equal to the normal velocity of the box girder at point P.
[0098] Let θ be the angle of inclination between the boundary containing point P and the positive x-axis. The normal velocity of point P can then be calculated as: u pn =(u x +ωy p )sinθ-(u y -ωx p cosθ
[0099] The condition of no penetration can be written as:
[0100] Where c represents the box girder boundary, substituting the former equation into the latter and integrating along the box girder boundary, we obtain the stream function as follows:
[0101] In the formula, Const represents a constant.
[0102] Let z = x + iy, u = u x +iu y Define the following functions:
[0103] This formula represents the complex potential function at the boundary of the box girder, i.e.
[0104] To obtain the complex potential function of the box girder during motion, the following transformation is required.
[0105] Let z = f(ζ) be the conformal mapping function from the unit circle in the ζ-plane to the box girder in the z-plane. Let ζ u =e iθ Let B(ζu) be the boundary function of the box girder, located on the unit circle boundary. The relationship between the complex potential function on the circumference and the boundary conditions is established as follows:
[0106] Cauchy's integral formula can establish a connection between the solutions on the boundary and the solutions at the internal and external points. Using Cauchy's integral formula, the complex potential function expression of the outer domain of the box girder can be obtained as: w(ζ)=B1(ζ).
[0107] The conformal mapping function from the unit circle in the ζ-plane to the box girder in the z-plane can be written as:
[0108] Among them, c k =a k +ib k a k b k For the coefficients to be determined, substitute this formula into the complex potential function of the box girder boundary. Extracting the negative exponent terms, we can obtain the complex potential function of the box girder during motion as follows:
[0109] In this invention, in order to solve the pressure equation of the flow field, therefore:
[0110] According to the unsteady Bernoulli equation, the pressure equation in an ideal incompressible flow field can be written as: Where p is pressure, ρ represents air density, and V = (u x u y ) represents the incoming flow velocity vector, and Const(t) is a constant.
[0111] like Figure 2 As shown, the reference frame undergoes both translational and rotational motions along with the box girder. Let this reference frame be x. * O * y * If the angle between p and the absolutely stationary frame is α, then p and V are consistent with the absolutely stationary frame. Let p be an angle of α. * and V * The velocity components are represented by u. * x and u * y Let the incoming flow velocity be V0, then we have:
[0112] The velocities between a stationary frame of reference and a moving frame of reference satisfy the following relationship: V = ▽φ = V0 + u rx e x +u ry e y , where u r =u rx +iu ry For relative velocity, the following condition must be met:
[0113] Substituting all the above equations into the unsteady Bernoulli equation:
[0114] The pressure equation can be obtained as follows:
[0115] In this invention, in order to solve the unsteady aerodynamic forces of the box girder based on the potential flow solution, namely aerodynamic drag, aerodynamic lift, and aerodynamic torque, therefore:
[0116] To determine the aerodynamic forces acting on the box girder during its motion, it is necessary to integrate the pressure equation obtained in step two of the equation.
[0117] According to complex function theory
[0118] Then the aerodynamic drag F x and aerodynamic lift F y It can be written as:
[0119] Substituting the first equation into the second equation, we get:
[0120]
[0121] Solving for each integral separately, the final expressions for aerodynamic drag and aerodynamic lift are:
[0122] Where A is the area of the box girder, Re represents the real part, Im represents the imaginary part, and F is expressed as:
[0123]
[0124] By integrating the pressure torque on the box girder surface, the aerodynamic torque can be expressed as:
[0125]
[0126] Substituting the pressure equation into this expression and solving the integral, we obtain the expression for the aerodynamic torque as follows:
[0127]
[0128] dyn = min{n, n-l+k}
[0129] dyx = max{3, l + kn}.
[0130] In this invention, in order to compare the aerodynamic potential flow solution and the viscous flow solution and establish the relationship between the potential flow solution and the viscous flow solution, therefore:
[0131] The unsteady aerodynamic drag, lift, and torque of a box girder under potential flow are functions of its motion states ux, uy, ω, and shape parameter c. For a box girder with known motion, the above aerodynamic calculation method can quickly and conveniently calculate the aerodynamic forces it experiences. However, the airflow field in reality is viscous, therefore a comparative study of the potential flow solution and the viscous flow solution is needed. The aerodynamic forces of the box girder under viscous flow were calculated using Fluent software, and the differences between the viscous aerodynamic force results for different box girders at different wind attack angles and the potential flow results calculated by the above formulas were analyzed. This method uses the Dadaidong Bridge as the analysis object, and the reliability of the Fluent numerical model has been verified by comparing the numerical solution of flutter performance with wind tunnel test values.
