A fast construction method of reduced order model for large flexible structures

Abstract

The application discloses a method for quickly constructing a large flexible structure reduced model, which comprises the following steps: establishing a structure finite element model; performing structure modal calculation to obtain different order modal information; establishing a structure dynamics equation considering geometric nonlinear factors to obtain a regression equation; obtaining a test load, adjusting a proportional coefficient to form a test load set required for solving a nonlinear stiffness coefficient, selecting sample points in the test load set by using a Latin hypercube method, loading the sample point test load on the finite element model in a dynamic form and calculating a wing deformation to form a test load and deformation required for solving the nonlinear stiffness coefficient; and solving the nonlinear stiffness coefficient by using a recursive least square method; compared with a traditional finite element method, the method effectively reduces the consumption of calculation resources, improves model applicability, and compared with a traditional model reduction method, the method reduces sample points required for solving the nonlinear stiffness coefficient and improves the efficiency of modeling and regression solving of the stiffness coefficient.

Description

Technical Field

[0001] This invention relates to the field of structural dynamics, and more specifically, to a method for rapidly constructing a reduced-order model of a highly flexible structure. Background Technology

[0002] With the development of engineering technology and materials science, the demand for structural large deformation analysis is becoming increasingly urgent. The flexibility of some typical engineering structures is gradually increasing, posing challenges to design and analysis. For example, in the field of aerospace engineering, the requirements for flight performance in modern aircraft design are constantly increasing. Highly flexible aircraft, represented by high-altitude long-endurance unmanned aerial vehicles (UAVs) and flying-wing UAVs, have gradually become a research focus for major aerospace powers since the 1990s. These aircraft can perform tasks such as military reconnaissance, civilian scientific exploration, and communication relay in a more flexible and continuous manner, possessing flight altitudes and endurance far exceeding those of traditional aircraft, and have broad application prospects. However, due to the high requirements for flight performance in their design objectives, these aircraft typically utilize a large wing aspect ratio to improve the lift-to-drag ratio, while also increasing the proportion of composite materials used. These factors lead to high flexibility in these aircraft, resulting in large structural deformations caused by aerodynamic loading, which brings structural safety issues.

[0003] When an engineering structure exhibits high flexibility, the deformation after loading is significant, and its dynamic characteristics depend nonlinearly on the instantaneous deformation and stress state. Mechanically, this manifests as a nonlinear relationship between strain and displacement, a nonlinear relationship between force equilibrium, while the constitutive relationship between stress and strain remains linear. This type of problem is called a geometric nonlinear problem, which has a significant impact on engineering structural design. Taking aerospace engineering as an example, considering geometric nonlinearity, the assumption of linear small deformation no longer applies in aircraft structural dynamics analysis. The aircraft's flutter velocity decreases, and the dynamic response amplitude increases, posing a threat to aircraft safety.

[0004] Accurate large deformation structural modeling methods are fundamental to structural dynamics analysis. The large deformation beam theory commonly used in theoretical research is difficult to apply to practical engineering models. Engineering analysis typically uses existing commercial finite element software, which suffers from large degrees of freedom, high nonlinear order, poor convergence, computational inefficiency, and difficulty in conducting mechanistic studies of structural dynamics. Nonlinear structural reduced-order models can better balance solution efficiency, computational accuracy, and applicability to complex models, making them suitable for geometrically nonlinear aeroelastic analysis. The applicant has introduced a nonlinear structural order reduction model into aeroelastic analysis in the following patents: "202011479068.4 A nonlinear aeroelastic dynamic response analysis method based on a structural order reduction model", "202011479061.2 A nonlinear substructure method applicable to modeling complex large flexible aircraft", "202110746615.9 A large flexible structure order reduction model based on dynamic response identification", and published articles: "Static aeroelastic analysis including geometric nonlinearities based on reduced order model" Xie Changchuan et al., Chinese Journal of Aeronautics, pp. 638-650, 20170216; "Flutter and gustresponse analysis of a wing model including geometric nonlinearities based on a modified structural ROM" An Chao et al., Chinese Journal of Aeronautics, pp. 48-63, 20190731, to construct an aeroelastic analysis framework. However, the test loads used to construct the reduced-order model are all aerodynamic load test sets under certain deformations, which involves a large amount of computation. This makes the computational and time costs of constructing the reduced-order structural model too high, affecting the modeling efficiency of the reduced-order model and limiting the applicability of the reduced-order structural model in engineering.

