Calculation method for optimal design length of wind fairing in longitudinal direction for suppressing vortex vibration of long-span bridge

Abstract

The application discloses a calculation method for the longitudinal optimal design length of a wind fairing for inhibiting vortex vibration of a long-span bridge, comprising the following steps: determining a main beam section without a wind fairing and a main beam section with a wind fairing of the long-span bridge; respectively performing a section model wind tunnel test on the main beam section without the wind fairing and the main beam section with the wind fairing and identifying aerodynamic parameters; determining a vortex vibration amplitude of the bridge under an arbitrary arrangement length, obtaining vortex vibration responses under the arrangement length of 0-100% of the wind fairing by iteratively calculating the vortex vibration responses under each arrangement length; determining a vibration suppression effect of the bridge; and finally determining an optimal arrangement length according to the vibration suppression effect. The optimal longitudinal arrangement length of the wind fairing calculated by using the application can greatly save the steel consumption compared with the full-length arrangement of a conventional bridge design, and the vibration suppression effect is remarkable. The aerodynamic data required by the calculation method provided by the application are all obtained from a conventional section model test, so that the high-cost full-bridge aeroelastic test is avoided, and the section model wind tunnel test result data is secondarily utilized.

Description

Technical Field

[0001] This invention relates to a method for calculating the optimal longitudinal design length of a wind nozzle used to suppress vortex-induced vibration in long-span bridges, belonging to the field of wind-induced vibration calculation and wind-resistant design of civil engineering bridges. Background Technology

[0002] Vortex-induced vibration (VEV) in bridges is a limited-amplitude vibration that occurs at low wind speeds. Recent incidents involving bridges such as the Humen Bridge and the Wuhan Yingwuzhou Bridge in my country have demonstrated that large-amplitude VEVs can lead to traffic disruptions and public panic. Therefore, avoiding or suppressing VEVs has significant engineering and social value.

[0003] Currently, the main method for suppressing vortex-induced vibration in long-span bridges is to add vents laterally on both sides of the main girder, thereby optimizing the aerodynamic shape of the main girder cross-section to achieve a vibration suppression effect. Most current projects adopt a scheme where the vents are arranged along the longitudinal length of the main girder, i.e., vents are added along the entire length of the bridge, such as the Nanjing Xianxin Road Yangtze River Bridge and the Bianyuzhou Yangtze River Bridge. Since the vents are mostly made of steel and can be several meters wide, installing vents along the entire length of the bridge would be very expensive. In reality, due to the non-uniform modal vibration of the main girder and the amplitude sensitivity of vortex-induced vibration, arranging vents across the entire span is unnecessary; vents only need to be placed near the peak value of a certain vibration mode to achieve a significant vibration suppression effect. However, there are currently no reports on how to calculate the optimal longitudinal arrangement length in engineering practice. Summary of the Invention

[0004] To overcome the shortcomings of existing technologies, this invention aims to provide a method for calculating the optimal longitudinal design length of air nozzles for suppressing vortex-induced vibration in long-span bridges. The technical problem this invention addresses is how to accurately calculate the optimal longitudinal installation length of bridge air nozzles, thereby achieving vibration suppression while significantly reducing the engineering cost of the air nozzles.

[0005] The technical solution provided by this invention to solve the above-mentioned technical problems is: a method for calculating the optimal longitudinal design length of a ventilator for suppressing vortex-induced vibration in long-span bridges, comprising the following steps:

[0006] Step S10: Determine the cross-section of the main beam of the long-span bridge without air nozzles and the cross-section of the main beam with air nozzles installed;

[0007] Step S20: Conduct segmental model wind tunnel tests on the main beam section without air nozzles and the main beam section with air nozzles installed, and identify the aerodynamic parameters.

[0008] Step S30: Determine the vortex-induced vibration amplitude of the bridge under any arrangement length. By traversing and calculating the vortex-induced vibration response under each arrangement length, obtain the vortex-induced vibration response of the wind nozzle arrangement length from 0 to 100%.

[0009] Step S40: Determine the vibration suppression effect of the bridge based on the vortex-induced vibration amplitude;

[0010] Step S50: Finally, determine the optimal arrangement length based on the vibration suppression effect.

