Dynamic and pneumatic elasticity calculation method based on structure reduced-order model

Abstract

The invention discloses a dynamic and pneumatic elasticity calculation method based on a structure reduced-order model, and the method comprises the steps: constructing a three-dimensional model of a to-be-analyzed part, carrying out the modal analysis, and obtaining all-order modals and structure vibration modes of a part structure; simplifying the three-dimensional model of the component to obtain the aerodynamic configuration of the component; generating a flow field grid for pneumatic calculation on the pneumatic shape of the component; utilizing a radial basis function neural network to perform interpolation of a flow field grid based on each order mode of the component structure and the structural vibration mode to obtain an interpolation result of the structural vibration mode; on the basis of an interpolation result of a structural vibration mode, a computational fluid dynamics method is adopted to calculate unsteady aerodynamic force, and then a structural model order reduction method is utilized to calculate transient displacement so as to obtain an aeroelastic response result. According to the method, the precision and efficiency of aeroelasticity calculation can be effectively improved.

Description

Technical Field

[0001] The invention belongs to the field of aircraft aerodynamics, and in particular relates to a dynamic aeroelasticity calculation method based on a structural reduced-order model. Background Art

[0002] As material technology and manufacturing processes become more mature, and design methods become more advanced, the slenderness ratio / aspect ratio of aircraft becomes larger and larger. With the continuous increase in slenderness ratio and wingspan and the urgent need to reduce weight, the stiffness of aircraft is relatively lower, and the role of aeroelastic analysis in aircraft design becomes more and more important. Flutter is a typical aeroelastic phenomenon. This self-excited vibration can cause the structure to vibrate and destroy in a short time of just a few seconds. The extremely destructive aeroelastic phenomenon has extremely serious consequences in the field of aerospace. Due to the huge destructiveness of flutter, it is very difficult to conduct critical and supercritical flight tests of flutter; at the same time, due to the huge cost and long cycle of wind tunnel tests, numerical analysis methods have become a major method for studying the flutter characteristics of aircraft.

[0003] Among the existing dynamic aeroelastic numerical analysis methods, one is a frequency domain method that simplifies unsteady aerodynamic forces based on potential flow and linearized equations as theoretical foundations, and uses flutter determinants to determine critical points. The computational efficiency is very high, but it is difficult to consider the nonlinear effects of aerodynamic forces such as the complex geometry of the aircraft, the position and intensity of shock waves, etc. The other is a time domain solution method that couples computational fluid dynamics (CFD) with structural finite element methods. The accuracy of solving unsteady aerodynamic loads and transient displacements of structures is very high, but the convergence is poor and the computational efficiency is low. In addition, the finite element method is difficult to carry out the mechanism analysis of structural dynamic characteristics. Summary of the invention

[0004] The purpose of the present invention is to provide a dynamic aeroelastic calculation method based on a structural reduced-order model to improve the accuracy and efficiency of aeroelastic calculations.

[0005] In order to achieve the above tasks, the present invention adopts the following technical solutions:

[0006] A dynamic aeroelastic calculation method based on a structural reduced-order model, comprising:

[0007] Construct a three-dimensional model for the component to be analyzed and perform modal analysis to obtain the various modes and structural vibration shapes of the component structure;

[0008] Simplify the three-dimensional model of the component to obtain the aerodynamic shape of the component; generate the flow field grid for aerodynamic calculation based on the aerodynamic shape of the component;

[0009] Using radial basis function neural network, the flow field grid is interpolated based on each order mode and structural vibration shape of the component structure to obtain the interpolation result of the structural vibration shape;

[0010] Based on the interpolation results of the structural vibration mode, the computational fluid dynamics method is used to first calculate the unsteady aerodynamic force, and then the structural model reduction method is used to calculate the transient displacement to obtain the aeroelastic response result.

[0011] Furthermore, the three-dimensional model is constructed for the component to be analyzed and modal analysis is performed to obtain various modes and structural vibration shapes of the component structure, including:

[0012] Use modeling software to build a three-dimensional model of the component and divide the finite element mesh, set the material properties of the component, define constraints and external loads, build the local stiffness matrix and mass matrix of the component, and assemble the global stiffness matrix and mass matrix; by solving the generalized eigenvalue problem, the eigenvalues ​​and eigenvectors obtained are the various modes and structural vibration shapes of the component structure.