[0005] This invention addresses the modeling problem of large flexible structures. It researches a rapid modeling method for large flexible structures based on a nonlinear structural order reduction model, recursive least squares method, and Latin hypercube sampling method. The research draws upon authorized patent "202011479068.4 A Nonlinear Aeroelastic Dynamic Response Analysis Method Based on Structural Order Reduction Model", published patents "202011479061.2 A Nonlinear Substructure Method Applicable to Modeling Complex Large Flexible Aircraft", "202110746615.9 A Large Flexible Structure Order Reduction Model Based on Dynamic Response Identification", and published articles such as "Static aeroelastic analysis including geometric nonlinearities based on reduced order model" (Xie Changchuan et al., *Chinese Journal of Aeronautics*, pp. 638-650, 20170216) and "Flutter and gust response analysis of a wing model including geometric nonlinearities based on a modified structural ROM" (An Chao et al., *Chinese Journal of...*). This paper improves upon the structural order reduction model method established in "Aeronautics" (pages 48-63, 20190731), and provides an efficient and accurate method for constructing nonlinear structural order reduction models for complex models, especially aircraft component models.

[0006] To overcome the shortcomings of existing large flexible structure modeling methods, such as poor engineering applicability of beam theory, low computational efficiency of nonlinear finite element methods, and high modeling cost of reduced-order models of nonlinear structures, this invention provides a rapid construction method for reduced-order models of large flexible structures. Summary of the Invention

[0007] The present invention aims to provide a method for rapidly constructing a reduced-order model of a large flexible structure, so as to solve or improve at least one of the above-mentioned technical problems.

[0008] In view of this, the first aspect of the present invention is to provide a method for rapidly constructing a reduced-order model of a large flexible structure.

[0009] The first aspect of this invention provides a method for rapidly constructing a reduced-order model of a large flexible structure, comprising: S1, establishing a finite element model of the large flexible structure; S2, performing structural modal calculations on the finite element model to obtain modal information of different orders, including bending and torsional modes; S3, establishing a structural dynamic equation considering the effects of large geometric nonlinear deformation, and taking the static part of the structural dynamic equation to obtain a regression equation; S4, combining the bending and torsional modes to obtain test loads, applying the test loads to the finite element model in the form of dynamic loads and calculating the structural deformation, adjusting the scaling factor to keep the structural deformation within the nonlinear deformation range; S5, forming a set of test loads required to solve the nonlinear stiffness coefficient based on the test loads, and using the Latin hypercube sampling method. S6. Select different sample points that satisfy the Latin hypercube condition from the test load set; S7. Based on the test load of the sample points, load the structural deformation in the nonlinear static deformation calculation module of the finite element software, and the structural deformation is the test deformation corresponding to the test load; S8. Based on the test load and test deformation of the sample points and the regression equation, solve the nonlinear stiffness coefficient using the recursive least squares method; S9. Repeat S5-S7, expanding the sample points selected each time to the sample set of the previous iteration step to calculate the correction term in the recursive least squares method until the nonlinear stiffness coefficient converges and remains unchanged. Substitute the obtained nonlinear stiffness coefficient into the structural dynamics equation to obtain the reduced-order model of the large flexible structure; wherein, in step S5, the number of sample points in each selection is 3-5.

[0010] This invention provides a method for rapidly constructing a reduced-order model of a large flexible structure. It utilizes nonlinear stiffness coefficients to construct the dynamic equations of a large deformation structure. Based on this, it constructs a test load set using modal combination multiplication by a proportionality coefficient. Then, it selects sample points from the test load set using the Latin hypercube sampling method, performs least squares analysis, and continues to use the Latin hypercube sampling method to select new sample points from the test load set and add them to the original sample points. Finally, it updates the nonlinear stiffness coefficients using a recursive least squares method, repeating the above sampling and recursive least squares process until the nonlinear stiffness coefficients converge.