[0132] The external dimensions of the box girder, the computational domain of the numerical model, and the mesh generation are as follows: Figure 3 This method compares the differences between the potential flow solution and the viscous flow solution of unsteady aerodynamic forces for five box girder sections. The five box girder sections are shown below. Figure 4 As shown, different aspect ratios represent different degrees of streamline, with B3 representing the box girder section of the Dadaidong Bridge. Aerodynamic forces are expressed using aerodynamic coefficients.
[0133] Taking section B3 as an example, Figure 5 The aerodynamic time histories of the box girder section at different angles of attack are compared. It can be seen that at any angle of attack, the first-order component of drag contributes more than the second-order component, consistent with the phenomenon observed in the potential flow solution. The potential flow solution for lift agrees well with the viscous flow solution, while the torque shows little difference in amplitude but exhibits a certain phase lag, consistent with the case at 0° angle of attack. Therefore, the aerodynamic potential flow solution and viscous flow solution proposed in this method show significant similarity in the magnitude and frequency of unsteady aerodynamic forces. The accuracy of the results can be improved by correcting the potential flow solution.
[0134] In this invention, in order to correct the aerodynamic potential flow solution, therefore:
[0135] While aerodynamic potential flow solutions are computationally efficient due to their explicit expressions, their accuracy still needs improvement as they neglect viscous effects. This method, based on aerodynamic numerical simulations of 77 box girder sections, calculates correction coefficients for the amplitude and phase of the corresponding potential flow aerodynamic self-excited force. The numerical model settings are consistent with... Figure 3 The results are consistent with those shown. By training a neural network model, the relationship between the box girder's shape parameters and correction coefficients is established, and relatively accurate aerodynamic forces are directly calculated based on the box girder's shape parameters and motion state.
[0136] Since there is a one-to-one correspondence between the box girder shape and the correction coefficient, there is a certain correlation between the two, which can be determined through regression analysis. After assuming multiple variables and conducting multiple rounds of linear regression on the correction coefficient, a highly complex nonlinear relationship was found, requiring a more reasonable mathematical model to effectively predict the correction coefficient.
[0137] To avoid overfitting, a fully connected neural network is used to fit the correction coefficients. Input features include... The meanings of each parameter are as follows: Figure 6As shown, the output features consist of eight correction coefficients: Ccl, Ccm, Cclp, Ccmp, Ccd1, Ccd2, Ccd1p, and Cccd2p. cd, cl, and cm represent the drag, lift, and torque amplitude correction coefficients, respectively; the suffixes 1 and 2 represent the first-order and second-order components, respectively; and the suffix p represents the phase correction coefficient. The neural network model in this method is trained using the Levenberg-Marquardt algorithm, with the tansig activation function. A schematic diagram of a neural network structure is shown below. Figure 7 As shown, 70% of the 77 sets of sample data were used for training, 15% for overfitting validation, and 15% for model testing. That is, there were 53 sets of training data and 12 sets of validation and testing data.
[0138] Taking a box girder not included in the training library of the correction coefficient neural network model as an example, the model is scaled down to 1:50 and has a vibration frequency of 2Hz. The corrected potential flow aerodynamic time history and numerical simulation (CFD) results are compared. The comparison results are shown below. Figure 8 It can be seen that the corrected aerodynamic drag, lift, and torque potential flow solutions agree well with the viscous flow solutions, especially lift and torque, which almost overlap, indicating that the neural network model with the correction coefficients is reliable.
[0139] In this invention, in order to calculate the flutter derivative and the flutter critical wind speed, therefore:
[0140] Since each equation in the multivariate linear equation system of flutter derivative and aerodynamic self-excited force contains three flutter derivatives to be calculated, it is necessary to increase the number of equations by changing the amplitude twice. To simplify the calculation, the amplitudes of the second and third vertical bending and torsional movements can be set to be twice the amplitude of the first movement, resulting in the following formula. The flutter derivative can then be calculated from the aerodynamic self-excited force using the following formula.
[0141] Three-dimensional flutter derivative:
[0142]
[0143]
[0144]
[0145]
[0146]
[0147]
[0148] Two-dimensional flutter derivative:
[0149]
[0150]
[0151]
[0152]
[0153] The slanted stroke ' represents the amplitude and phase of the self-excited force obtained from the second vibration, " represents the amplitude and phase of the self-excited force obtained from the third vibration, D0, L0, and M0 represent drag, lift, and torque, respectively, and λ, β, and γ represent the phases corresponding to drag, lift, and torque, respectively.
