An internally loaded branch mode shape fitting method and system

Abstract

An internal load branch modal shape fitting method and system, the aircraft shell is simplified as a main beam structure of elastic beam series connection concentrated mass, the internal load is simplified as a branch beam structure of elastic beam series connection concentrated mass, the weak connection structure between the internal load and the aircraft is simplified as a linear spring and a torsional spring connecting the main beam and the branch beam, the system modal parameters are calculated, and the main beam structure is preliminarily corrected in combination with modal test results, the fitting branch shape meeting the requirement of inertial balance is generated by selecting key positions, adopting a spline interpolation function, and adjusting the size of the branch beam key position shape, the correlation between the calculated branch beam shape and the fitting shape is adjusted in the calculation model, the connection stiffness between the branch beam and the main beam is iteratively calculated, the system modal parameters are iteratively calculated until the correlation meets the requirement, and the main beam shape is recorded, the correlation between the calculated main beam shape and the main beam test shape is evaluated, and the final branch fitting shape is obtained by iteratively adjusting according to the correlation result to complete the fitting.

Description

Technical Field

[0001] This invention relates to a method and system for fitting mode shapes of internally loaded branch modes, belonging to the field of modal parameter identification technology. Background Technology

[0002] During flight, the control system detects attitude angle deviations and sends commands to the servo system after processing through the attitude control network. The servo system then corrects the aircraft's attitude using actuators, ensuring that the aircraft flies normally according to the predetermined attitude. The aircraft's attitude motion includes not only rigid body rotation but also elastic motion about its own rigid axis; therefore, attitude control design must consider the elastic motion of the entire aircraft.

[0003] With the increasing demand for internal payloads in aerospace applications, higher requirements are being placed on the attitude control design of aircraft. This is particularly true for internal payloads that are large in size, have low stiffness, and exhibit boundary variations. On the one hand, the high aspect ratio of these payloads easily induces low-frequency branched modes; on the other hand, insufficient identification of these internal branched modes will affect the design of the aircraft's modal parameters (including mode shapes and generalized mass). As dynamic characteristic simulation technology advances, modal testing of the entire aircraft system is increasingly being eliminated during the engineering development phase. Instead, modal measurements are conducted only at measurement points attached to the outer surface of the aircraft shell after final assembly. In this case, it is impossible to obtain modal test data of the internal payloads under specific boundary conditions. Therefore, to fully identify the aircraft's modal parameters for use in attitude control design, the correction of the internal payload mode shapes based on the aircraft shell modal parameters is crucial. Summary of the Invention

[0004] The technical problem solved by this invention is to address the shortcomings of existing technologies by proposing a method and system for fitting mode shapes with internal load branches, based on existing modal parameter calculation and experimental methods.

[0005] The present invention solves the above-mentioned technical problem through the following technical solution:

[0006] A method for fitting mode shapes of internally loaded branched modes includes:

[0007] The aircraft shell is simplified into a main beam structure, and the internal load of the aircraft is simplified into a branch beam structure.

[0008] The connection structure between the aircraft shell and the internal load is simplified to an equivalent stiffness spring connector;

[0009] Establish the system dynamic equations, solve the homogeneous dynamic equations, and obtain the initial calculated modal parameters;

[0010] Record the location information of measuring points on the outer surface of the aircraft shell during the modal test of the aircraft system, and obtain the test vibration mode of the main beam;

[0011] The main beam structure was modified based on the frequency and mode shape parameters of the experimental modal parameters, and the modal parameters were re-solved.

[0012] The axial coordinates of the branch beam with the largest calculated vibration mode and the axial coordinates of the connection between the branch beam and the main beam are extracted as key positions. The vibration modes of the branch beam at the key positions are set as control points and spline interpolation function calculations are carried out. The vibration mode sizes of the control points are adjusted to generate the fitted branch beam vibration mode that meets the requirements of inertial equilibrium.

[0013] The correlation between the calculated mode shape and the fitted mode shape of the branch beam is evaluated. If the correlation is higher than the preset standard, the calculated mode shape of the main beam is recorded. If the correlation is lower than the preset standard, the stiffness of the spring connection between the branch beam structure and the main beam structure in the calculation model is corrected, and the test modal parameters are solved again.

[0014] The correlation between the calculated mode shape and the experimental mode shape of the main beam is evaluated. If the correlation meets the standard and the difference between the calculated frequency and the experimental frequency does not exceed the predetermined standard, then the calculated mode shape of the branch beam is determined as the final fitted mode shape.

