Box girder flutter performance rapid evaluation method based on potential flow theory

Abstract

The invention relates to the technical field of structure wind resistance theories and design, and discloses a box girder flutter performance rapid evaluation method based on a potential flow theory, the potential flow solution of streamline box girder unsteady aerodynamic force is deduced based on the potential flow theory, the aerodynamic force potential flow solution has a clear expression, the calculation efficiency is high, and the box girder flutter performance rapid evaluation method can be applied to the field of box girder flutter performance rapid evaluation. However, the viscosity effect is neglected, and the precision still needs to be improved, so that the method compares and analyzes the difference between the potential flow solution and the viscosity flow solution. According to the box girder flutter performance rapid evaluation method based on the potential flow theory, the powerful nonlinear capability of a neural network model is utilized, after the model is trained, a target result can be rapidly calculated according to input parameters, then the neural network model is established based on corrected potential flow solution data, wind tunnel test equipment is not used, and the flutter performance of the box girder can be rapidly evaluated. And finally, the aerodynamic potential flow solution is well matched with the viscous flow solution after being corrected, and the flutter performance prediction effect is good when the method is applied to flutter performance prediction.

Description

Technical Field

[0001] The invention relates to the technical field of structural wind resistance theory and design, and in particular to a method for quickly evaluating the flutter performance of a box girder based on potential flow theory. Background Art

[0002] The vibration risk of bridge structures under wind loads is a key issue in long-span bridge engineering. With the increase in bridge spans, especially the widespread application of flexible structures such as streamlined box girders, further research and innovation on wind load calculation methods are particularly important.

[0003] The classic Scanlan aerodynamic model is a linear function of the structural motion state. The aerodynamic frequency is consistent with the coupled vibration frequency. But in fact, at a single coupled vibration frequency, the aerodynamic force still has high-order components, which is beyond the explanation of the traditional model. At present, a nonlinear aerodynamic model considering high-order terms has been proposed, but the mechanism of the generation of high-order terms has not been deeply studied. Potential flow theory, as the basic theory of fluid mechanics, can describe the motion laws of fluids and provide tools for understanding and discovering problem laws and trends. However, the advancement of potential flow related technologies under streamlined box girders is not yet in-depth.

[0004] For a long time, the most commonly used method to derive the aerodynamic force of the main beam is to use flutter derivatives, which are usually obtained through wind tunnel tests or numerical simulations. However, these methods are costly and consume huge computing 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 quickly and accurately predicted.

[0005] In summary, the existing technology has achieved remarkable 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 promoted. How to efficiently predict the flutter performance of streamlined box girders and realize rapid comparison and selection of box girder design schemes has become a problem that technical personnel in this field need to solve urgently. Summary of the invention

[0006] 1. Technical issues to be solved

[0007] In view of the deficiencies in the prior art, the present invention provides a method for quickly evaluating the flutter performance of a box girder based on potential flow theory.

[0008] (II) Technical solution

[0009] To achieve the above purpose, the present invention provides the following technical solutions: a method for rapid evaluation of box girder flutter performance based on potential flow theory. The present invention derives the potential flow solution of the unsteady aerodynamic force of a streamlined box girder based on the potential flow theory. The aerodynamic potential flow solution has a clear expression and high calculation efficiency. However, since the viscosity effect is ignored, the accuracy still needs to be improved. Therefore, the method compares and analyzes the difference between the potential flow solution and the viscous flow solution, establishes a neural network model for calculating the potential flow aerodynamic correction coefficient, conducts research on the prediction of the flutter performance of a streamlined box girder, and finally proposes a rapid prediction method, which includes the following steps:

[0010] (1) Solve the complex potential function of the box girder motion;

[0011] (2) Solve the pressure equation of 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 with the viscous flow solution and 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 of the box girder motion is solved as follows:

[0017] Box beam made as Figure 1 In the motion shown, since the gas satisfies the no-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 point P of the box girder.

[0018] Assuming the inclination angle between the boundary where point P is located and the positive direction of the x-axis is θ, the normal velocity of point P can be obtained as: u pn =(u x +ωy p )sinθ-(u y -ωx p )cosθ

[0019] The no-penetration condition can be written as:

[0020] Where c is the box girder boundary. Substituting the above formula into the latter one and integrating along the box girder boundary, the stream function is:

[0021] In the formula, Const represents a constant.