[0011] A further technical solution is that, in step S20, a rigid segment model is used to simulate the aerodynamic characteristics of the main beam, an elastic suspension mechanism is used to simulate the structural dynamic characteristics, experiments are conducted in the studied wind speed range, and a laser displacement meter is used to measure the model response. The vortex-induced aerodynamic parameters of the bridge section are identified through the experiment.

[0012] A further technical solution is that, in step S20, the aerodynamic parameters are identified by testing using the attenuation-resonance method, the growth-resonance method, or the free attenuation method.

[0013] A further technical solution is that the specific process of step S30 is as follows:

[0014] Step S31: Calculate the vortex amplitude of the bridge with arbitrary arrangement length using the following formula;

[0015]

[0016] M = [φ] T [m][φ]

[0017]

[0018] In the formula: M is the generalized mass of the main beam; [φ] is the mode shape vector; [m] is the mass matrix of the main beam; ξ(t) is the generalized coordinate; D is the characteristic length; ω is the vibration frequency; ζ m ρ is the structural damping ratio; U is the air density; U is the incoming air velocity; l is the unit length. The amplitude is dimensionless; K is the reduced frequency. It is the product of aerodynamic parameters, which is the reduced frequency K and the dimensionless amplitude. The function;

[0019] Step S32: Perform segmental model wind tunnel tests on the original cross-section model and the cross-section model with the installed nozzle, and identify the aerodynamic parameter H1 to obtain the dimensionless amplitude curves of the aerodynamic parameter H1 of the two cross-sections at various wind speeds.

[0020] Step S33: Set the nozzle arrangement length to remain constant, and select a dimensionless amplitude at a certain wind speed. The equation is then iteratively calculated together with the dimensionless amplitude curve of the aerodynamic parameter H1 at that wind speed; when the two sides of the equation are unequal, the next dimensionless amplitude value is selected. Repeat the calculation until both sides of the equation are equal; at this point, the corresponding dimensionless amplitude is... This is the dimensionless vortex amplitude value at mid-span under the wind speed; according to the definition of generalized coordinates, the vortex vibration response at other positions in the span is obtained according to the mode shape; change the wind speed and repeat this step to calculate all wind speed points in the wind speed range under the study, and obtain the bridge vortex vibration response under any wind nozzle arrangement length.

[0021] Step S34: Change the length of the air nozzle arrangement and repeat step S33 to finally obtain the bridge vortex-induced vibration response with the air nozzle arrangement length from 0 to 100%.

[0022] A further technical solution is that the dimensionless amplitude in step S33 Substitute the dimensionless amplitude curve of the aerodynamic parameter H1 into the following formula for iterative calculation;

[0023]

[0024] In the formula: M is the generalized mass of the main beam; D is the characteristic length; ω is the vibration frequency; ζ m ρ is the structural damping ratio; U is the air density; U is the incoming air velocity; l is the unit length. is the dimensionless amplitude; K is the reduced frequency.

[0025] A further technical solution is that the calculation formula in step S40 is:

[0026]

[0027] In the formula: E represents the vibration suppression effect; A * The main beam's dimensionless amplitude.

[0028] A further technical solution is that the specific process of step S50 is as follows: draw the nozzle arrangement length-nozzle vibration suppression effect curve for each vortex vibration interval according to the vibration suppression effect; then determine the nozzle arrangement length corresponding to the maximum vibration suppression effect in each vortex vibration interval from the nozzle arrangement length-nozzle vibration suppression effect curve as the optimal arrangement length.

[0029] The present invention has the following beneficial effects:

[0030] 1. The optimal longitudinal arrangement length of the air nozzles calculated using this invention can significantly save steel compared to the full-length arrangement in conventional bridge designs, and also has a significant vibration suppression effect.

[0031] 2. The aerodynamic data required for the calculation method provided by this invention are all from conventional segmental model tests, avoiding the expensive full-bridge aeroelastic test, and are a secondary use of the segmental model wind tunnel test results data. Attached Figure Description

[0032] Figure 1 This is a flowchart of the present invention;

[0033] Figure 2 The diagram shows the ergonomic calculation results of the vortex-induced vibration response under various arrangement lengths.