[0013] Furthermore, the three-dimensional model of the component is simplified to obtain the aerodynamic shape of the component, including:

[0014] First, the internal structure of the 3D model of the component is deleted and only the outer surface of the 3D model of the component is retained. After removing the complex local details that have little impact on aerodynamics, a concise and complete aerodynamic shape of the component is obtained.

[0015] Furthermore, the generation of a flow field grid for aerodynamic calculation of the aerodynamic shape of the component includes:

[0016] The flow field grid includes a surface grid and a volume grid, wherein:

[0017] When generating surface meshes, the regular areas on the aerodynamic shape are divided into quadrilateral structured surface meshes, and the irregular areas are filled with triangular unstructured meshes; the surface meshes of the head and leading edge areas of the aerodynamic shape are encrypted along the flow change direction; the surface meshes of the far-field boundary are uniform triangular meshes with sizes matching the components;

[0018] When generating a volume mesh, the volume mesh includes the prismatic mesh of the boundary layer of the aerodynamic shape; the Reynolds number model and the number of layers of the prismatic mesh are set, and the height of the prismatic mesh increases exponentially from the first layer; after all prismatic meshes are generated, tetrahedral meshes are used to fill the remaining space except the surface mesh and volume mesh to obtain the entire flow field mesh of the aerodynamic shape.

[0019] Furthermore, the height of the first layer of prism grid on the boundary layer is given by the following formula:

[0020] ;

[0021] in:

[0022] ;

[0023] In the above formula, is the height of the first prism grid, is the dimensionless wall distance, are the kinematic viscosity coefficient, density, velocity and dynamic viscosity coefficient of the incoming flow, is the wall friction velocity, is the wall shear stress, is the surface friction coefficient, is the characteristic length of the aerodynamic shape, and Re is the Reynolds number.

[0024] Furthermore, the radial basis function neural network is used to interpolate the flow field grid based on each order mode and structural vibration shape of the component structure to obtain the interpolation result of the structural vibration shape, including:

[0025] The kernel function of the radial basis function neural network uses a Gaussian function; the coordinates of the finite element grid of the three-dimensional model, the modes of each order on the finite element grid and the structural vibration mode are used as input vectors to train the radial basis function neural network to obtain a fitting model of the spatial distribution of the structural vibration mode; the coordinates of the flow field grid are input into the fitting model, and the output of the fitting model is the interpolation result of the structural vibration mode from the finite element grid to the flow field grid.

[0026] Furthermore, the computational fluid dynamics method is used to calculate the unsteady aerodynamic force, including:

[0027] Firstly, the density-based or pressure-based solver of Fluent software is used, and the second-order method is used for spatial discretization. Multiple implicit iterations are performed based on the interpolation results of the structural vibration mode to converge the steady flow field, where the control equation is the NS equation.

[0028] Secondly, after the steady flow field calculation is completed, switch to the unsteady calculation mode; set the physical time step and the total calculation time based on the period of each mode of the component structure, load the externally compiled UDF code, assign an initial value to the first-order mode generalized velocity of the component structure to apply the initial disturbance, and start the fluid-solid coupling unsteady calculation; wherein the UDF code is responsible for calculating the unsteady aerodynamic force of each mode in each physical time step.

[0029] Furthermore, the calculation of transient displacement using a structural model reduction method includes:

[0030] Based on the modal superposition method, the displacement of each mode is solved and the structural dynamics reduced-order model is constructed;

[0031] The displacement and velocity of each mode are used to construct state variables, and the structural equation is established based on the state variables;

[0032] The second-order explicit / implicit hybrid linear multi-step method is used to solve the structural equations and obtain the estimated value of the state variables at the next moment;

[0033] The transient displacement of the structure at the next moment is obtained by superimposing the modes based on the estimated values.

[0034] Furthermore, the method of calculating the transient displacement by using the structural model reduction method further includes:

[0035] Update the surface position of the aerodynamic shape, and finally use the grid deformation function to update the position of all flow field grids; after the flow field grid position is updated, enter the next physical time step and repeat the calculation process of unsteady aerodynamic force and transient displacement. First calculate the unsteady aerodynamic force and then calculate the transient displacement of the structure until the given total calculation time is reached and the calculation is stopped.

[0036] A terminal device comprises a processor, a memory and a computer program stored in the memory; when the processor executes the computer program, the dynamic aeroelastic calculation method based on the structural reduced-order model is implemented.

[0037] A computer-readable storage medium stores a computer program; when the computer program is executed by a processor, the dynamic aeroelasticity calculation method based on a structural reduced-order model is implemented.