[0011] This method does not require excessive test set loading calculations when modeling large flexible structures, thus improving modeling efficiency. It can be applied to the dynamic response analysis and calculation of large flexible structures such as aerospace vehicles. Traditional methods do not select sample points but directly calculate the corresponding deformations of all test load sets and put the load deformations into the regression equation for solution. Often there are hundreds of points, and it takes a lot of time to calculate the deformations of hundreds of points to build samples. This invention first selects a few load sample points, calculates the deformation of these points, calculates a round of nonlinear stiffness coefficients, and then repeats this process until the coefficients to be solved converge. Often, it can be satisfied by a dozen or so calculations, which significantly improves the computational efficiency.

[0012] In addition, the technical solutions provided by embodiments of the present invention may also have the following additional technical features:

[0013] In any of the above technical solutions, the structural dynamics equation is specifically the following formula: Among them, M m K represents the generalized mass term of the m-th structural mode; m For the m-th structural mode, is the generalized stiffness term; All are nonlinear stiffness terms, where the superscript indicates the order of the generalized coordinate polynomial, and the subscript indicates the modal order of the generalized coordinate; q m q n q l and q p Let F be the generalized modal coordinates of order m, n, l, and p, respectively, and satisfy the Einstein summation convention; m For the m-th structural mode, the generalized force is denoted as . Let be the second derivative of the m-th modal coordinates with respect to time.

[0014] In this technical solution, the structural dynamics equations have The parameters take into account the effects of large geometric nonlinear deformation.

[0015] In any of the above technical solutions, the step of obtaining the regression equation by taking the statics component of the structural dynamics specifically involves: deleting the dynamics component to obtain the following formula: By moving the known linear stiffness component to the right-hand side of the equation, we obtain the regression equation:

[0016] In this technical solution, the obtained regression equation can be transformed into a regression problem for analysis, and then the unknown nonlinear stiffness coefficient term can be solved.

[0017] In any of the above technical solutions, the test load is obtained using the following formula: F=∑p i φ ib +∑p j φ jt ; where p i p j These are the proportionality coefficients; φ ib For bending; φ jt For torsional modes; i represents the i-th bending mode; j represents the j-th torsional mode; b represents bending; t represents torsion.

[0018] In this technical solution, the given test load is a key part of establishing the reduced-order model. Whether the test load is appropriate directly affects the accuracy of the regression analysis and the rationality of the reduced-order model. The NT group test load is applied to the finite element model in the form of dynamic load. The wing deformation is calculated using MSC.Nastran finite element software. The scaling factor is adjusted so that the final NT group wing deformation is within a suitable nonlinear deformation range, which serves as the test deformation required to establish the reduced-order model.

[0019] In any of the above technical solutions, step S2 obtains the modal information by taking the first 5 and 8th modes, and obtains the generalized mass term M for each mode. m and generalized stiffness term K m The names of each mode are, in order: vertical bend 1, vertical bend 2, vertical bend 3, first-order torsion, horizontal bend 1, and second-order torsion.

[0020] In this technical solution, the structural modes are calculated using the Nastran software SOL103 linear modal solver. The first five modes and the eighth mode are selected as the second torsional mode. The first mode is a vertical single-bending mode with a low natural frequency and high model flexibility; the second mode is a vertical double-bending mode; the third mode is a vertical triple-bending mode; the fourth mode is a first torsional mode; the fifth mode is a horizontal single-bending mode; and the eighth mode is a second torsional mode.

[0021] In any of the above technical solutions, in step S5, the number of sample points selected each time is 3-5.

[0022] In this technical solution, in order to keep the nonlinear stiffness coefficient convergent, convergence can generally be completed within ten repetitions, and the number of updated sample points each time is only three, which greatly reduces the overall computational load; specifically, the number of sampling points each time is 3.

[0023] The beneficial effects of this invention compared to the prior art are as follows:

[0024] This invention presents a rapid modeling method for structural order reduction models based on recursive least squares and Latin hypercube sampling, which effectively reduces computational resource consumption and improves computational efficiency compared with traditional structural analysis based on nonlinear finite element methods.

[0025] The finite element model is used for dynamic analysis, and the finite element model is more applicable to complex models than beam theory. Therefore, it improves the applicability of the model compared with the traditional structural analysis method based on beam theory.

[0026] Compared with traditional structural analysis methods based on structural order reduction models, the Latin hypercube approach and recursive least squares approach significantly reduce the number of sample points required to solve for nonlinear stiffness coefficients, thereby improving the efficiency of modeling and stiffness coefficient regression solutions.