[0034] Figure 3 A graph showing the vibration suppression effect of the nozzles on the length of the nozzle arrangement in each vortex-induced vibration zone.

[0035] Figure 4 The experimental results are shown in the figure. Detailed Implementation

[0036] The technical solution of the present invention will now be clearly and completely described with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. 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.

[0037] like Figure 1 As shown, the method for calculating the optimal longitudinal design length of the wind nozzle for suppressing vortex-induced vibration of long-span bridges according to the present invention includes the following steps:

[0038] Step 1: Determine the cross-section of the main girder of the long-span bridge without air nozzles and the cross-section of the main girder with air nozzles installed;

[0039] Step 2: Conduct segmental model wind tunnel tests on the main beam sections without air nozzles and with air nozzles installed, respectively, and identify aerodynamic parameters for subsequent vortex-induced vibration response and length optimization calculations.

[0040] The segmental model wind tunnel test follows the conventional procedure, which uses a rigid segmental model to simulate the aerodynamic characteristics of the main beam and an elastic suspension mechanism to simulate the structural dynamic characteristics. The test is conducted in the wind speed range studied and the model response is measured using a laser displacement meter. The vortex-induced aerodynamic parameters of the bridge section are identified through the "attenuation-resonance" method, the "growth-resonance" method and the free attenuation test.

[0041] Step 3: Determine the vortex-induced vibration amplitude of the bridge under any arrangement length. By traversing and calculating the vortex-induced vibration response under each arrangement length, obtain the vortex-induced vibration response of the vent arrangement length from 0 to 100%.

[0042] To determine the optimal longitudinal arrangement length of the air nozzles, it is necessary to clarify the vortex-induced vibration amplitude of the bridge under any arrangement length. Subsequently, the influence of the air nozzle arrangement length on the vortex-induced vibration of the main beam is quantitatively analyzed through traversal calculation. The traversal algorithm proposed in this invention is as follows:

[0043] (1) When the two cross sections are arbitrarily combined, the nonlinear vortex-induced vibration motion of the bridge can be expressed as the superposition motion under the nonlinear negative vortex excitation force and the linear positive damping force:

[0044]

[0045] In the formula, M represents the generalized mass of the main beam, and M = [φ]. T [m][φ], where [φ] is the mode shape vector, [m] is the main beam mass matrix; ξ(t) is the generalized coordinate, [y] = [φ]ξ(t)D, where D is the characteristic length; ω is the vibration frequency; ζ m ρ is the structural damping ratio; U is the air density; l is the incoming air velocity; and l is the unit length. It is the product of aerodynamic parameters, which is the reduced frequency K and the dimensionless amplitude. The function is expressed as follows, where the subscript mid indicates the mid-span position:

[0046]

[0047] (2) Perform segmental model wind tunnel tests on the original cross-section model and the cross-section model with installed nozzles respectively, and identify the aerodynamic parameter H1 to obtain the dimensionless amplitude curves of H1 for the two cross-sections at various wind speeds.

[0048] (3) With the length of the air nozzle arrangement unchanged, select a dimensionless amplitude at a certain wind speed. And together with the H1-dimensionless amplitude curve under this wind speed, they are substituted into the following formula for iterative calculation:

[0049]

[0050] When the two sides of the equation are unequal, select the next dimensionless amplitude. Repeat the calculation until both sides of the equation are equal; at this point, the corresponding dimensionless amplitude is... This is the dimensionless vortex amplitude value at mid-span under this wind speed. According to the definition of generalized coordinates, the vortex-induced vibration response at other locations along the span can be obtained according to the mode shape. By changing the wind speed and repeating this step, the vortex-induced vibration response of the bridge under any wind nozzle arrangement length can be obtained for all wind speed points within the studied wind speed range.

[0051] (4) Change the length of the air nozzle arrangement and repeat step (3) to finally obtain the bridge vortex vibration response with the air nozzle arrangement length from 0 to 100%.

