Numerical simulation method for multi-modal vibration of aeroelastic structure, terminal device and storage medium

Abstract

The application discloses a kind of gas-spring structure multimode vibration numerical simulation method, terminal equipment and storage medium, based on finite element modeling software and computational fluid dynamics dynamics software Fluent, using mode superposition method to decouple the multi-order vibration equation of system and compile UDF secondary development program embedded solver calculation, realize three-dimensional structure and wind flow field two-way fluid-structure coupling multimode calculation.The application can truly reflect the multimode vibration of actual three-dimensional structure.

Description

Technical Field

[0001] This invention relates to the field of multimodal vibration research of three-dimensional structures, and in particular to a numerical simulation method for multimodal vibration of aeroelastic structures. Background Technology

[0002] In recent years, vortex-induced vibration has repeatedly occurred, attracting widespread attention. Steel, compared to ordinary concrete, is more environmentally friendly and lighter, and is widely used in structures such as bridges. However, with the further application of steel, structures have become lighter and more flexible, with lower damping, making them more sensitive to wind. When fluid passes through a structure, vortices form at the tail end and detach, exerting alternating forces on the structure. As wind speed increases, the frequency of vortex shedding also increases. When the shedding frequency approaches the structure's natural frequency, vortex-induced resonance occurs. Cases of vortex-induced vibration in bridges are common. Furthermore, vortex-induced vibration also frequently occurs in cables, bridge towers, and high-rise buildings. Although vortex-induced vibration is amplitude-limited and does not exhibit divergent vibrations like flutter and galloping, it is prone to occur at low wind speeds and has a high frequency. Over time, this can cause fatigue damage to the structure and affect traffic safety. Therefore, vortex-induced vibration has attracted the attention of many scholars and engineers.

[0003] Currently, the main research methods for vortex-induced vibration (vortex-induced vibration) are theoretical methods, wind tunnel tests, and numerical simulation methods. In the preliminary design stage of bridge structures, aerodynamic selection of the bridge cross-section is generally required, primarily through wind tunnel tests and numerical simulation methods. Wind tunnel tests include segmental model tests and full-bridge aeroelastic model tests. Segmental model wind tunnel tests can perform two-degree-of-freedom vortex-induced vibration response tests on bridges, often using spring suspension. The results of the segmental model are further verified through full-bridge aeroelastic model tests. With the continuous development of science and technology, computational fluid dynamics is increasingly being applied to wind engineering. Two-dimensional numerical simulation methods, with their advantages of visualization and fast computation speed, are also being applied to vortex-induced vibration testing of structures. However, segmental model wind tunnel tests, based on two-dimensional sheet theory, cannot accurately simulate the three-dimensional effects of actual structures and cannot accurately reproduce multimodal vortex-induced vibration phenomena. Full-bridge aeroelastic models, due to limitations in the size of the wind tunnel test section, suffer from insufficient accuracy after scaling down. Furthermore, the main control measures for vortex-induced vibration include aerodynamic and mechanical measures. Aerodynamic control, by introducing a certain amount of flow around the flow field, aims to improve the vortex-induced vibration performance of bridges, offering advantages such as directness, simplicity, and economy. This is generally achieved by appropriately altering the aerodynamic shape of the bridge (adjusting the angle of the air nozzles, adjusting the location of maintenance walkways, etc.) or adding devices (such as guide vanes, flow deflectors, and vortex nets) to obtain a bridge cross-section flow characteristic with good wind resistance. However, due to the complexity of bridge cross-section flow, the selection of current bridge aerodynamic measures is mostly based on experimental experience. Two-dimensional numerical simulation retains the continuous components of the three-dimensional bridge structure while omitting non-continuous components, neglecting the three-dimensional characteristics of the vortex structure, resulting in some deviation between the calculation results and the actual three-dimensional flow field. Furthermore, two-dimensional numerical simulation is limited to the simulation of continuous components, making it difficult to simulate and study the aerodynamic measures of railing permeability and the central stabilizing plate. Moreover, two-dimensional numerical simulation is limited to single-order vortex-induced vibration research, unable to achieve realistic multi-order simulations. Therefore, the numerical simulation of vortex-induced vibration of structures mainly focuses on single-mode two-dimensional vibration, while numerical simulation research on vortex-induced vibration of three-dimensional structures is relatively limited and mainly focuses on a single mode. However, wind-induced vibration phenomena in real structures exhibit multiple modes. For example, cables exhibit multimodal coupled vortex-induced vibration, and bridges exhibit higher-order vortex-induced vibration. Current numerical simulation methods can only simulate vortex-induced vibration in one mode. For bridges and high-rise building structures, simulating higher-order vortex-induced vibration modes requires exponentially more computational scenarios, consuming significant human and material resources. For cable-stayed structures, single-mode numerical simulation is insufficient to reflect the true multimodal coupled vortex-induced vibration phenomenon. Therefore, researching a three-dimensional aeroelastic numerical simulation method that can simultaneously simulate multiple modes is of great significance. Summary of the Invention

[0004] The technical problem to be solved by the present invention is to provide a numerical simulation method, terminal equipment and storage medium for multimodal vibration of aeroelastic structures, which can realistically reflect the multimodal vibration of actual three-dimensional structures, in order to address the shortcomings of the existing technology.