[0022] Let z = x + iy, u = u x +iu y , define the following function:

[0023] This formula is the complex potential function on the box beam boundary, that is,

[0024] In order to obtain the complex potential function of the box girder during motion, the following transformation is required.

[0025] Assume that the conformal mapping function from the unit circle in the ζ plane to the box beam in the z plane is z = f(ζ), let ζ u =e iθ is a point on the boundary of the unit circle, the boundary function of the box beam is written as B(ζu), and the relationship between the complex potential function on the circumference and the boundary condition is established as

[0026] The Cauchy integral formula can establish a connection between the solution on the boundary and the solution of the internal and external points. Using the Cauchy integral formula, the complex potential function expression of the outer domain of the box girder can be obtained as: w(ζ)=B 1 (ζ)

[0027] The conformal mapping function from the unit circle in the ζ plane to the box beam in the z plane can be written as:

[0028] Among them, c k =a k +ib k , a k , b k is the unknown coefficient, and the formula is substituted into the complex potential function of the box beam boundary By extracting the negative exponential term, we can get the complex potential function of the box beam during motion:

[0029] Preferably, the pressure equation of 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 is air density, V = (u x ,u y ) is the incoming flow velocity vector, and Const(t) is a constant.

[0031] like Figure 2 As shown in the figure, the reference system moves in translation and rotation with the box beam at the same time. Let the reference system be x * O * y * , the angle between p and V is α, then p and V are consistent with the absolute rest system, respectively. * and V * The velocity components are represented by u * x and u * yIndicates that, assuming the incoming flow velocity is V 0 , then:

[0032] The velocity between the absolute stationary system and the moving reference system satisfies the following relationship: V = ▽φ = V 0 +u rx e x +u ry e y , where u r =u rx +iu ry is the relative speed, satisfying:

[0033] Substituting all the above equations into the unsteady Bernoulli equation:

[0034] The pressure equation is:

[0035] Preferably, the unsteady aerodynamic force of the box girder based on the potential flow solution, namely, aerodynamic drag, aerodynamic lift and aerodynamic torque, is solved as follows:

[0036] In order to calculate the aerodynamic force acting on the box girder during its movement, it is necessary to integrate the pressure equation obtained in step 2.

[0037] According to the theory of complex variable functions

[0038] The aerodynamic drag F x and aerodynamic lift F y It can be written as:

[0039] Substituting the former into the latter, we can get:

[0040]

[0041] Solve each integral separately, and the final aerodynamic drag and aerodynamic lift expressions are:

[0042] Among them, A is the area of ​​the box beam, Re represents the real part, Im represents the imaginary part, and the expression of F is:

[0043]

[0044] By integrating the pressure moment on the box beam surface, the aerodynamic torque can be expressed as:

[0045]

[0046] Substituting the pressure equation into this formula and solving the integral, the expression of the aerodynamic torque can be obtained 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 is compared with the viscous flow solution, and the relationship between the potential flow solution and the viscous flow solution is established as follows:

[0052] The unsteady aerodynamic drag, lift and torque of a box girder under potential flow are functions of its motion state ux, uy, ω and shape parameter c. For a box girder with known motion, the aerodynamic force it is subjected to can be quickly and conveniently calculated using the above aerodynamic force calculation method. However, the airflow field in reality is viscous, so it is necessary to conduct a comparative study of the aerodynamic potential flow solution and the viscous flow solution. The aerodynamic force of the box girder under viscous flow is calculated using the Fluent calculation software, and the differences between the viscous aerodynamic results of different box girders at different wind attack angles and the potential flow results calculated using the above calculation formula are analyzed. This method uses the Dadaidong Bridge as the analysis object, and has verified the reliability of the Fluent numerical model by comparing the numerical solution of flutter performance with the wind tunnel test value.

[0053] Box girder dimensions, computational domain of numerical model and mesh division are as follows: Figure 3 This method compares the difference between the potential flow solution and the viscous flow solution of the unsteady aerodynamics of five box girder sections. Figure 4 As shown in the figure, different aspect ratios represent different streamline levels, where B3 is the box girder section of the Dadaidong Bridge. The aerodynamic force is expressed in the form of aerodynamic coefficients.