[0015] The main beam structure is a model structure consisting of elastic beams connected in series with concentrated mass from the aircraft shell, and the branch beam structure is a model structure consisting of elastic beams connected in series with concentrated mass from the internal load. The main beam structure and the branch beam structure together form the model structure of the aircraft system.

[0016] The spring connectors include linear springs and torsion springs, both of which are used to connect the main beam structure and the branch beam structure under the model structure.

[0017] The dynamic equations of the aircraft system are as follows:

[0018]

[0019] In the formula, M is the mass matrix, K is the stiffness matrix, F is the external force vector, and x and These are displacement and acceleration vectors;

[0020] The specific method for calculating the modal parameters is as follows:

[0021] The displacement of an n-degree-of-freedom system can be expressed by the modal displacements of each order as follows:

[0022] x=Φq (2)

[0023] In the formula, Φ is the mode shape matrix, and q = [q1 q2 … q n ] T q n It is the nth modal displacement;

[0024] Solve the simultaneous dynamic equations and the displacement of the n-degree-of-freedom system:

[0025]

[0026] To determine the natural frequencies and mode shapes of the aircraft system, the external forces in equation (3) are set to zero, and the generalized eigenvalue equations of the system are obtained:

[0027] (-ω 2 M+K)Φ=0 (4)

[0028] Solving equation (4) will yield the natural frequency parameters and mode parameters of the system.

[0029] The modal test specifically refers to the modal test conducted after the aircraft has completed final assembly. The purpose is to obtain the modal parameters of the aircraft structure in the lateral, longitudinal, and torsional directions, namely the modal frequencies, mode shapes, and damping ratios, to provide information for the design of the flight control system. The measurement point location information is arranged on the outer surface of the aircraft shell according to the principle that the geometric configuration reflects the highest-order mode shape to be tested. Since the modal test cannot attach measurement points to the internal load, it is impossible to obtain the mode shape of the load inside the aircraft. When the load is partially exposed to the outside, measurement points are placed on the surface as the basis for fitting the branch mode shape.

[0030] The spline interpolation function is specifically defined as follows: The branch beam is divided into N-1 intervals [(x1,x2),…,(x...] at N key locations. k ,x k+1 ),…,(x N-1 ,x N )],x k Let w be the axial coordinate of the k-th key position. k For the branch beam at x k The calculated mode shape at point X is achieved using N control points (x). k ,w k (k=1,2,…,N), the mode shape curve of the branch beam in each interval is represented as a cubic function: y k (x)=a k +b k x+c k x 2 +d k x 3 (k = 1, 2, ..., N-1), where y k (x) is the mode shape function of the branch beam in the k-th interval, (a k ,b k ,c k ,d k ) represents the constant term in the function, is the unknown to be solved, and x is the axial geometric coordinate;

[0031] The method for calculating the spline curve for each interval is as follows:

[0032] Solve for the 4 unknowns in each interval, for a total of 4(N-1) unknowns, based on the continuous (y) control points. k (x k ) = w k y k (x k+1 ) = w k+1 (k = 1, 2, ..., N-1), first derivative continuity at control points (y′) k (x k+1 )=y′ k+1 (x k+1 ), k=1,2,…,N-2), control point second derivative continuity (y″ k (x k+1 )=y″ k+1 (x k+1 ), k=1,2,…,N-2), two-end boundary constraints (y″′1(x1)=y″′2(x2), y′ N " -2 (x N-1 )=y′ N " -1 (x N Establish 4(N-1) equations and solve for 4(N-1) unknowns. Based on the obtained unknowns, fit the branch beam between each pair of adjacent key positions into a cubic spline curve.

[0033] The inertial balance requirements are specifically as follows:

[0034] The total inertial force and total inertial moment of the elastic vibration system consisting of the main beam and branch beams are zero, as follows:

[0035]

[0036] In the formula, J represents the number of positions for the main beam, and x j M is the axial coordinate of the j-th station of the main beam. j The quality of the j-th station of the main beam, W j The test vibration mode at the j-th station of the main beam; I represents the number of stations for the branch beam, x i Let m be the axial coordinate of the i-th station of the branch beam. i For the mass of the i-th station of the branch beam, w i The calculated vibration mode is for the i-th station of the branch beam.

[0037] By adjusting the control point w k The value is determined so that equation (5) holds, and the corresponding fitted branch mode shape under this process is recorded.

[0038] The Modal Confidence Criterion (MAC) is used to evaluate the geometric correlation between two mode shape vectors. The calculation formula is as follows:

[0039]

[0040] In the formula, Let be the two mode shape vectors whose correlation is to be determined. When the MAC value calculated by equation (6) is close to 1, the two mode shape vectors describe the mode shape of the same mode;

[0041] If the MAC value between the calculated mode shape and the fitted mode shape of the branch beam is above 80%, it is considered to have a high degree of correlation. If the MAC value between the calculated mode shape and the experimental mode shape of the main beam in the model is between 95% and 100%, it indicates that the two modes of the main beam are consistent, and the final fitted mode shape of the branch beam is determined.