[0005] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is: a numerical simulation method for multimodal vibration of aeroelastic structures, comprising the following steps:

[0006] S1. Establish a three-dimensional model of the aeroelastic structure, perform modal calculations on the three-dimensional model, and extract the first n frequencies of the three-dimensional model in the x and y directions. and and the mode shape coordinates corresponding to each frequency. , i = 1, 2, ..., n; coordinates corresponding to each frequency order. , After performing mode shape normalization, the normalized coordinates are obtained. , ; for the normalized coordinates , By fitting the data, the mode shape function in the x-direction corresponding to each frequency is obtained. and the mode shape function in the y direction ;

[0007] A three-dimensional numerical model was established based on the aeroelastic structure, and a three-dimensional mesh file was drawn using preprocessing software.

[0008] S2. Import the 3D mesh file into the Fluent solver and extract the forces in the x and y directions of the 3D numerical model; based on the forces on the wall and the mode shape functions in the x and y directions, obtain the generalized forces in the x and y directions respectively.

[0009] S3, utilizing the generalized forces in the x and y directions, and the first n frequencies in the x and y directions. and Generalized mass at each order Mode coordinates corresponding to each frequency , And for each order of damping, construct the vibration equations for each order in the x and y directions;

[0010] S4. Calculate the generalized displacements in the x and y directions using the vibration equations of each order in the x and y directions, and then determine the actual displacement deformation of each node in the x and y directions at the current moment, as well as the actual displacement of each node in the x and y directions.

[0011] S5. Determine whether the actual displacement amplitude in the x or y direction is stable. If yes, end the process. Otherwise, input the actual displacement deformation of each node in the 3D mesh in the x and y directions at the current moment into the Fluent solver, update the coordinates of the 3D mesh nodes, and return to step S2 until the actual displacement amplitude in the x or y direction is stable.

[0012] After obtaining the mode shape functions corresponding to each frequency, this invention calculates the generalized displacements of each order by combining them with generalized forces, thereby obtaining the actual displacement of each node at the current moment. Finally, the obtained displacements of each node are updated in the software to the new displacements of each node in the three-dimensional structure, realizing the multimodal vibration of the actual three-dimensional structure and truly reflecting the multimodal vibration of the actual three-dimensional structure.

[0013] In step S2, the formula for calculating the generalized force in the y-direction is: Where L is the number of vibration modes, Let be the force acting on the y-direction of the three-dimensional numerical model. Let be the mode shape function in the y-direction of the nth mode. .

[0014] In step S3, the expressions for the vibration equations of each order in the y-direction are as follows: ;in, , and Let be the generalized displacement, velocity, and acceleration of the nth mode, respectively. , and Let be the generalized modal mass, angular frequency, and damping of the nth-order mode, respectively. It represents the generalized stiffness of the nth-order mode.

[0015] , = .

[0016] m is the mass of the aeroelastic structure.

[0017] In step S4, the actual displacement deformation in the x-direction at time t The calculation formula is: ; , Let be the generalized force of the i-th mode.

[0018] In step S4, the actual displacements of the node in the x and y directions are the generalized displacements of the node under the first n modes and the sum of these displacements. The sum of products This is the mode shape function corresponding to each order.

[0019] In step S5, the specific implementation process for determining whether the actual displacement amplitude in the x-direction or y-direction is stable includes:

[0020] Calculate the difference between the actual displacement in the x or y direction at the current moment and the actual displacement in the x or y direction at the previous moment. If the difference is less than a first set threshold, the system is considered stable.

[0021] or,

[0022] Calculate the difference between the actual displacement in the x or y direction at the current moment and the actual displacement in the x or y direction at the previous moment, and then calculate the percentage of the difference to the actual displacement in the x or y direction at the current moment. If the percentage is less than a second set threshold, it is determined to be stable.

[0023] As an inventive concept, the present invention also provides a terminal device, including a memory, a processor, and a computer program stored in the memory; the processor executes the computer program to implement the steps of the method described above.