[0054] Taking the B3 section as an example, Figure 5 The aerodynamic time history comparison of the box girder section at different angles of attack is shown. It can be seen that at any angle of attack, the first-order component of the drag force contributes more than the second-order component, which is consistent with the phenomenon of the potential flow solution. The potential flow solution of lift is in good agreement with the viscous flow solution, while the torque has a small difference in amplitude, but there is a certain phase lag, which is consistent with the case of 0° angle of attack. Therefore, the aerodynamic potential flow solution and the viscous solution proposed by this method show significant similarities in the magnitude and frequency of the unsteady aerodynamic force, and the potential flow solution can be corrected to improve the accuracy of the results.

[0055] Preferably, the aerodynamic potential flow solution is modified as follows:

[0056] The aerodynamic potential flow solution has a clear expression and high computational efficiency, but the viscosity effect is ignored and the accuracy still needs to be improved. This method is based on the aerodynamic numerical simulation results of 77 box girder sections to obtain the corresponding potential flow aerodynamic self-excitation force amplitude and phase correction coefficients. The numerical model is set to Figure 3 By training the neural network model, the relationship between the box girder shape parameters and the correction coefficient is established, and a more accurate aerodynamic force is directly calculated based on the box girder shape parameters and motion state.

[0057] Since the box girder shape and the correction coefficient are one-to-one corresponding, there is a certain correlation between the two, which can be determined by regression analysis. Assuming multiple variables in advance, after multiple rounds of linear regression on the correction coefficient, it is found that there is a very complex nonlinear relationship between the two, and a more reasonable mathematical model is needed to effectively predict the correction coefficient.

[0058] In order to avoid overfitting, a fully connected neural network is used to fit the correction coefficient. The input features include The meaning of each parameter is as follows Figure 6 As shown, the output features are 8 correction coefficients Ccl, Ccm, Cclp, Ccmp, Ccd1, Ccd2, Ccd1p, Cccd2p. cd, cl, cm represent the drag, lift and torque amplitude correction coefficients respectively, the suffixes 1 and 2 represent the first-order component and the second-order component respectively, and the suffix p represents the phase correction coefficient. The neural network model of this method uses the Levenberg-Marquardt algorithm to train the neural network, and the activation function is the tansig function. The neural network structure is shown as follows Figure 7 As shown, 70% of the 77 sets of sample data are used for training, 15% are used for overfitting verification, and 15% are used for model testing, that is, 53 sets of training data and 12 sets of verification and testing data.

[0059] Taking a box girder that is not in the training library of the correction coefficient neural network model as an example, the model is scaled at a ratio of 1:50 and the vibration frequency is 2Hz. The corrected potential flow aerodynamic time history is compared with the numerical simulation (CFD) results. The comparison results are shown in Figure 8 It can be seen that the corrected aerodynamic drag, lift and torque potential flow solutions are in good agreement with the viscous flow solutions, especially lift and torque, which are almost identical, indicating that the neural network model of the correction coefficient 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 group of flutter derivatives and aerodynamic self-excitation 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 second and third vertical bending and torsional amplitudes can be set to twice the first amplitude, that is, the following formula is obtained. The flutter derivative is calculated from the aerodynamic self-excitation force through the following formula.

[0062] 3D flutter derivatives:

[0063]

[0064]

[0065]

[0066]

[0067]

[0068]

[0069] Two-dimensional flutter derivatives:

[0070]

[0071]

[0072]

[0073]

[0074] The upper slash ' represents the amplitude and phase of the self-excited force obtained by the second vibration, and " represents the amplitude and phase of the self-excited force obtained by the third vibration, D 0 , L 0 、M 0 They represent drag, lift and torque respectively, and λ, β and γ are the phases corresponding to drag, lift and torque respectively.

[0075] (III) Beneficial effects

[0076] Compared with the prior art, the present invention provides a method for rapid evaluation of box girder flutter performance based on potential flow theory, which has the following beneficial effects:

[0077] 1. This rapid evaluation method for box girder flutter performance based on potential flow theory utilizes the powerful nonlinear ability of the neural network model. After the model is trained, the target result can be quickly calculated according to the input parameters. Subsequently, the neural network model is established based on the corrected potential flow solution data. Wind tunnel test equipment is not used, and computing resources for numerical simulation can be saved. Finally, the aerodynamic potential flow solution is well matched with the viscous flow solution after correction, and the effect of applying it to flutter performance prediction is good. BRIEF DESCRIPTION OF THE DRAWINGS

[0078] Figure 1 It is a schematic diagram of the box girder movement of the present invention;