[0038] Compared with the prior art, the present invention has the following technical features:

[0039] 1. High-precision and efficient structural calculation: The structural reduction model is used to solve the structural displacement. Compared with the finite element method, the displacement solution accuracy is guaranteed while the solution degrees of freedom are greatly reduced. The structural displacement solution time in each time step is reduced to seconds, and the calculation efficiency is significantly improved.

[0040] 2. The computational fluid dynamics (CFD) method is used to solve the aerodynamic force, and the structural reduction model is used to solve the structural displacement. The unsteady coupling of the two forms a high-precision and efficient dynamic aeroelastic calculation method, which is more convenient for the mechanism analysis of aeroelastic problems than the finite element method. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] Figure 1 A schematic diagram of a method in one embodiment of the present invention;

[0042] Figure 2 A flow field space grid diagram in one embodiment of the present invention;

[0043] Figure 3 The structural vibration response near the flutter critical speed in one embodiment of the present invention;

[0044] Figure 4 The calculation and experimental comparison of the critical flutter speed in one embodiment of the present invention;

[0045] Figure 5 Calculation and test comparison of the critical frequency of flutter in one embodiment of the present invention. DETAILED DESCRIPTION

[0046] The present invention provides a dynamic aeroelastic calculation method based on a structural reduced-order model. The unsteady aerodynamic force is calculated using a high-precision computational fluid dynamics (CFD) method, and the transient displacement of the structure is calculated using a structural reduced-order model, providing a high-precision and efficient numerical calculation method for the analysis of aeroelastic problems of elastic aircraft.

[0047] A dynamic aeroelastic calculation method based on a reduced-order structural model, see Figure 1 , including the following steps:

[0048] Step 1: Build a three-dimensional model for the component to be analyzed and perform modal analysis to obtain the various modes and structural vibration shapes of the component structure.

[0049] Use modeling software to build a three-dimensional model of the component and divide the finite element mesh, set the material properties of the component, define constraints and external loads, build the local stiffness matrix and mass matrix of the component, and assemble the global stiffness matrix and mass matrix; by solving the generalized eigenvalue problem, the eigenvalues ​​and eigenvectors obtained are the various modes and structural vibration shapes of the component structure.

[0050] Step 2: Simplify the three-dimensional model of the component to obtain the aerodynamic shape of the component; generate a flow field grid for aerodynamic calculation based on the aerodynamic shape of the component.

[0051] Among them, when simplifying the three-dimensional model of the component, the internal structure of the three-dimensional model of the component is first deleted and only the outer surface of the three-dimensional model of the component is retained. After removing the complex local details that have little effect on aerodynamics (which can be specified by setting a threshold or based on experience), a concise and complete aerodynamic shape of the component is obtained.

[0052] The flow field grid is divided for the aerodynamic shape; the flow field grid includes surface grid and volume grid, among which:

[0053] When generating surface meshes, regular areas on the aerodynamic shape (for example, when the component is a wing, the wing surface is a regular area) are divided into quadrilateral structured surface meshes, and irregular areas are filled with triangular unstructured meshes; the surface meshes are encrypted along the direction of flow change in areas such as the head and leading edge of the aerodynamic shape where the flow changes dramatically; and the distance between the far-field boundary and the aerodynamic shape is no less than 20 times the length of the component, and the surface mesh of the far-field boundary is a uniform triangular mesh of a size comparable to that of the component.

[0054] When generating the volume mesh, the volume mesh includes the prismatic mesh of the aerodynamic shape boundary layer; the Reynolds number model and the number of prismatic mesh layers are set (about 30 layers of prismatic mesh are generated), and the height of the prismatic mesh increases exponentially from the first layer, with a growth rate of about 1.2 to ensure that there are enough prismatic meshes in the boundary layer and the transition is natural; after all the prismatic meshes are generated, tetrahedral meshes are used to fill the remaining space except the surface mesh and volume mesh to obtain the entire flow field mesh of the aerodynamic shape.

[0055] The height of the first layer of prism grid on the boundary layer is given by the following formula:

[0056] ;

[0057] in:

[0058] ;

[0059] In the above formula, is the height of the first prism grid, is the dimensionless wall distance, are the kinematic viscosity coefficient, density, velocity and dynamic viscosity coefficient of the incoming flow, is the wall friction velocity, is the wall shear stress, is the surface friction coefficient, is the characteristic length of the aerodynamic shape, and Re is the Reynolds number. For high Reynolds number models, such as Model, Reynolds stress model, etc. Take about 30, for low Reynolds number models, such as SA model, Models, etc. Take about 1.