[0024] As an inventive concept, the present invention also provides a computer-readable storage medium having a computer program / instructions stored thereon; when the computer program / instructions are executed by a processor, they implement the steps of the method described above.

[0025] Compared with existing technologies, the beneficial effects of this invention are as follows: This invention provides a numerical simulation method for multimodal vibration of aeroelastic structures based on two-way fluid-structure interaction (FSI) using Fluent. Based on finite element modeling software and computational fluid dynamics software Fluent, it utilizes the modal superposition method to decouple the multi-order vibration equations of the system and compiles a UDF secondary development program to embed the solver for calculation, realizing two-way FSI multimodal calculation of the three-dimensional structure and the airflow field. This invention can realistically reflect the multimodal vibration of actual three-dimensional structures, such as multimodal coupled vortex-induced vibration of cables, high-order vortex-induced vibration of bridge structures and high-rise building structures, as well as the aerodynamic optimization effects of structures. Post-processing yields the flow field of the structure, such as vorticity contour maps, velocity contour maps, and pressure contour maps, which helps in analyzing the vibration mechanism of the structure. This can be further used in the three-dimensional mechanism research of vortex-induced aerodynamic measures for structures, providing guidance for the three-dimensional mechanism analysis and aerodynamic optimization of wind-induced vibration of structures. Attached Figure Description

[0026] Figure 1 This is a flowchart of the method in Embodiment 1 of the present invention;

[0027] Figure 2 This is a cross-section and arrangement diagram of the cable in application example 1 of the present invention;

[0028] Figure 3 This is a three-dimensional finite element model of a cable, which is an application example of the present invention.

[0029] Figure 4 This is the cable vibration mode diagram for application example 1 of the present invention;

[0030] Figure 5 This is a schematic diagram of the numerical model mesh and computational domain in application example 1 of the present invention;

[0031] Figure 6 This is the displacement time history diagram of the cable at L / 4 in Application Example 1 of the present invention;

[0032] Figure 7 This is application example 1 of the invention: the displacement spectrum of the cable at L / 4.

[0033] Figure 8 This is a contour map of the cable pressure at a certain moment in application example 1 of the present invention;

[0034] Figure 9 This is a cross-sectional layout diagram of application example 2 of the present invention;

[0035] Figure 10 This is a schematic diagram of the mode shapes of each order in application example 2 of the present invention;

[0036] Figure 11 This is a schematic diagram of the computational domain and mesh in application example 2 of the present invention;

[0037] Figures 12(a) and 12(b) are generalized displacement time history diagrams of each mode in application case 2 of the present invention; wherein, Figure 12(a) is U=3.6m / s (second-order positive symmetric mode); Figure 12(b) is U=5.0m / s (second-order antisymmetric mode).

[0038] Figures 13(a) and 13(b) are generalized displacement time history diagrams of each mode in application case 2 of the present invention; wherein, Figure 13(a) is U=3.6m / s (second-order positive symmetric mode); Figure 13(b) is U=5.0m / s (second-order antisymmetric mode).

[0039] Figure 14 This is the vorticity cloud diagram of a rectangular aeroelastic model at a certain moment in Application Case 2 of the present invention. Detailed Implementation

[0040] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, 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, 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.

[0041] In this document, the terms "first," "second," and other similar words are not intended to imply any order, quantity, or importance, but are merely used to distinguish different elements. The terms "one," "a," and other similar words are not intended to indicate the existence of only one of the stated things, but rather that the description pertains to only one of the two stated things, which may include one or more. The terms "comprising," "including," and other similar words are intended to indicate a logical relationship, not a spatial relationship. For example, "A includes B" means that logically B belongs to A, not that spatially B is located inside A. Furthermore, the meanings of the terms "comprising," "including," and other similar words should be considered open-ended, not closed. For example, "A includes B" means that B belongs to A, but B does not necessarily constitute all of A; A may also include other elements such as C, D, and E.

[0042] Example 1

[0043] This embodiment provides a numerical simulation method for multimodal vibration of aeroelastic structures (aeroelastic structures are structures that deform under the action of gas (wind)) based on Fluent bidirectional fluid-structure interaction. The implementation flowchart is as follows. Figure 1 As shown, the specific operation steps are as follows:

[0044] Step 1: Build a 3D model using ANSYS APDL. After performing modal calculations on the 3D model, extract the first n frequencies in the x and y directions. and Extract the coordinates corresponding to each frequency order. , i = 1, 2, ..., n;

[0045] Step 2: Normalize the mode shape of the coordinates for each frequency in Step 1 (i.e., normalize the coordinates). , (After normalization), the normalized coordinates are obtained. , ;

[0046] Step 3: Fit the coordinates obtained in Step 2 to obtain the mode shape function corresponding to each frequency. ;

[0047] Step 4: Calculate the generalized modal masses of the structure using the following formula, based on the mode shape function obtained in Step 3 and the mass of the actual model (i.e., the aeroelastic structure). Circular frequencies of various orders Generalized force and generalized damping Taking the y-direction as an example, the calculation is as follows:

[0048] The vibration equation of the structure is: ;

[0049] Where t is time, z is the model's longitudinal coordinate positioning, and m, c, and k are the mass, damping, and stiffness per unit length of the 3D model, respectively. , , These represent the displacement, velocity, and acceleration of the 3D model in the y-direction, respectively. This represents the force acting on the 3D model in the y-direction.