[0154] The method of this invention utilizes modified aerodynamics to calculate the flutter derivative of box girders and conducts flutter critical wind speed analysis for box girders with different cross-sections. The specific method flow is as follows: Figure 9 As shown, we obtain Figure 10 The results shown indicate that the relative magnitudes of flutter performance at different cross sections are consistent with the wind tunnel test results.
[0155] The method of this invention can rapidly predict the flutter performance of box girders based solely on their shape and dynamic characteristic parameters. From aerodynamic calculations and flutter derivative identification to flutter performance evaluation, the entire process takes less than 0.5 seconds on a typical personal computer. Given its computational efficiency, this method can be applied to the rapid evaluation of the flutter performance of streamlined box girders, for example, in the preliminary design stage of bridges, providing valuable reference for the rapid comparison of multiple design schemes. Compared with existing technologies, it has the following advantages:
[0156] 1. High speed: Utilizing the powerful non-linear capabilities of neural network models, once the model is trained, the target result can be calculated quickly based on the input parameters.
[0157] 2. Low cost: The neural network model is built based on the corrected potential flow solution data, without the use of wind tunnel testing equipment, and can save computational resources for numerical simulation.
[0158] 3. High accuracy: The corrected aerodynamic potential flow solution matches well with the viscous flow solution, and it performs well in flutter performance prediction.
[0159] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.
Claims
1. A rapid evaluation method for the flutter performance of box girders based on potential flow theory, characterized in that, Includes the following steps: (1) Solve for the complex potential function of the box girder motion; (2) Solve the pressure equation for the flow field; (3) Solve the unsteady aerodynamic forces of the box girder based on the potential flow solution, namely aerodynamic drag, aerodynamic lift and aerodynamic torque; (4) Compare the aerodynamic potential flow solution and the viscous flow solution to establish the relationship between the potential flow solution and the viscous flow solution; (5) Correction of aerodynamic potential flow solution; Based on the aerodynamic numerical simulation results of 77 box girder sections, correction coefficients for the amplitude and phase of the corresponding potential flow aerodynamic self-excited force were obtained. By training a neural network model, the relationship between the box girder shape parameters and the correction coefficients was established. Based on the box girder shape parameters and motion state, relatively accurate aerodynamic forces were directly calculated. Since there is a one-to-one correspondence between the box girder shape and the correction coefficient, there is a certain correlation between the two. This relationship can be determined through regression analysis. After assuming multiple variables and conducting multiple rounds of linear regression on the correction coefficient, a highly complex nonlinear relationship was found between the two. A mathematical model is needed to effectively predict the correction coefficient. To avoid overfitting, a fully connected neural network is used to fit the correction coefficients. The input features include... , Indicates the width of the box girder; Indicates the height of the box girder; Indicates the width of the upper bridge deck; Indicates the width of the lower bridge deck; This represents the distance between the nozzle and the lower bridge surface; the output features are eight correction coefficients: Ccl, Ccm, Cclp, Ccmp, Ccd1, Ccd2, Ccd1p, and Ccd2p; cd, cl, and cm represent the drag, lift, and torque amplitude correction coefficients, respectively. The neural network model is trained using the Levenberg-Marquardt algorithm, with the tansig function as the activation function. Of the 77 sets of sample data, 70% were used for training, 15% for overfitting validation, and 15% for model testing. That is, there were 53 sets of training data and 12 sets each for validation and testing. (6) Calculate the flutter derivative and the flutter critical wind speed.
2. The rapid evaluation method for box girder flutter performance based on potential flow theory according to claim 1, characterized in that: The complex potential function for the box girder motion is solved as follows: As the box girder moves, since the gas on the box girder surface satisfies the condition of no penetration, the normal velocity of the air flowing through point P is equal to the normal velocity of the box girder at point P. Let θ be the angle of inclination between the boundary containing point P and the positive x-axis. The normal velocity of point P can then be calculated as: Official (1), in, Indicates the horizontal movement speed of the box girder; Indicates the vertical movement speed of the box girder; Represents the x-coordinate of point P; This represents the ordinate of point P; express Direction clockwise to Angle of direction; The condition of no penetration can be written as: Formula (2), Where c represents the boundary of the box girder. Substituting formula (1) into formula (2) and integrating along the box girder boundary, the stream function is obtained as follows: In the formula, Const represents a constant. Let z = x + iy, u = u x +iu y Define the following functions: This is the complex potential function on the boundary of the box girder, i.e. , To obtain the complex potential function of the box girder during motion, the following transformation is required. Let z = f(ζ) be the conformal mapping function from the unit circle in the ζ-plane to the box girder in the z-plane. Let ζ u =e iθ For a point on the boundary of the unit circle, the boundary function of the box girder is written as B(ζ). u Establish the relationship between the complex potential function and the boundary conditions on the circumference as follows: , Cauchy's integral formula can establish a relationship between the solutions on the boundary and the solutions at the interior and exterior points. Using Cauchy's integral formula, the complex potential function expression of the outer domain of the box girder can be obtained as follows: , The conformal mapping function from the unit circle in the ζ-plane to the box girder in the z-plane can be written as: Formula (3), where ck = ak + ibk, ak and bk are undetermined coefficients. Substituting formula (3) into the complex potential function of the box girder boundary By extracting the negative exponent terms, the complex potential function of the box girder during motion can be obtained as follows: .