[0079] Figure 2 It is a schematic diagram of the absolute static and box beam reference system of the present invention;

[0080] Figure 3 It is a schematic diagram of mesh division of the numerical network model of the present invention;

[0081] Figure 4 Schematic diagram of different box beam cross sections of the present invention;

[0082] Figure 5 It is a schematic diagram of the comparison of aerodynamic time history of the box girder of the present invention at wind attack angles of -3°, 0°, and +3°;

[0083] Figure 6 This is a schematic diagram of the box girder parameter settings of the present invention;

[0084] Figure 7 This is a schematic diagram of the neural network structure of the present invention;

[0085] Figure 8 It is a schematic diagram comparing the modified aerodynamic potential flow solution and the viscous flow solution of the present invention;

[0086] Fig. 9 It is a schematic diagram of the flow chart of the calculation of the critical wind speed of flutter of the streamlined box girder of the present invention;

[0087] Fig.10 It is a schematic diagram of the prediction result of the flutter critical wind speed of the present invention. DETAILED DESCRIPTION

[0088] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0089] See also Figure 1-10The present invention provides a technical solution: a rapid evaluation method for the flutter performance of a box girder based on potential flow theory. The present invention derives the potential flow solution of the unsteady aerodynamic force of a streamlined box girder based on the potential flow theory. The aerodynamic potential flow solution has a clear expression and high calculation efficiency. However, since the viscosity effect is ignored, the accuracy still needs to be improved. Therefore, the present method compares and analyzes the difference between the potential flow solution and the viscous flow solution, establishes a neural network model for calculating the potential flow aerodynamic correction coefficient, and conducts a study on the prediction of the flutter performance of a streamlined box girder. Finally, a rapid prediction method is proposed, which includes the following steps:

[0090] (1) Solve the complex potential function of the box girder motion;

[0091] (2) Solve the pressure equation of 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 with the viscous flow solution and 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 the present invention, in order to solve the complex potential function of the box girder motion, therefore:

[0097] Box beam made as Figure 1 In the motion shown, since the gas satisfies the no-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 point P of the box girder.

[0098] Assuming the inclination angle between the boundary where point P is located and the positive direction of the x-axis is θ, the normal velocity of point P can be obtained as: u pn =(u x +ωy p )sinθ-(u y -ωx p )cosθ

[0099] The no-penetration condition can be written as:

[0100] Where c is the box girder boundary. Substituting the above formula into the latter one and integrating along the box girder boundary, the stream function is:

[0101] In the formula, Const represents a constant.

[0102] Let z = x + iy, u = u x +iu y , define the following function:

[0103] This formula is the complex potential function on the box beam boundary, that is,

[0104] In order to obtain the complex potential function of the box girder during motion, the following transformation is required.

[0105] Assume that the conformal mapping function from the unit circle in the ζ plane to the box beam in the z plane is z = f(ζ), let ζ u =e iθ is a point on the boundary of the unit circle, the boundary function of the box beam is written as B(ζu), and the relationship between the complex potential function on the circumference and the boundary condition is established as

[0106] The Cauchy integral formula can establish a connection between the solution on the boundary and the solution of the internal and external points. Using the Cauchy integral formula, the complex potential function expression of the outer domain of the box girder can be obtained as: w(ζ)=B 1 (ζ)

[0107] The conformal mapping function from the unit circle in the ζ plane to the box beam in the z plane can be written as:

[0108] Among them, c k =a k +ib k , a k , b k is the unknown coefficient, and the formula is substituted into the complex potential function of the box beam boundary By extracting the negative exponential term, we can get the complex potential function of the box beam during motion:

[0109] In the present 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 is air density, V = (u x ,u y ) is the incoming flow velocity vector, and Const(t) is a constant.

[0111] like Figure 2 As shown in the figure, the reference system moves in translation and rotation with the box beam at the same time. Let the reference system be x * O * y * , the angle between p and V is α, then p and V are consistent with the absolute rest system, respectively. * and V * The velocity components are represented by u * x and u * yIndicates that, assuming the incoming flow velocity is V 0 , then:

[0112] The velocity between the absolute stationary system and the moving reference system satisfies the following relationship: V = ▽φ = V 0 +u rx e x +u ry e y , where u r =u rx +iu ry is the relative speed, satisfying:

[0113] Substituting all the above equations into the unsteady Bernoulli equation:

[0114] The pressure equation is:

[0115] In the present invention, in order to solve the unsteady aerodynamic force of the box girder based on the potential flow solution, namely, aerodynamic drag, aerodynamic lift and aerodynamic torque, therefore:

[0116] In order to calculate the aerodynamic force acting on the box girder during its movement, it is necessary to integrate the pressure equation obtained in step 2.