[0050] The longitudinal displacement of the structure can be decomposed into a superposition of multiple vibration modes: , For the generalized displacement of the nth order of the model, L is the corresponding mode shape function, and L is the span of the three-dimensional model (i.e., the length along the length direction; for example, if the three-dimensional model is a bridge, then the length of the bridge is the span length, and if the three-dimensional model is a column, then the length along the height direction of the column is the span length).

[0051] Based on the orthogonality of the mode shapes, we can obtain: , Let be the mode shape function of the m-th order.

[0052] Therefore, the vibration equation of the structure can be transformed into: .

[0053] Where n is the modal order; , and These represent the generalized displacement, velocity, and acceleration of the nth mode, respectively. For the mode shape function of the n-mode; , and These are the generalized modal mass, circular frequency, and damping, respectively. For generalized stiffness of each order; This refers to the generalized force that actually acts on the structure.

[0054] Finally, we obtain the generalized modal mass: .

[0055] Generalized stiffness at each order: .

[0056] The generalized damping of each order is obtained by calculating Rayleigh damping based on the actual first two orders of damping. :

[0057] ;

[0058] in, , It is a proportionality coefficient, determined by the structural damping ratio obtained through actual measurement.

[0059] The generalized forces that actually act on the structure are: .

[0060] Step 5: Write a UDF secondary development program to convert the frequencies of each order from Step 1 ( and The mode shape functions obtained in step 3 ( and The dynamic characteristic parameters (generalized modal mass) obtained in step 4 are as follows. angular frequency and generalized damping Input the parameters into the UDF secondary development program to obtain the parameters required to calculate the structural vibration equation;

[0061] Step 6: Establish a three-dimensional numerical model based on the structure and draw a three-dimensional mesh file using preprocessing software such as Gambit, ICEM, and Fluentmeshing;

[0062] Step 7: Import the mesh file from Step 6 into the Fluent solver and calculate the steady-state flow field until the residuals of the steady-state flow field converge to... This provides a better initial flow field;

[0063] Step 8: In Fluent, change the steady-state solution to a transient solution, compile and load the UDF secondary development program from Step 5, and set the dynamic mesh parameters;

[0064] In this embodiment of the invention, the initial calculation first uses step 7 to perform a steady-state calculation, and the result of the steady-state calculation is used as the initial value for the transient calculation. This provides a relatively accurate result for calculating the transient equations with respect to the time term t in subsequent steps (steps 8 and 9), since the transient includes time t, and each time step... It also includes an internal loop iteration, which is computationally intensive. If the transient state is calculated from the beginning, it will take a long time to calculate the iteration to a stable result, which is resource-intensive.

[0065] Step 9: Solve the Navier-Stokes equations for the flow field.

[0066] ;

[0067] For fluid density; ( () represents the velocity in each direction; Dynamic viscosity; The pressure of the flow field; This represents shear stress. The pressure near the wall in the 3D numerical model established in step 6 is extracted using Fluent, and the resultant force f in the x and y directions is calculated. Combined with the formula from step 4, the generalized force is then calculated. .

[0068] In this embodiment, after solving the Navier-Stokes equations, the pressure of the flow field can be determined. The pressure of the flow field can be obtained using the pressure of the flow field. The generalized force can be calculated using the pressure and the velocity in each direction (i.e., the generalized force can be calculated using the formula in step 4).

[0069] Step 10: Solve the vibration equations for each order:

[0070] Solving the structural vibration equations using the Adams method (linear multistep method):

[0071]

[0072] Obtain the generalized displacement of each order and .

[0073] Step 11: Calculate the actual displacement and deformation at time t of each point in the three-dimensional numerical model using the modal superposition method:

[0074] ;

[0075] Step 12: Call the macro command DEFINE_GRID_MOTION to animate each 3D network node, and output the time and generalized displacement of each order at the corresponding moment. and ;

[0076] Step 13: Determine whether the response results (displacement amplitude, convergence residual, etc.) in Step 12 are stable. If yes, end the calculation; if no, update the mesh nodes using the spring and mesh reconstruction function in Fluent software, and repeat Steps 9 to 12.