3. The rapid evaluation method for the flutter performance of box girders based on potential flow theory according to claim 1, characterized in that: The pressure equations for the flow field are solved as follows: According to the unsteady Bernoulli equation, the pressure equation in an ideal incompressible flow field can be written as: , in, For pressure, ρ V represents air density, V=(u x ,u y Let t be the incoming flow velocity vector, and Const(t) be a constant. The reference frame undergoes both translational and rotational motions along with the box girder; let this reference frame be x. * O * y * If the angle between the system and the absolutely stationary system is α, then And V is consistent with the absolutely stationary frame, respectively, using p * and V * The velocity components are represented by u. * x and u * y Let the incoming flow velocity be V0, then we have: Formula (4), Official (5), The velocities between a perfectly stationary frame of reference and a moving frame of reference satisfy the following relationship: , where u r =u rx +iu ry For relative velocity, the following condition must be met: Formula (6), Substituting the above formulas (4), (5), and (6) into the unsteady Bernoulli equation: , The pressure equation can be obtained as follows: Formula (7).
4. The rapid evaluation method for the flutter performance of box girders based on potential flow theory according to claim 3, characterized in that: The unsteady aerodynamic forces of the box girder based on the potential flow solution, namely aerodynamic drag, aerodynamic lift, and aerodynamic torque, are solved as follows: To determine the aerodynamic forces acting on the box girder during its motion, it is necessary to integrate the pressure equation obtained in step (2). According to complex function theory , Then the aerodynamic drag F x and aerodynamic lift F y It can be written as: Formula (8), Substituting formula (7) into formula (8), we get: Solving for each integral separately, the final expressions for aerodynamic drag and aerodynamic lift are: , , Where A is the area of the box girder, Re represents the real part, Im represents the imaginary part, and F is expressed as: By integrating the pressure torque on the box girder surface, the aerodynamic torque can be expressed as: Official (9), Substituting the pressure equation into formula (9) and solving the integral, we obtain the expression for the aerodynamic torque as follows: in: 。 5. The rapid evaluation method for the flutter performance of a box girder based on potential flow theory according to claim 4, characterized in that: By comparing the aerodynamic potential flow solution and the viscous flow solution, the relationship between the potential flow solution and the viscous flow solution is established as follows: The unsteady aerodynamic drag, lift, and torque of the box girder under potential flow are its motion state. u x , u y The aerodynamic forces acting on a box girder are functions of ω and the shape parameter c. For a box girder with known motion, the above aerodynamic calculation method can quickly and conveniently calculate the aerodynamic forces acting on it. However, the airflow field in reality is viscous. Therefore, it is necessary to conduct a comparative study of the aerodynamic potential flow solution and the viscous flow solution. The aerodynamic forces of the box girder under viscous flow are calculated using Fluent calculation software. The differences between the viscous aerodynamic force results of different box girders under different wind attack angles and the potential flow results calculated by the above aerodynamic calculation method are analyzed.
6. The rapid evaluation method for the flutter performance of box girders based on potential flow theory according to claim 1, characterized in that: The flutter derivative and flutter critical wind speed are calculated as follows: Since each equation in the multivariate linear equations relating flutter derivatives and aerodynamic self-excited forces contains three flutter derivatives to be determined, it is necessary to increase the number of equations by changing the amplitude twice. To simplify the calculation, the amplitudes of the second and third vertical bending and torsional movements can be set to be twice the amplitude of the first movement, resulting in the following formula. The flutter derivative can then be calculated from the aerodynamic self-excited force using this formula. Three-dimensional flutter derivative: Two-dimensional flutter derivative: Among them, the upward slant is left-falling. This indicates the amplitude and phase of the self-excited force obtained during the second vibration. The amplitude and phase of the self-excited force obtained in the third vibration are represented by D0, L0, and M0, which represent drag, lift, and torque, respectively. λ, β, and γ are the phases corresponding to drag, lift, and torque, respectively.