[0052] By developing a program to perform ergonomic calculations of the vortex-induced vibration response of the real bridge according to steps (1)-(4) above, the results are as follows: Figure 2 As shown in the figure, the horizontal axis V represents the dimensionless wind speed, and the vertical axis A represents the wind speed. * The main beam has a dimensionless amplitude. According to the calculation results, the installation of the air nozzles can effectively suppress the overall vortex amplitude value, and the larger the arrangement length, the smaller the vortex amplitude value, and the "narrower" the corresponding vortex vibration wind speed range.

[0053] Step 4: Determine the vibration suppression effect of the bridge based on the vortex-induced vibration amplitude, and plot the nozzle arrangement length-nozzle vibration suppression effect curve for each vortex-induced vibration interval; then, determine the optimal nozzle arrangement length as the one that achieves the maximum vibration suppression effect in each vortex-induced vibration interval from the nozzle arrangement length-nozzle vibration suppression effect curve.

[0054] The optimal length of the wind nozzles needs to be considered from two aspects: reducing the amplitude of vortex-induced vibration and shortening the occurrence time of vortex-induced vibration. While reducing the amplitude of vortex-induced vibration, the overall vortex-induced vibration performance of the bridge should be improved by narrowing the vortex-induced vibration locking wind speed range. After installing wind nozzles of a certain length along the longitudinal direction, the vibration suppression effect E of the bridge is:

[0055]

[0056] Figure 3 The curves showing the damping effect of the nozzle length versus the damping effect are presented for each of the two vortex-induced vibration zones. It can be seen that the damping effect increases with the increase of the nozzle length. In this case, both vortex-induced vibration zones reach their maximum damping effect after the nozzle length exceeds 40%. At this point, further increasing the longitudinal length of the nozzles will not further improve the structural vortex-induced vibration performance, but will only increase the project cost.

[0057] Therefore, placing vents at 40.0% of their length in the middle of the span is the optimal arrangement. When this arrangement is adopted, the vibration damping effect provided by the vents is maximized, and compared with the full-span arrangement, the steel consumption is reduced by 60%, which significantly reduces the overall cost of the bridge while achieving a vibration damping effect comparable to the full-span arrangement.

[0058] To ensure the accuracy of the theoretical calculation method of this invention, wind tunnel tests were conducted for verification. The wind tunnel test model was centered at the mid-span of the bridge, with 40.0% of the wind nozzles arranged longitudinally. For the segmental wind tunnel model, its vibration mode is 1, and the vortex-induced vibration response calculation of the model can be modified from the formula as follows:

[0059]

[0060] The vortex vibration of the verification model is calculated using the above formula and compared with the experimental values. The comparison results are as follows: Figure 4 As shown in the figure, the verification effect is good. This method can accurately calculate the maximum vortex amplitude value, which is of most concern in actual engineering.

[0061] This invention combines the distribution characteristics of bridge mode shapes with nonlinear vortex vibration theory to derive the nonlinear relationship between vortex vibration amplitude and main beam modal coordinates. By utilizing the influence characteristics of bridge mode shapes on vortex vibration, the invention achieves the best balance between vortex vibration performance and vortex nozzle cost by setting and installing vents only near the peak value of the modal coordinates, while not setting them at other locations.

[0062] The design method provided by this invention can be used not only for main beam wind deflectors, but also extended to the design of layout schemes for other bridge aerodynamic measures such as guide vanes and wind barriers, optimizing cost indicators while meeting bridge vibration requirements. Furthermore, this invention can be implemented based on conventional bridge segment model wind tunnel tests and vortex-induced vibration nonlinear algorithms, eliminating the need for expensive full-bridge aeroelastic wind tunnel tests, making it convenient to apply and saving on testing costs and labor.

[0063] The above description is not intended to limit the present invention in any way. Although the present invention has been disclosed through the above embodiments, it is not intended to limit the present invention. Any person skilled in the art can make some changes or modifications to the above-disclosed technical content to create equivalent embodiments without departing from the scope of the present invention. Any simple modifications, equivalent changes and modifications made to the above embodiments based on the technical essence of the present invention without departing from the scope of the present invention shall still fall within the scope of the present invention.