[0027] Additional aspects and advantages of embodiments of the invention will become apparent in the following description or may be learned by practice of embodiments of the invention. Attached Figure Description

[0028] The accompanying drawings are for illustrative purposes only and are not intended to limit the scope of the invention.

[0029] Figure 1 A flowchart is established for the nonlinear structure order reduction model of this invention;

[0030] Figure 2 This is a schematic diagram of an example wing model of the present invention;

[0031] Figure 3 This is a schematic diagram of the finite element model of an example wing of the present invention;

[0032] Figure 4 This is a schematic diagram of the vertical flex mode of an example wing of the present invention;

[0033] Figure 5 This is a schematic diagram of the vertical two-bend mode of an example wing of the present invention;

[0034] Figure 6 This is a schematic diagram of the vertical three-bend mode of an example wing of the present invention;

[0035] Figure 7 This is a schematic diagram of the first-order torsional mode of an example wing of the present invention;

[0036] Figure 8 This is a schematic diagram of the horizontal flex mode of an example wing of the present invention;

[0037] Figure 9 This is a schematic diagram of the second-order torsional mode of an example wing of the present invention. Detailed Implementation

[0038] To better understand the above-mentioned objectives, features, and advantages of the present invention, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be noted that, unless otherwise specified, the embodiments and features described in these embodiments can be combined with each other.

[0039] Many specific details are set forth in the following description in order to provide a full understanding of the invention. However, the invention may also be practiced in other ways different from those described herein, and therefore the scope of protection of the invention is not limited to the specific embodiments disclosed below.

[0040] Example 1

[0041] Please see Figure 1-9 The first aspect of this invention provides a method for rapid construction of a reduced-order model of a large flexible structure. In this embodiment, a large flexible wing is used in the large flexible structure, with the NACA0015 symmetrical airfoil selected and the wing root fully fixed. The wing parameters are as follows: wing root chord length 100mm, wingtip chord length 100mm, span 1000mm, sweep angle 0Deg, and no twist angle. The wing main spars have a rectangular cross-section, 35mm long and 1.5mm wide, located at 50% chord length. The wing shape is maintained by eight balsa wood box segments, each consisting of a balsa wood frame and heat-shrink film skin. To reduce the impact on wing stiffness caused by the box segments pressing against each other due to bending deformation, the box segments are connected to the main spars at a single point, and a certain gap is left between adjacent box segments. To adjust the wing's dynamic characteristics and structural deformation, a counterweight rod with a total length of 200mm is installed at the wingtip. The total weight of the model is 0.613kg. A schematic diagram of the wing model is shown below. Figure 2 As shown, the method includes the following steps:

[0042] Step 1: Calculate initialization:

[0043] Establish the finite element model of the computational model, divide the structural finite element mesh of the model, define the element properties and material properties of the structural finite element mesh, and set the computational boundary conditions;

[0044] A finite element model of the wing was established using the finite element software MSC.Nasrtan. The finite element model used CBEAM elements to simulate the main beam and wing ribs, CONM2 elements to simulate the lumped mass, and FORCE1 to add dynamic structural loads. The wing was fixed at the root with six degrees of freedom. The finite element model information is shown in Table 1. The finite element model has 213 nodes, 212 beam elements, and 65 lumped mass elements. Dynamic loads were applied at 51 nodes. A schematic diagram of the finite element model is shown below. Figure 3 As shown.

[0045] Table 1 Finite element model information

[0046] Number of beam elements in the model 212 Mass number in model set 65 Follow the dynamic number 51

[0047] Step 2: Calculate structural modes:

[0048] The nonlinear structural order reduction model is based on the linear modes of the structure. Before establishing the structural order reduction model, the linear modes of the structure in the vertical bending, torsion and horizontal bending directions are calculated.

[0049] The nonlinear structural order reduction model is based on the linear modes of the structure. Before establishing the structural order reduction model, the linear modes of the structure in the vertical bending, torsion and horizontal bending directions are calculated.

[0050] After the finite element model was established, the structural modes were calculated using the Nastran SOL103 linear modal solver. Information on the first five modes and the second torsional mode of the eighth mode is shown in Table 2 (the sixth and seventh modes are higher-order bending modes and are therefore not selected). Mode shape information is as follows: Figure 4 As shown.