[0077] Step 14: Compile a MATLAB program to calculate the actual displacement time history of each point on the three-dimensional numerical model, and process it with post-processing software to obtain the flow field of the structure.

[0078] Furthermore, in step 10, the fourth-order Runge-Kutta method is used to solve the dynamic equations for the first four time steps, and the Adams method is used from the fifth time step onwards to improve the computational accuracy.

[0079] The following is an application example of this embodiment:

[0080] Application Case 1

[0081] The cross-section and arrangement of the cable-stayed model are as follows: Figure 2 As shown, the cable is internally composed of 12mm steel wire rope and multiple layers of flexible foam. Counterweights are evenly spaced along the cable's axis, and the model's unit length mass is 1.21 kg / m. The cable length is 10.48m, the wind deflection angle is 31.47°, the inclination angle is 13.85°, and the diameter is 0.08m. The modal damping ratio is 0.27%, and the bottom is H above the ground. b =0.16m, the height of the top from the ground is H t =2.69m, with a sag ratio of 0.133%.

[0082] Step 1: Model the actual cable structure using 3D ANSYS APDL. The 3D finite element model is as follows: Figure 3 As shown, after performing modal calculations on the 3D model, the first n frequencies of the model in the x and y directions are extracted. and Extract the coordinates corresponding to each frequency order. , Because the cable has the same properties in the x and y directions, that is... = , = Therefore, the frequencies f of the first seven orders of the model are obtained through modal analysis. n The generalized mass [M] and damping [C] are shown in Table 1.

[0083] Table 1 Calculation parameters for the first seven orders of cable

[0084] Serial Number Mode shape Frequency (Hz) Damping ratio (%) Generalized mass (kg) mode function 1 First stage 2.22 0.27 6.3403 <![CDATA[φ1= sin(-0.3*z+3.14)]]> 2 Second stage 3.96 0.27 6.3405 <![CDATA[φ2= sin(0.6*z+3.14)]]> 3 Third stage 6.02 0.27 6.3403 <![CDATA[φ3= sin(0.899*z+3.14)]]> 4 Fourth stage 7.98 0.27 6.3455 <![CDATA[φ4= sin(1.199081*z-3.14)]]> 5 Fifth stage 9.96 0.27 6.3403 <![CDATA[φ5= sin(1.498852*z-6.28)]]> 6 Sixth level 12.02 0.27 6.3404 <![CDATA[φ6= sin(1.798622*z-3.14)]]> 7 Seventh level 14.04 0.27 6.3405 <![CDATA[φ7= sin(2.098393*z-3.14)]]>

[0085] Step 2: Normalize the coordinates of each frequency from Step 1 to obtain the normalized coordinates. , ;

[0086] Step 3: Fit the coordinates obtained in Step 2 to obtain the mode shape function corresponding to each frequency. As shown in Table 1, the mode shapes for each order are as follows: Figure 4 As shown.

[0087] Step 4: Calculate the generalized modal masses M of the structure using the modal functions obtained in Step 3 and the masses of the actual model, according to the following formula. n ,frequency and generalized damping As shown in Table 1.

[0088] Step 5: Compile the UDF secondary development program, and input the frequencies obtained in Step 1, the mode shape functions obtained in Step 3, and the dynamic characteristic parameters obtained in Step 4 into the UDF secondary development program;

[0089] Step 6: Establish a 3D numerical model based on the structure and discretize and draw the 3D mesh file, such as... Figure 5 As shown. The left boundary condition is set as the velocity inlet, the right boundary condition as the pressure outlet, the front and rear boundaries are set as symmetrical boundaries, the cable surface is set as a no-slip wall, and a circular computational domain of 60D is used. A rigid domain is set within 5D of the wall surface, displacing synchronously with the cable; a dynamic mesh domain is set within 5D to 60D, where the mesh deforms to adapt to the structural displacement. A fully structured hexahedral mesh is used to ensure computational accuracy.

[0090] Step 7: Import the mesh file from Step 6 into the Fluent solver and calculate the steady-state flow field until the residuals converge, providing a good initial flow field. The calculation is performed under the condition of an incoming wind speed of 4.5 m / s, and the turbulence model uses three-dimensional large eddy simulation (LES).

[0091] Step 8: Change the steady-state solution to a transient solution, and compile and load the UDF secondary development program from Step 5. The dynamic mesh motion mode adopts the Diffusion method in Smoothing. The time step is set to 0.001s.