[0117] According to the theory of complex variable functions

[0118] The aerodynamic drag F x and aerodynamic lift F y It can be written as:

[0119] Substituting the former into the latter, we can get:

[0120]

[0121] Solve each integral separately, and the final aerodynamic drag and aerodynamic lift expressions are:

[0122] Among them, A is the area of ​​the box beam, Re represents the real part, Im represents the imaginary part, and the expression of F is:

[0123]

[0124] By integrating the pressure moment on the box beam surface, the aerodynamic torque can be expressed as:

[0125]

[0126] Substituting the pressure equation into this formula and solving the integral, the expression of the aerodynamic torque can be obtained as follows:

[0127]

[0128] dyn=min{n,n-l+k}

[0129] dyx=max{3,l+kn}.

[0130] In the present invention, in order to compare the aerodynamic potential flow solution with the viscous flow solution, the relationship between the potential flow solution and the viscous flow solution is established, therefore:

[0131] The unsteady aerodynamic drag, lift and torque of a box girder under potential flow are functions of its motion state ux, uy, ω and shape parameter c. For a box girder with known motion, the aerodynamic force it is subjected to can be quickly and conveniently calculated using the above aerodynamic force calculation method. However, the airflow field in reality is viscous, so it is necessary to conduct a comparative study of the aerodynamic potential flow solution and the viscous flow solution. The aerodynamic force of the box girder under viscous flow is calculated using the Fluent calculation software, and the differences between the viscous aerodynamic results of different box girders at different wind attack angles and the potential flow results calculated using the above calculation formula are analyzed. This method uses the Dadaidong Bridge as the analysis object, and has verified the reliability of the Fluent numerical model by comparing the numerical solution of flutter performance with the wind tunnel test value.

[0132] Box girder dimensions, computational domain of numerical model and mesh division are as follows: Figure 3 This method compares the difference between the potential flow solution and the viscous flow solution of the unsteady aerodynamics of five box girder sections. Figure 4 As shown in the figure, different aspect ratios represent different streamline levels, where B3 is the box girder section of the Dadaidong Bridge. The aerodynamic force is expressed in the form of aerodynamic coefficients.

[0133] Taking the B3 section as an example, Figure 5 The aerodynamic time history comparison of the box girder section at different angles of attack is shown. It can be seen that at any angle of attack, the first-order component of the drag force contributes more than the second-order component, which is consistent with the phenomenon of the potential flow solution. The potential flow solution of lift is in good agreement with the viscous flow solution, while the torque has a small difference in amplitude, but there is a certain phase lag, which is consistent with the case of 0° angle of attack. Therefore, the aerodynamic potential flow solution and the viscous solution proposed by this method show significant similarities in the magnitude and frequency of the unsteady aerodynamic force, and the potential flow solution can be corrected to improve the accuracy of the results.

[0134] In the present invention, in order to correct the aerodynamic potential flow solution, therefore:

[0135] The aerodynamic potential flow solution has a clear expression and high computational efficiency, but the viscosity effect is ignored and the accuracy still needs to be improved. This method is based on the aerodynamic numerical simulation results of 77 box girder sections to obtain the corresponding potential flow aerodynamic self-excitation force amplitude and phase correction coefficients. The numerical model is set to Figure 3 By training the neural network model, the relationship between the box girder shape parameters and the correction coefficient is established, and a more accurate aerodynamic force is directly calculated based on the box girder shape parameters and motion state.

[0136] Since the box girder shape and the correction coefficient are one-to-one corresponding, there is a certain correlation between the two, which can be determined by regression analysis. Assuming multiple variables in advance, after multiple rounds of linear regression on the correction coefficient, it is found that there is a very complex nonlinear relationship between the two, and a more reasonable mathematical model is needed to effectively predict the correction coefficient.