[0060] Step three, using radial basis function neural network, interpolate the flow field grid based on the various modes and structural vibration shapes of the component structure to obtain the interpolation result of the structural vibration shape.

[0061] This step uses a radial basis function (RBF) neural network, whose kernel function uses the widely used Gaussian function; the coordinates of the finite element grid of the three-dimensional model in step one, the modes of each order on the finite element grid and the structural vibration mode are used as input vectors to train the radial basis function neural network to obtain a fitting model of the spatial distribution of the structural vibration mode; the coordinates of the flow field grid are input into the fitting model, and the output of the fitting model is the interpolation result of the structural vibration mode from the finite element grid to the flow field grid.

[0062] Step 4: Based on the interpolation results of the structural vibration mode, the computational fluid dynamics method is used to first calculate the unsteady aerodynamic force, and then the structural model reduction method is used to calculate the transient displacement to obtain the aeroelastic response result.

[0063] The computational fluid dynamics method is used to calculate the unsteady aerodynamic force, including:

[0064] First, the density-based or pressure-based solver of Fluent software is used, and the second-order method is used for spatial discretization. Multiple implicit iterations are performed based on the interpolation results of the structural vibration mode to converge the steady flow field, where the control equation is the NS equation:

[0065] ;

[0066] In the formula , and are the conserved variables, convective fluxes and viscous fluxes, respectively. , are discrete control volumes and volume elements, , , is the component surface, the surface unit external normal vector and the area element, is the time parameter.

[0067] Secondly, after the steady flow field calculation is completed, switch to the unsteady calculation mode; to ensure sufficient unsteady time simulation accuracy, the physical time step is not less than 1 / 50 of the minimum period in each mode of the component structure. In order to clearly and accurately judge the response trend of the structural vibration, the total calculation time exceeds 10 times the longest period in each mode of the component structure; load the externally compiled UDF code, assign an initial value ranging from 0.001 to 0.01 to the first-order modal generalized velocity of the component structure to apply an initial disturbance, and start the fluid-solid coupling unsteady calculation; wherein the UDF code is responsible for calculating the unsteady aerodynamic force of each mode in each physical time step.

[0068] The method of calculating transient displacement by using a structural model reduction method comprises:

[0069] Based on the mode superposition method, the displacement of each mode is solved, and the corresponding structural dynamics reduced-order model is:

[0070] ;

[0071] In the formula They are the generalized displacement, generalized mass, generalized damping, generalized stiffness and generalized aerodynamic force matrix of the structural mode respectively; , represents generalized velocity and generalized acceleration.

[0072] Introducing state variables ,in , Indicates The displacement and velocity of the modal order, n represents the total modal order, and the superscript T represents the transpose.

[0073] Construct the structural equation:

[0074] ;

[0075] In the formula, Represents state variables The first derivative of , , is a zero matrix, is the identity matrix; Represents the transient displacement and time of the structure Related functions.

[0076] The second-order explicit / implicit hybrid linear multi-step method is used to solve the structural equation and obtain the displacement at the next moment:

[0077] ;

[0078] ;

[0079] In the formula is the time increment, are the state variables of the previous moment, current moment and next moment respectively, are the generalized aerodynamic forces at the previous moment, the current moment, and the next moment, respectively. It is the estimated value of the state variable at the next moment;

[0080] Based on the estimated The displacement of the first-order mode, after the mode superposition, the instantaneous displacement of the structure at the next moment is obtained:

[0081] ;

[0082] In the formula is the transient displacement of the structure, , Respectively The displacement and structural vibration shape of the order mode, is the total mode order.

[0083] Finally, the GRID_MOTION function provided by Fluent is used to update the surface position of the aerodynamic shape, and finally the grid deformation functions such as the spring method and the diffusion method are used to update the grid positions of all flow fields. After the flow field grid positions are updated, the next physical time step is entered and the above steps are repeated. The unsteady aerodynamic force is calculated first and then the transient displacement of the structure is calculated. The calculation is stopped after the given total calculation time is reached.

[0084] Utilizing the high-precision and efficient numerical simulation capabilities of Fluent software, compared to self-developed CFD programs, it has rich physical models and advanced algorithms, and can simulate a variety of complex flow phenomena from incompressible to highly compressible, including laminar flow, turbulence, chemical reactions, heat transfer, etc.; high-performance parallel algorithms combined with a variety of acceleration algorithms significantly improve computing efficiency.