[0051] The first-order mode is a vertical bending mode with a natural frequency of 1.179 Hz and a modal stiffness of 5.488E+01. The natural frequency is relatively low, and the model has a relatively high flexibility.

[0052] The second-order mode is a vertical two-bend mode with a natural frequency of 7.724 Hz and a modal stiffness of 2.355E+03.

[0053] The third mode is a vertical three-bend mode with a natural frequency of 22.19 Hz and a modal stiffness of 1.944E+04.

[0054] The fourth mode is a first-order torsional mode with a natural frequency of 22.95 Hz and a modal stiffness of 2.080E+04.

[0055] The fifth mode is a horizontal bending mode with a natural frequency of 27.47 Hz and a modal stiffness of 2.978E+04.

[0056] The 8th mode is a second-order torsional mode with a natural frequency of 95.72 Hz and a modal stiffness of 3.617E+05.

[0057] Table 2 Linear Mode Information

[0058] 1 A vertical bend 1.179 5.488E+01 2 Vertical double bend 7.724 2.355E+03 3 Vertical Three Bends 22.19 1.944E+04 4 First-order torsion 22.95 2.080E+04 5 A horizontal bend 27.47 2.978E+04 8 Second-order torsion 95.72 3.617E+05

[0059] Step 3: Determine the structural dynamics equations:

[0060] The structural dynamics equations considering large geometric nonlinear deformation are shown in equation (1):

[0061]

[0062] This equation corresponds to the m-th structural mode and applies the Einstein summation convention; M m The generalized mass term corresponding to the m-th structural mode; K m The generalized stiffness term corresponding to the m-th structural mode; For nonlinear stiffness terms, the superscript indicates the order of the corresponding generalized coordinate polynomial, and the subscript corresponds to the modal order of the generalized coordinates; q represents the modal generalized coordinates, and the subscript corresponds to the modal order; F m The generalized force corresponds to the m-th structural mode. The structural dynamics are taken as the static part, as shown in equation (2):

[0063]

[0064] Moving the known linear stiffness part to the right side of the equation, we get:

[0065]

[0066] This equation can be transformed into a regression problem for analysis, and then the unknown nonlinear stiffness coefficient term can be solved.

[0067] The structural dynamics equations are in the form of equation (1). In this example, the first 5 linear modes and the 8th mode, a total of 6 modes, are used as the modal basis to establish a reduced-order structural model. The known terms in equation (1) have the following values:

[0068] M1=1 M2=1 M3=1

[0069] M4=1 M5=1 M6=1

[0070] K1=5.488E+01 K2=2.355E+03 K3=1.944E+04

[0071] K4=2.080E+04 K5=2.978E+04 K6=3.617E+05

[0072] Step 4: Determine the test load and test deformation required for establishing the reduced-order model:

[0073] The first five linear modes and the eighth mode, totaling six modes, are used as structural analysis modes, including: vertical first bend {φ1}, vertical second bend {φ2}, vertical third bend {φ3}, first torsion {φ4}, horizontal first bend {φ5}, and second torsion {φ6}.

[0074] The test load was selected as the force resulting from the combination of the first bending mode and the first torsional mode.

[0075] F=∑p i φ ib +∑p j φ jt (4)

[0076] Modal weighting coefficient p i The modal weighting coefficient p takes values ​​of 0, 100, 200, 300, 400, and 500. jThe values ​​are 0, 3, 6, 9, 12, and 15.

[0077] Step 5: Select points using the Latin hypercube sampling method:

[0078] Assuming that NT sets of static test loads are provided, a set of test loads is formed to solve for the nonlinear stiffness coefficient. The Latin hypercube sampling method is used to select w sample points in the test load set that satisfy the Latin hypercube condition (the value of w ranges from 3 to 5, specifically, 3 are selected).

[0079] 270 sets of static test loads are provided to form the test load set required to solve the nonlinear stiffness coefficient. The Latin hypercube sampling method is used to select 3 sample points that satisfy the Latin hypercube condition from the test load set.

[0080] Step 6: Based on the test load at the sample points, apply it to the structure in the SOL106 geometric nonlinear static deformation solver in the finite element software NASTRAN and calculate the structural deformation.

[0081] Step 7: Solve for the nonlinear stiffness coefficients using the recursive least squares method:

[0082] Combining the three sample points obtained in step five and the regression equation (3), the nonlinear stiffness coefficient is solved using the recursive least squares method. Each newly added sample point is used to solve the correction term in the recursive least squares method. The newly added sample points are used to correct the solution results, and the correction term is added to the existing results.