[0092] Step 9: Solve the Navier-Stokes equations for the flow field. By extracting the pressure near the wall in the three-dimensional numerical model, calculate the resultant force f in the x and y directions, and calculate the generalized force.

[0093] Step 10: Solve the vibration equations for each order, and use the Adams method (linear multistep method) to solve the dynamic equations to obtain the generalized displacement Y for each order. nx Y ny .

[0094] Step 11: Calculate the actual displacement and deformation of each point in the three-dimensional model at time t using the modal superposition method.

[0095] Step 12: Call the macro command DEFINE_GRID_MOTION to move each node, and output the time and generalized displacement of each order at the corresponding moment.

[0096] Step 13: Determine if the response result is stable. If yes, end the calculation; if no, update the grid nodes and repeat steps 9 to 12.

[0097] Step 14: Calculate the actual displacement time history of each point on the model, taking the L / 4 position as an example. At an incoming wind speed of 4.5 m / s, the vertical displacement amplitude is 0.13 m. Figure 6 As shown. Figure 7As shown, spectral analysis of the displacement time history reveals that the cable exhibits multimodal vibration at this wind speed, primarily vortex-induced vibration due to the coupling of fourth and fifth-order modal frequencies. The flow field of the structure was obtained through post-processing software, and the pressure contour map of the cable at a certain moment is shown below. Figure 8 As shown.

[0098] Application Case 2

[0099] Numerical simulations were performed on the vertical vortex-induced vibration modes of a rectangular aeroelastic model with multi-point elastic support. The model is 6 m long, and its basic parameters are shown in Table 2. The cross-sectional layout is as follows. Figure 9 As shown.

[0100] Step 1: Model the actual cable structure using ANSYS 18.0 APDL. The center of the rectangular cross-section is used as the origin of the XY plane coordinate system, and the center of the model's length direction is used as the origin of the Z-direction coordinate system. Since the rectangular cable test values ​​simulate vortex-induced vibration in the y-direction, only the y-direction is considered in the calculation. After modal calculation of the 3D model, the first five frequencies f in the y-direction are extracted, and the coordinates corresponding to each frequency are extracted. , .

[0101] Table 2 Basic parameters of the gas bullet model

[0102] D / mm B / mm L / mm B / D <![CDATA[m e / (kg·m−1)]]> 60 300 6000 5:1 2.4

[0103] Table 3 Calculation parameters for the first five vertical modes

[0104] Serial Number Mode shape Frequency (Hz) Damping ratio (%) Generalized mass (kg) mode function 1 First-order positive symmetry 4.75 0.092 6.6344 <![CDATA[φ1= 0.9636*sin(2.604*z+1.571)]]> 2 First-order antisymmetric 5.15 0.058 6.4201 <![CDATA[φ2= 0.9991*sin(2.091*z)]]> 3 Second-order positive symmetry 6.61 0.103 6.7188 <![CDATA[φ3= 1.013*sin(1.569*z-1.571)]]> 4 Second-order antisymmetric 9.45 0.305 6.5388 <![CDATA[φ4= 0.9907*sin(1.047*z+-3.142)]]> 5 Third-order positive symmetry 13.52 0.542 6.1051 <![CDATA[φ5= 1.007*sin(0.5234*z+1.571)]]>

[0105] Step 2: Normalize the coordinates of each frequency from Step 1 to obtain the normalized coordinates. , ;

[0106] Step 3: Fit the coordinates obtained in Step 2 to obtain the mode shape function corresponding to each frequency. As shown in Table 3, the mode shapes for each order are as follows: Figure 10 As shown.

[0107] Step 4: Calculate the generalized modal masses M of the structure using the modal functions obtained in Step 3 and the masses of the actual model, according to the following formula. n ,frequency and generalized damping As shown in Table 3.

[0108] Step 5: Compile the UDF secondary development program, and input the frequencies obtained in Step 1, the mode shape functions obtained in Step 3, and the dynamic characteristic parameters obtained in Step 4 into the UDF secondary development program;

[0109] Step 6: Establish a 3D numerical model based on the structure and discretize and draw the 3D mesh file. Use pre-processing software to draw the mesh, employing a cylindrical computational domain. The mode shapes of the model are obtained using a circular computational domain with a radius of 15B. A rigid domain is set within a 3B radius outside the wall, and the outermost layer is a dynamic mesh domain. The left boundary condition is set as a velocity inlet, the right boundary condition as a pressure outlet, the front and rear walls as symmetrical boundaries, and the rectangular cross-section walls as slip boundaries ("wall"). The first layer of mesh has a height of 5e-4B, and the mesh Yplus value is controlled to around 1. The computational domain and the overall mesh are as follows: Figure 11 As shown, a fully structured hexahedral mesh is used to ensure the computational accuracy of the mesh.