[0137] In order to avoid overfitting, a fully connected neural network is used to fit the correction coefficient. The input features include The meaning of each parameter is as follows Figure 6 As shown, the output features are 8 correction coefficients Ccl, Ccm, Cclp, Ccmp, Ccd1, Ccd2, Ccd1p, Cccd2p. cd, cl, cm represent the drag, lift and torque amplitude correction coefficients respectively, the suffixes 1 and 2 represent the first-order component and the second-order component respectively, and the suffix p represents the phase correction coefficient. The neural network model of this method uses the Levenberg-Marquardt algorithm to train the neural network, and the activation function is the tansig function. The neural network structure is shown as follows Figure 7 As shown, 70% of the 77 sets of sample data are used for training, 15% are used for overfitting verification, and 15% are used for model testing, that is, 53 sets of training data and 12 sets of verification and testing data.

[0138] Taking a box girder that is not in the training library of the correction coefficient neural network model as an example, the model is scaled at a ratio of 1:50 and the vibration frequency is 2Hz. The corrected potential flow aerodynamic time history is compared with the numerical simulation (CFD) results. The comparison results are shown in Figure 8 It can be seen that the corrected aerodynamic drag, lift and torque potential flow solutions are in good agreement with the viscous flow solutions, especially lift and torque, which are almost identical, indicating that the neural network model of the correction coefficient is reliable.

[0139] In the present invention, in order to calculate the flutter derivative and the flutter critical wind speed, therefore:

[0140] Since each equation in the multivariate linear equation group of flutter derivatives and aerodynamic self-excitation 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 second and third vertical bending and torsional amplitudes can be set to twice the first amplitude, that is, the following formula is obtained. The flutter derivative is calculated from the aerodynamic self-excitation force through the following formula.

[0141] 3D flutter derivatives:

[0142]

[0143]

[0144]

[0145]

[0146]

[0147]

[0148] Two-dimensional flutter derivatives:

[0149]

[0150]

[0151]

[0152]

[0153] The upper slash ' represents the amplitude and phase of the self-excited force obtained by the second vibration, and " represents the amplitude and phase of the self-excited force obtained by the third vibration, D 0 , L 0 、M 0 They represent drag, lift and torque respectively, and λ, β and γ are the phases corresponding to drag, lift and torque respectively.

[0154] The method of the present invention uses the corrected aerodynamic force to calculate the flutter derivative of the box girder and conducts flutter critical wind speed analysis of box girders with different cross-sections. The specific method flow is as follows: Fig. 9 As shown, we get Fig.10 The results shown show that the relative magnitude of the flutter performance of different cross sections is consistent with the wind tunnel test results.

[0155] The method of the present invention can quickly predict the flutter performance of the box girder based only on its shape and dynamic characteristic parameters. The entire process from aerodynamic calculation, flutter derivative identification to flutter performance evaluation takes no more than 0.5 seconds to calculate on an ordinary personal computer. In view of the high efficiency of the calculation, the method of the present invention can be applied to the rapid evaluation of the flutter performance of streamlined box girders. For example, in the preliminary design stage of bridges, it can provide valuable reference for the rapid comparison of multiple design schemes. Compared with the prior art, it has the following advantages:

[0156] 1. Fast speed: By utilizing the powerful nonlinear ability of the neural network model, after the model is trained, the target result can be quickly calculated based on the input parameters.

[0157] 2. Low cost: The neural network model is established based on the corrected potential flow solution data, without using wind tunnel test equipment, and can save computing resources for numerical simulation.

[0158] 3. High accuracy: The aerodynamic potential flow solution is well matched with the viscous flow solution after correction, and has good effect in predicting flutter performance.

[0159] Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions and variations may be made to the embodiments without departing from the principles and spirit of the present invention, and that the scope of the present invention is defined by the appended claims and their equivalents.

Claims

1. A method for rapid evaluation of box girder flutter performance based on potential flow theory. The present invention derives the potential flow solution of the unsteady aerodynamic force of a streamlined box girder based on the potential flow theory. The aerodynamic potential flow solution has a clear expression and high calculation efficiency. However, since the viscosity effect is ignored, the accuracy still needs to be improved. Therefore, the method compares and analyzes the difference between the potential flow solution and the viscous flow solution, establishes a neural network model for calculating the potential flow aerodynamic correction coefficient, and conducts a study on the prediction of the flutter performance of a streamlined box girder. Finally, a rapid prediction method is proposed, which includes the following steps: (1) Solve the complex potential function of the box girder motion; (2) Solve the pressure equation of 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 with the viscous flow solution and establish the relationship between the potential flow solution and the viscous flow solution; (5) Correction of aerodynamic potential flow solution; (6) Calculate the flutter derivative and the flutter critical wind speed.