[0085] In one embodiment of the present invention, a wing is used as the component to be analyzed, and after performing modal analysis, the generalized mass, frequency, and vibration mode data of the first four wing modes are extracted. Based on the wing shape, a set of flow field grids required for aerodynamic calculation is generated, and the distance between the far field boundary and the wing is not less than 20 times the wing length, such as Figure 2 As shown. The meshing can be done using ICEM, Pointwise and other software. The mesh type is unstructured mesh. The height of the first layer of prism mesh near the wall satisfies the dimensionless wall distance y. + ~1, and 30 layers of prismatic grids are generated in the boundary layer. In Matlab, the radial basis neural network function newrb is used to fit the spatial distribution of vibration modes on the finite element grid of the wing, and then the grid node coordinates in the flow field grid are input into the fitting model to complete the interpolation of the vibration modes of the wing from the finite element grid to the flow field grid.

[0086] When performing unsteady aerodynamic calculations, the physical time step is 1 / 60 of the minimum period in each mode, and the total calculation time is more than 20 times the longest period in each mode. The initial disturbance is applied by assigning an initial value of 0.001 to the generalized velocity of the first-order mode of the structure, and starting the fluid-structure coupling unsteady calculation.

[0087] After the fluid-solid coupling unsteady calculation is completed, the time history results of the transient displacement stack of each order mode are output. After the transient displacement is superimposed, the actual deformation of the wing is obtained, that is, the vibration response of the wing under aerodynamic load over time is obtained. Under the same Mach number, if the vibration amplitude of the wing gradually decays over time at a certain incoming flow speed, then the speed is lower than the flutter critical speed. On the contrary, if the vibration amplitude increases exponentially with time, then the speed is higher than the flutter critical speed. By gradually changing the incoming flow speed range according to this criterion, the flutter critical speed of the wing can be obtained. At this time, the corresponding vibration frequency is also the flutter critical frequency.

[0088] The critical flutter state of the wing at different Mach numbers was calculated. Figure 3 The figure shows the wing vibration response results under the condition of Mach number Ma=0.678. When the speed is less than the flutter speed, the displacements of each modal decay to zero over time. Conversely, when the speed is greater than the flutter speed, the first-order and second-order modal displacements increase exponentially over time. Figure 4 and Figure 5The critical flutter speeds and frequencies at different Mach numbers obtained from experiments and calculations were compared respectively. The calculated and experimental results are very consistent in regularity and magnitude, and can better capture the typical "pit" phenomenon at transonic speeds. This shows that the dynamic aeroelastic calculation method based on the structural reduced-order model proposed in the present invention is reasonable. The time taken to solve the structural displacement in each step is less than 1% of the aerodynamic force calculation, which greatly improves the efficiency compared with the finite element method.

[0089] The above embodiments are only used to illustrate the technical solutions of the present application, rather than to limit them. Although the present application has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. These modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present application, and should all be included in the protection scope of the present application.

Claims

1. A dynamic aeroelastic calculation method based on a structural reduced-order model, characterized in that: include: Construct a three-dimensional model for the component to be analyzed and perform modal analysis to obtain the various modes and structural vibration shapes of the component structure; Simplify the three-dimensional model of the component to obtain the aerodynamic shape of the component; generate the flow field grid for aerodynamic calculation based on the aerodynamic shape of the component; Using radial basis function neural network, the flow field grid is interpolated based on each order mode and structural vibration shape of the component structure to obtain the interpolation result of the structural vibration shape; Based on the interpolation results of the structural vibration mode, the computational fluid dynamics method is used to first calculate the unsteady aerodynamic force, and then the structural model reduction method is used to calculate the transient displacement to obtain the aeroelastic response result.

2. The dynamic aeroelastic calculation method based on the structural reduced-order model according to claim 1 is characterized in that: The three-dimensional model is constructed for the component to be analyzed and modal analysis is performed to obtain various modes and structural vibration shapes of the component structure, including: Use modeling software to build a three-dimensional model of the component and divide the finite element mesh, set the material properties of the component, define constraints and external loads, build the local stiffness matrix and mass matrix of the component, and assemble the global stiffness matrix and mass matrix; by solving the generalized eigenvalue problem, the eigenvalues ​​and eigenvectors obtained are the various modes and structural vibration shapes of the component structure.