[0110] Step 7: Import the mesh file from Step 6 into the Fluent solver to calculate the steady-state flow field until the residuals converge, providing a good initial flow field. Calculations are performed under inflow wind speeds of 3.6 m / s and 5.0 m / s, corresponding to second-order positive symmetric and second-order antisymmetric vortex-induced vibration modes. The turbulence model uses three-dimensional large eddy simulation (LES).

[0111] Step 8: Change the steady-state solution to a transient solution, and compile and load the UDF secondary development program from Step 5. The dynamic mesh motion mode adopts the Diffusion method in Smoothing. The time step is set to 0.00025s.

[0112] Step 9: Solve the Navier-Stokes equations for the flow field. By extracting the pressure near the wall in the three-dimensional numerical model, calculate the resultant force f in the x and y directions, and calculate the generalized force.

[0113] Step 10: Solve the vibration equations for each order, and use the Adams method (linear multistep method) to solve the dynamic equations to obtain the generalized displacement Q for each order. nx Q ny .

[0114] Step 11: Calculate the actual displacement and deformation of each point in the three-dimensional model at time t using the modal superposition method.

[0115] Step 12: Call the macro command DEFINE_GRID_MOTION to move each node, and output the time and generalized displacement of each order at the corresponding moment.

[0116] Step 13: Determine if the response result is stable. If yes, end the calculation; if no, update the grid nodes and repeat steps 9 to 12.

[0117] Step 14: Calculate the actual displacement time history of each point on the model. The generalized displacement time history diagrams for each mode corresponding to incoming wind speeds U=3.6m / s and U=5.0m / s are shown in Figure 12(a) and Figure 12(b). From Figure 12(a), it can be seen that when the incoming wind speed is 3.6m / s, the generalized displacement amplitude corresponding to the second-order positive symmetry is 0.0077m, while the displacement amplitudes corresponding to other modes are relatively small. From Figure 12(b), it can be seen that when the incoming wind speed is 5m / s, the generalized displacement amplitude corresponding to the second-order antisymmetry is 0.0087m, while the displacement amplitudes corresponding to other modes are relatively small. Therefore, the vortex-induced vibration mode occurring at U=3.6m / s is a second-order positive symmetry mode, and the vortex-induced vibration mode occurring at U=5.0m / s is a second-order antisymmetric mode, reproducing the vortex-induced vibration modes of the rectangular cross-section tie rod under different wind speeds.

[0118] The displacement-time history diagrams of each mode at different locations corresponding to incoming wind velocities U=3.6m / s and U=5.0m / s are shown below. Figure 11 As shown in Figure 13(a), when the incoming wind speed is 3.6 m / s, the displacement at L / 3 is basically 0, while the displacements at L / 2 and L / 6 are the largest, corresponding to the mode shapes of the second-order positive symmetric mode. Figure 11 The inflection point is at L / 3, and the peak values ​​of the mode shapes are at L / 2 and L / 6, respectively. As shown in Figure 13(b), when the incoming wind speed is 5.0 m / s, the displacements at L / 2 and L / 4 are essentially zero, while the displacement at L / 8 is the largest, corresponding to the mode shape of the second antisymmetric mode. Figure 11 The method accurately reconstructs the mode shapes along the spanwise direction of the model for the corresponding vibration modes, and can effectively realize the three-dimensional aeroelastic effect of the model. The inflection points of the mode shapes are located at L / 2 and L / 4, while the peak value of the mode shape is at L / 8.

[0119] The flow field of the structure was obtained through post-processing software. The vorticity contour maps at L / 8, L / 2, and 7L / 8 at a certain moment are shown below. Figure 14 As shown, there is a phase difference in vortex shedding at different locations.

[0120] Example 2

[0121] Embodiment 2 of the present invention provides a terminal device corresponding to Embodiment 1 above. The terminal device can be a processing device for a client, such as a mobile phone, a laptop, a tablet computer, a desktop computer, etc., to execute the method of the above embodiments.

[0122] The terminal device in this embodiment includes a memory, a processor, and a computer program stored in the memory; the processor executes the computer program in the memory to implement the steps of the method in Embodiment 1 described above.

[0123] In some implementations, the memory may be high-speed random access memory (RAM), and may also include non-volatile memory, such as at least one disk storage device.

[0124] In other implementations, the processor can be any type of general-purpose processor, such as a central processing unit (CPU) or a digital signal processor (DSP), and there is no limitation here.

[0125] Example 3

[0126] Embodiment 3 of the present invention provides a computer-readable storage medium corresponding to Embodiment 1 above, on which a computer program / instructions are stored. When the computer program / instructions are executed by a processor, they implement the steps of the method of Embodiment 1 above.