2. The method for rapid evaluation of box girder flutter performance based on potential flow theory according to claim 1 is characterized in that: Solve the complex potential function of the box girder motion as follows: The box girder moves as shown in Figure 1. Since the gas meets the no-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 point P of the box girder. Assuming the inclination angle between the boundary where point P is located and the positive direction of the x-axis is θ, the normal velocity of point P can be obtained as: u pn =(u x +ωy p )sinθ-(u y -ωx p )cosθ The no-penetration condition can be written as: Where c is the box girder boundary. Substituting the above formula into the latter one and integrating along the box girder boundary, the stream function is: In the formula, Const represents a constant. Let z = x + iy, u = u x +iu y , define the following function: This formula is the complex potential function on the box beam boundary, that is, In order to obtain the complex potential function of the box girder during motion, the following transformation is required. Assume that the conformal mapping function from the unit circle in the ζ plane to the box beam in the z plane is z = f(ζ), let ζ u =e iθ is a point on the boundary of the unit circle, the boundary function of the box beam is written as B(ζu), and the relationship between the complex potential function on the circumference and the boundary condition is established as The Cauchy integral formula can establish a connection between the solution on the boundary and the solution of the internal and external points. Using the Cauchy integral formula, the complex potential function expression of the outer domain of the box girder can be obtained as: w(ζ)=B1(ζ) The conformal mapping function from the unit circle in the ζ plane to the box beam in the z plane can be written as: Among them, c k =a k +ib k , a k 、b k is the unknown coefficient, and the formula is substituted into the complex potential function of the box beam boundary By extracting the negative exponential term, we can get the complex potential function of the box beam during motion:

3. The method for rapid evaluation of box girder flutter performance based on potential flow theory according to claim 1 is characterized in that: Solve the pressure equation of the flow field as follows: According to the unsteady Bernoulli equation, the pressure equation in an ideal incompressible flow field can be written as: Where p is pressure, ρ is air density, V = (u x ,u y ) is the incoming flow velocity vector, and Const(t) is a constant. As shown in Figure 2, the reference system moves in translation and rotation with the box girder. Let the reference system be x * O * y * , the angle between p and V is α, then p and V are consistent with the absolute rest system, respectively. * and V * The velocity components are represented by u * x and u * y Indicates that, assuming the incoming flow velocity is V0, then: The velocity between the absolute stationary system and the moving reference system satisfies the following relationship: where u r =u rx +iu ry is the relative speed, satisfying: Substituting all the above equations into the unsteady Bernoulli equation: The pressure equation is:

4. The method for rapid evaluation of box girder flutter performance based on potential flow theory according to claim 1 is characterized in that: The unsteady aerodynamic forces of the box girder based on the potential flow solution, namely the aerodynamic drag, aerodynamic lift and aerodynamic torque, are solved as follows: In order to calculate the aerodynamic force acting on the box girder during its movement, it is necessary to integrate the pressure equation obtained in step 2. According to the complex function theory, dz = dze -i2β The aerodynamic drag F x and aerodynamic lift F y It can be written as: Substituting the former into the latter, we can get: Solve each integral separately, and the final aerodynamic drag and aerodynamic lift expressions are: Among them, A is the area of ​​the box beam, Re represents the real part, Im represents the imaginary part, and the expression of F is: By integrating the pressure moment on the box beam surface, the aerodynamic torque can be expressed as: Substituting the pressure equation into this formula and solving the integral, the expression of the aerodynamic torque can be obtained as: in: dyn=min{n,n-l+k} dyx=max{3,l+kn}.