[0083] Step 8: Obtain the order-reduced model of the highly flexible structure:

[0084] Repeat steps 5 and 7, each time adding 3 sampling points to the sample set of the previous iteration step to calculate the correction term in the recursive least squares method until the nonlinear stiffness coefficient converges and remains unchanged. Generally, convergence can be completed within ten repetitions. Substitute the obtained nonlinear stiffness coefficient into equation (1) to obtain the large flexible structure order reduction model.

[0085] In the description of this invention, it should be understood that the terms "longitudinal", "lateral", "up", "down", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings, and are only for the convenience of describing this invention, and are not intended to indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation of this invention.

[0086] The embodiments described above are merely preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Various modifications and improvements made by those skilled in the art to the technical solutions of the present invention without departing from the spirit of the present invention should fall within the protection scope defined by the claims of the present invention.

Claims

1. A method for rapidly constructing a reduced-order model of a highly flexible structure, characterized in that, Includes the following steps: S1, Establish the finite element model of the large flexible structure; S2, perform structural modal calculations on the finite element model to obtain modal information of different orders, including bending and torsional modes; S3. Establish the structural dynamics equations that take into account the effects of large geometric nonlinear deformations, and take the static part of the structural dynamics equations to obtain the regression equations. S4. Based on the bending and torsional modes, the test load is obtained by combining them. The test load is applied to the finite element model in the form of dynamic loading and the structural deformation is calculated. The scaling factor is adjusted to make the structural deformation within the nonlinear deformation range. S5. Based on the test load, form a set of test loads needed to solve the nonlinear stiffness coefficient, and use the Latin hypercube sampling method to select different sample points in the set of test loads. S6. Based on the test load of the sample points, the structural deformation is obtained by loading in the nonlinear static deformation calculation module of the finite element software, and the structural deformation is the test deformation corresponding to the test load. S7. Based on the test load and test deformation of the sample points and the regression equation, the nonlinear stiffness coefficient is solved using the recursive least squares method. S8. Repeat S5-S7, expanding the selected sample points to the sample set of the previous iteration step to calculate the correction term in the recursive least squares method until the nonlinear stiffness coefficient converges and remains unchanged. Substitute the obtained nonlinear stiffness coefficient into the structural dynamics equation to obtain the reduced-order model of the large flexible structure. In step S5, the number of sample points selected in each step is 3-5.

2. The method for rapid construction of a reduced-order model of a large flexible structure according to claim 1, characterized in that, The structural dynamics equations are specifically the following formulas: (respectively) Among them, M m K represents the generalized mass term of the m-th structural mode; m For the m-th structural mode, is the generalized stiffness term; All are nonlinear stiffness terms, where the superscript indicates the order of the generalized coordinate polynomial, and the subscript indicates the modal order of the generalized coordinate; q m q n q l and q p Let F be the generalized modal coordinates of order m, n, l, and p, respectively, and satisfy the Einstein summation convention; m For the generalized force of the m-th structural mode; Let be the second derivative of the m-th modal coordinates with respect to time.

3. The method for rapid construction of a reduced-order model of a large flexible structure according to claim 2, characterized in that, The steps for obtaining the regression equation by taking the statics component of structural dynamics are as follows: Remove the dynamics part to obtain the following formula: By moving the known linear stiffness component to the right-hand side of the equation, we obtain the regression equation:

4. The method for rapid construction of a reduced-order model of a large flexible structure according to claim 1, characterized in that, The test load is obtained using the following formula: F=∑p i f ib +∑p j f jt ; Where, p i p j These are the proportionality coefficients; φ ib For bending; φ jt For torsional modes; i represents the i-th bending mode; j represents the j-th torsional mode; b represents bending; t represents torsion.

5. The method for rapid construction of a reduced-order model of a large flexible structure according to claim 2, characterized in that, In step S2, the modal information is obtained by taking the first 5 and 8th modes, and the generalized mass term M for each mode is obtained respectively. m and generalized stiffness term K m ; The names of each mode are, in order: vertical first bend, vertical second bend, vertical third bend, first-order torsion, horizontal first bend, and second-order torsion.

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