[0127] A computer-readable storage medium can be a tangible device that holds and stores instructions for use by an instruction execution device. A computer-readable storage medium can be, for example, but not limited to, an electrical storage device, a magnetic storage device, an optical storage device, an electromagnetic storage device, a semiconductor storage device, or any combination thereof.

[0128] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code. The solutions in the embodiments of this application can be implemented in various computer languages, such as the object-oriented programming language Java and the interpreted scripting language JavaScript.

[0129] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0130] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0131] Although preferred embodiments of this application have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments as well as all changes and modifications falling within the scope of this application.

[0132] Obviously, those skilled in the art can make various modifications and variations to this application without departing from the spirit and scope of this application. Therefore, if such modifications and variations fall within the scope of the claims of this application and their equivalents, this application also intends to include such modifications and variations.

Claims

1. A method for numerical simulation of multi-modal vibrations of an aeroelastic structure, characterized in that, Includes the following steps: S1. Establish a three-dimensional model of the aeroelastic structure, perform modal calculations on the three-dimensional model, and extract the first n frequencies of the three-dimensional model in the x and y directions. and and the mode shape coordinates corresponding to each frequency. , i = 1, 2, ..., n; coordinates corresponding to each frequency order. , After performing mode shape normalization, the normalized coordinates are obtained. , ; fitting the normalized coordinates , , to obtain the mode function of x direction and the mode function of y direction corresponding to each order frequency A three-dimensional numerical model was established based on the aeroelastic structure, and a three-dimensional mesh file was drawn using preprocessing software. S2. Import the 3D mesh file into the Fluent solver and extract the forces in the x and y directions of the 3D numerical model; based on the forces on the wall and the mode shape functions in the x and y directions, obtain the generalized forces in the x and y directions respectively. S3, utilizing the generalized forces in the x and y directions, and the first n frequencies in the x and y directions. and Generalized mass at each order Mode coordinates corresponding to each frequency , And for each order of damping, construct the vibration equations for each order in the x and y directions; S4. Calculate the generalized displacements in the x and y directions using the vibration equations of each order in the x and y directions, and then determine the actual displacement deformation of each node in the x and y directions at the current moment, as well as the actual displacement of each node in the x and y directions. S5. Determine whether the actual displacement amplitude in the x or y direction is stable. If yes, end the process. Otherwise, input the actual displacement deformation of each node in the 3D mesh in the x and y directions at the current moment into the Fluent solver, update the coordinates of the 3D mesh nodes, and return to step S2 until the actual displacement amplitude in the x or y direction is stable. In step S2, the generalized force calculation formula in the y direction is: ; wherein, L is the number of modes, is the force in the y direction received by the three-dimensional numerical model at time t, is the mode function in the y direction of the nth order mode, ; In step S3, the expressions for the vibration equations of each order in the y-direction are as follows: ;in, , and Let be the generalized displacement, velocity, and acceleration of the nth mode, respectively. , and Let be the generalized modal mass, angular frequency, and damping of the nth-order mode, respectively. For the generalized stiffness of the nth mode; , = ; m is the mass of the aeroelastic structure.

2. The aeroelastic multi-modal vibration numerical simulation method of claim 1, wherein, In step S4, the actual displacement deformation in the x-direction at time t The calculation formula is: ; , Let be the generalized force of the i-th mode.

3. The aeroelastic multi-modal vibration numerical simulation method of claim 1, wherein, In step S4, the actual displacements of the node in the x and y directions are the generalized displacements of the node under the first n modes and the sum of these displacements. The sum of products This is the mode shape function corresponding to each order.

4. The aeroelastic multi-modal vibration numerical simulation method of claim 1, wherein, In step S5, the specific implementation process for determining whether the actual displacement amplitude in the x-direction or y-direction is stable includes: Calculate the difference between the actual displacement in the x or y direction at the current moment and the actual displacement in the x or y direction at the previous moment. If the difference is less than a first set threshold, the system is considered stable. or, Calculate the difference between the actual displacement in the x or y direction at the current moment and the actual displacement in the x or y direction at the previous moment, and then calculate the percentage of the difference to the actual displacement in the x or y direction at the current moment. If the percentage is less than a second set threshold, it is determined to be stable.

5. A terminal device comprising a memory, a processor, and a computer program stored on the memory; characterized in that, The processor executes the computer program to implement the steps of the method according to any one of claims 1 to 4.

6. A computer readable storage medium having stored thereon computer programs / instructions; characterized in that, When the computer program / instructions are executed by the processor, they implement the steps of the method according to any one of claims 1 to 4.

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