5. The method for rapid evaluation of box girder flutter performance based on potential flow theory according to claim 1 is characterized in that: The aerodynamic potential flow solution is compared with the viscous flow solution, and the relationship between the potential flow solution and the viscous flow solution is established as follows: The unsteady aerodynamic drag, lift and torque of a box girder under potential flow are functions of its motion state ux, uy, ω and shape parameter c. For a box girder with known motion, the aerodynamic force it is subjected to can be quickly and conveniently calculated using the above aerodynamic force calculation method. However, the airflow field in reality is viscous, so it is necessary to conduct a comparative study of the aerodynamic potential flow solution and the viscous flow solution. The aerodynamic force of the box girder under viscous flow is calculated using the Fluent calculation software, and the differences between the viscous aerodynamic results of different box girders at different wind attack angles and the potential flow results calculated using the above calculation formula are analyzed. This method uses the Dadaidong Bridge as the analysis object, and has verified the reliability of the Fluent numerical model by comparing the numerical solution of flutter performance with the wind tunnel test value. The box girder dimensions, computational domain and meshing of the numerical model are shown in Figure 3. This method compares the differences between the potential flow solution and the viscous flow solution of the unsteady aerodynamic forces of five box girder sections. The five box girder sections are shown in Figure 4. Different aspect ratios represent different streamline levels, among which B3 is the box girder section of the Dadaidong Bridge. The aerodynamic force is expressed in the form of aerodynamic coefficients. Taking the B3 section as an example, Figure 5 shows the aerodynamic time history comparison of the box girder section at different angles of attack. It can be seen that at any angle of attack, the first-order component of the drag force contributes more than the second-order component, and the phenomenon of the potential flow solution is consistent with this. The potential flow solution of lift is consistent with the viscous flow solution, while the torque has a small difference in amplitude, but there is a certain phase lag, which is consistent with the case of 0° angle of attack. Therefore, the aerodynamic potential flow solution and the viscous solution proposed by this method show significant similarities in the magnitude and frequency of unsteady aerodynamic forces, and the potential flow solution can be corrected to achieve the purpose of improving the accuracy of the results.

6. The method for rapid evaluation of box girder flutter performance based on potential flow theory according to claim 1 is characterized in that: The correction of the aerodynamic potential flow solution is as follows: The aerodynamic potential flow solution has a clear expression and high computational efficiency, but the viscosity effect is ignored and the accuracy still needs to be improved. This method is based on the numerical simulation results of the aerodynamic force of 77 box girder sections to obtain the corresponding potential flow aerodynamic self-excitation force amplitude and phase correction coefficients, where the numerical model setting is consistent with that shown in Figure 3. By training the neural network model, the relationship between the box girder shape parameters and the correction coefficient is established, and a more accurate aerodynamic force is directly calculated based on the box girder shape parameters and motion state. Since the box girder shape and the correction coefficient are one-to-one corresponding, there is a certain correlation between the two, which can be determined by regression analysis. Assuming multiple variables in advance, after multiple rounds of linear regression on the correction coefficient, it is found that there is a very complex nonlinear relationship between the two, and a more reasonable mathematical model is needed to effectively predict the correction coefficient. In order to avoid overfitting, a fully connected neural network is used to fit the correction coefficient. The input features include The meaning of each parameter is shown in Figure 6. The output features are 8 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 component and the second-order component, respectively. The suffix p represents the phase correction coefficient. The neural network model of this method uses the Levenberg-Marquardt algorithm to train the neural network. The activation function is the tansig function. The schematic diagram of the neural network structure is shown in Figure 7. Among the 77 groups of sample data, 70% are used for training, 15% are used for overfitting verification, and 15% are used for model testing, that is, 53 groups of training data and 12 groups of verification and test data. Taking a box girder that is not in the training library of the correction coefficient neural network model as an example, the model is scaled at a ratio of 1:50, with a vibration frequency of 2Hz, and its corrected potential flow aerodynamic time history is compared with the numerical simulation (CFD) results, and the comparison results are shown in Figure 8. It can be seen that the corrected aerodynamic drag, lift and torque potential flow solutions are well consistent with the viscous flow solutions, especially lift and torque, which are almost the same, indicating that the correction coefficient neural network model is reliable.

7. The method for rapid evaluation of box girder flutter performance based on potential flow theory according to claim 1 is characterized in that: Calculate the flutter derivative and flutter critical wind speed as follows: Since each equation in the multivariate linear equation group of flutter derivatives and aerodynamic self-excitation 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 second and third vertical bending and torsional amplitudes can be set to twice the first amplitude, that is, the following formula is obtained. The flutter derivative is calculated from the aerodynamic self-excitation force through the following formula. 3D flutter derivatives: Two-dimensional flutter derivatives: The upper slash ' represents the amplitude and phase of the self-excited force obtained by the second vibration, " represents the amplitude and phase of the self-excited force obtained by the third vibration, D0, L0, M0 represent the drag, lift and torque respectively, and λ, β, γ represent the phases corresponding to the drag, lift and torque respectively.

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