3. The dynamic aeroelastic calculation method based on a structural reduced-order model according to claim 1, characterized in that: The three-dimensional model of the component is simplified to obtain the aerodynamic shape of the component, including: First, the internal structure of the 3D model of the component is deleted and only the outer surface of the 3D model of the component is retained. After removing the complex local details that have little impact on aerodynamics, a concise and complete aerodynamic shape of the component is obtained.

4. The dynamic aeroelastic calculation method based on a structural reduced-order model according to claim 1, characterized in that: The generation of a flow field grid for aerodynamic calculation of the aerodynamic shape of the component includes: The flow field grid includes a surface grid and a volume grid, wherein: When generating surface meshes, the regular areas on the aerodynamic shape are divided into quadrilateral structured surface meshes, and the irregular areas are filled with triangular unstructured meshes; the surface meshes of the head and leading edge areas of the aerodynamic shape are encrypted along the flow change direction; the surface meshes of the far-field boundary are uniform triangular meshes with sizes matching the components; When generating a volume mesh, the volume mesh includes the prismatic mesh of the boundary layer of the aerodynamic shape; the Reynolds number model and the number of layers of the prismatic mesh are set, and the height of the prismatic mesh increases exponentially from the first layer; after all prismatic meshes are generated, tetrahedral meshes are used to fill the remaining space except the surface mesh and volume mesh to obtain the entire flow field mesh of the aerodynamic shape.

5. The dynamic aeroelastic calculation method based on a structural reduced-order model according to claim 1, characterized in that: The radial basis function neural network is used to interpolate the flow field grid based on each order mode and structural vibration mode of the component structure to obtain the interpolation result of the structural vibration mode, including: The kernel function of the radial basis function neural network uses a Gaussian function; the coordinates of the finite element grid of the three-dimensional model, the modes of each order on the finite element grid and the structural vibration mode are used as input vectors to train the radial basis function neural network to obtain a fitting model of the spatial distribution of the structural vibration mode; the coordinates of the flow field grid are input into the fitting model, and the output of the fitting model is the interpolation result of the structural vibration mode from the finite element grid to the flow field grid.

6. The dynamic aeroelastic calculation method based on a structural reduced-order model according to claim 1, characterized in that: The computational fluid dynamics method is used to calculate the unsteady aerodynamic force, including: Firstly, the density-based or pressure-based solver of Fluent software is used, and the second-order method is used for spatial discretization. Multiple implicit iterations are performed based on the interpolation results of the structural vibration mode to converge the steady flow field, where the control equation is the NS equation. Secondly, after the steady flow field calculation is completed, switch to the unsteady calculation mode; set the physical time step and the total calculation time based on the period of each mode of the component structure, load the externally compiled UDF code, assign an initial value to the first-order mode generalized velocity of the component structure to apply the initial disturbance, and start the fluid-solid coupling unsteady calculation; wherein the UDF code is responsible for calculating the unsteady aerodynamic force of each mode in each physical time step.

7. The dynamic aeroelastic calculation method based on a structural reduced-order model according to claim 1, characterized in that: The method of calculating transient displacement by using a structural model reduction method comprises: Based on the modal superposition method, the displacement of each mode is solved and the structural dynamics reduced-order model is constructed; The displacement and velocity of each mode are used to construct state variables, and the structural equation is established based on the state variables; The second-order explicit / implicit hybrid linear multi-step method is used to solve the structural equations and obtain the estimated value of the state variables at the next moment; The transient displacement of the structure at the next moment is obtained by superimposing the modes based on the estimated values.

8. The dynamic aeroelastic calculation method based on a structural reduced-order model according to claim 7, characterized in that: The method of calculating transient displacement by using a structural model reduction method also includes: Update the surface position of the aerodynamic shape, and finally use the grid deformation function to update the position of all flow field grids; after the flow field grid position is updated, enter the next physical time step and repeat the calculation process of unsteady aerodynamic force and transient displacement. First calculate the unsteady aerodynamic force and then calculate the transient displacement of the structure until the given total calculation time is reached and the calculation is stopped.

9. A terminal device comprising a processor, a memory and a computer program stored in the memory; characterized in that: When the processor executes the computer program, the dynamic aeroelasticity calculation method based on the structural reduced-order model according to any one of claims 1 to 8 is implemented.

10. A computer-readable storage medium, wherein a computer program is stored in the medium; characterized in that: When the computer program is executed by a processor, the dynamic aeroelasticity calculation method based on a structural reduced-order model according to any one of claims 1 to 8 is implemented.

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