Claims

1. A method for calculating the optimal longitudinal design length of a ventilator used to suppress vortex-induced vibration in long-span bridges, characterized in that... Includes the following steps: Step S10: Determine the cross-section of the main beam of the long-span bridge without air nozzles and the cross-section of the main beam with air nozzles installed; Step S20: Conduct segmental model wind tunnel tests on the original cross-sectional model and the cross-sectional model with the installed nozzle, and identify the aerodynamic parameters. The aerodynamic parameters of the two cross sections at various wind speeds were obtained. Dimensionless amplitude curve; Step S30: Determine the vortex-induced vibration amplitude of the bridge under any arrangement length. By traversing and calculating the vortex-induced vibration response under each arrangement length, obtain the vortex-induced vibration response of the wind nozzle arrangement length from 0 to 100%. Step S31: Calculate the vortex amplitude of the bridge with arbitrary arrangement length using the following formula; In the formula: The generalized mass of the main beam; For mode shape vectors, The mass matrix of the main beam; For generalized coordinates, D The characteristic length; The vibration frequency; The structural damping ratio; air density; U For incoming air velocity; l The unit length; The amplitude is dimensionless. K For frequency conversion; The product of aerodynamic parameters is the reduced frequency. K With dimensionless amplitude The function; Step S32: Set the nozzle arrangement length to remain constant, and select a dimensionless amplitude at a certain wind speed. and the aerodynamic parameters at that wind speed The dimensionless amplitude curves are calculated iteratively together; when the two sides of the equation are unequal, the next dimensionless amplitude value is selected. Repeat the calculation until both sides of the equation are equal; at this point, the corresponding dimensionless amplitude is... This is the dimensionless vortex amplitude value at mid-span under the wind speed; according to the definition of generalized coordinates, the vortex vibration response at other positions in the span is obtained according to the mode shape; change the wind speed and repeat this step to calculate all wind speed points in the wind speed range under the study, and obtain the bridge vortex vibration response under any wind nozzle arrangement length. Step S33: Change the length of the air nozzle arrangement and repeat step S32 to finally obtain the bridge vortex-induced vibration response with the air nozzle arrangement length from 0 to 100%. Step S40: Determine the vibration suppression effect of the bridge based on the vortex-induced vibration amplitude; Step S50: Finally, determine the optimal arrangement length based on the vibration suppression effect.

2. The method for calculating the optimal longitudinal design length of the ventilator for suppressing vortex-induced vibration in long-span bridges according to claim 1, characterized in that, In step S20, a rigid segment model is used to simulate the aerodynamic characteristics of the main beam, and an elastic suspension mechanism is used to simulate the dynamic characteristics of the structure. Experiments are conducted in the studied wind speed range, and the model response is measured using a laser displacement meter. The vortex-induced aerodynamic parameters of the bridge section are identified through the experiments.

3. The method for calculating the optimal longitudinal design length of the wind nozzle for suppressing vortex-induced vibration of long-span bridges according to claim 2, characterized in that, In step S20, the aerodynamic parameters are identified by testing using the attenuation-resonance method, the growth-resonance method, or the free attenuation method.

4. The method for calculating the optimal longitudinal design length of the wind nozzle for suppressing vortex-induced vibration of long-span bridges according to claim 1, characterized in that, The dimensionless amplitude in step S33 With aerodynamic parameters Substitute the dimensionless amplitude curve into the following formula for iterative calculation; In the formula: The generalized mass of the main beam; D The characteristic length; The vibration frequency; The structural damping ratio; air density; U For incoming air velocity; l The unit length; The amplitude is dimensionless. K This is the frequency conversion.

5. The method for calculating the optimal longitudinal design length of the ventilator for suppressing vortex-induced vibration in long-span bridges according to claim 1, characterized in that, The calculation formula in step S40 is: In the formula: E For vibration damping effect; The main beam's dimensionless amplitude.

6. The method for calculating the optimal longitudinal design length of the wind nozzle for suppressing vortex-induced vibration of long-span bridges according to claim 1, characterized in that, The specific process of step S50 is as follows: draw the nozzle arrangement length-nozzle vibration suppression effect curve for each vortex vibration interval based on the vibration suppression effect; then determine the optimal arrangement length as the nozzle arrangement length that achieves the maximum vibration suppression effect in each vortex vibration interval from the nozzle arrangement length-nozzle vibration suppression effect curve.

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