[0042] An internal load-branched mode shape fitting system includes a modeling unit, a solution and model correction unit, and a comparison unit, wherein:

[0043] The modeling unit is used to build the aircraft system model, and simplifies the aircraft shell into a main beam structure, the internal load of the aircraft into a branch beam structure, and the connection structure between the aircraft shell and the internal load into a spring connector.

[0044] The solution and model correction unit establishes the dynamic equations and calculates the system modal parameters; based on the frequency of the experimental modal parameters and the main beam vibration mode parameters, the main beam structure is initially corrected, and the modal parameters are solved again; the axial coordinates of the largest calculated vibration mode of the branch beam and the axial coordinates of the connection between the branch beam and the main beam are extracted as key positions, the vibration mode of the branch beam at the key positions is set as control points, and spline interpolation function calculation is carried out. The size of the vibration mode of the control point is adjusted to generate a fitted branch beam vibration mode that meets the requirements of inertial equilibrium.

[0045] The comparison unit will evaluate the correlation between the calculated mode shape and the fitted mode shape of the branch beam. If the correlation is high, the calculated mode shape of the main beam will be recorded. If the correlation is low, the stiffness of the spring connection between the branch beam structure and the main beam structure in the calculation model will be corrected, and the modal parameters will be solved again. Then, the correlation between the calculated mode shape and the experimental mode shape of the main beam will be evaluated. If the correlation reaches 95% to 100% and the difference between the calculated frequency and the experimental frequency does not exceed 5%, the calculated mode shape of the branch beam will be determined as the final fitted mode shape. Otherwise, the unit will return to the step of correcting the main beam according to the experimental modal parameters until the calculated mode shape and the experimental mode shape of the main beam are consistent.

[0046] The advantages of this invention compared to the prior art are:

[0047] This invention provides a method and system for fitting branch mode shapes of internal loads. The aircraft shell is simplified as a main beam structure with elastic beams connected in series with concentrated mass, and the internal load is simplified as a branch beam structure with elastic beams connected in series with concentrated mass. The weak connection structure between the internal load and the aircraft is simplified to a linear spring and a torsion spring connecting the main beam and the branch beam. Modal parameters are calculated, and the main beam model is initially corrected based on modal test results. By repeatedly adjusting the calculated modal parameters in the calculation model, the final branch-fitted mode shape is obtained. This enables modal parameter identification under conditions where the internal load mode shape cannot be measured during aircraft modal testing, providing important support for improving the aircraft's attitude control design capabilities. Attached Figure Description

[0048] Figure 1 A schematic diagram of the internal load branch mode shape fitting process provided for the invention;

[0049] Figure 2 A schematic diagram comparing the first-order pitch bending mode and the experimental mode shape of the aircraft system provided for the invention;

[0050] Figure 3 A schematic diagram comparing the second-order pitch bending mode and the experimental mode shape of the aircraft system provided for the invention; Detailed Implementation

[0051] A method and system for fitting branch mode shapes of internal loads is disclosed. The aircraft shell is simplified as a main beam structure with elastic beams connected in series and concentrated mass, and the internal loads are simplified as branch beam structures with elastic beams connected in series and concentrated mass. The weak connection structure between the internal loads and the aircraft is simplified to linear springs and torsion springs connecting the main beam and the branch beams. System modal parameters are calculated, and the main beam structure is initially modified based on modal test results. By selecting key locations, using spline interpolation functions, and adjusting the mode shapes at key locations of the branch beams, fitted branch mode shapes that meet inertial equilibrium requirements are generated. Based on the correlation between the calculated mode shapes of the branch beams and the fitted mode shapes, the connection stiffness between the branch beams and the main beam is adjusted in the calculation model. The system modal parameters are iteratively calculated until the correlation meets the requirements, and the main beam mode shapes are recorded. The correlation between the calculated main beam mode shapes and the experimental mode shapes of the main beams is evaluated. Based on the correlation results, the final fitted branch mode shapes are obtained through iterative adjustments to complete the fitting process.

[0052] The internal load branch mode shape fitting system includes a modeling unit, a solution and model correction unit, and a comparison unit. According to the internal load branch mode shape fitting method, it performs modeling, model correction, parameter calculation, comparison of experimental results and calculation results, and final branch fitting mode shape verification, thus completing the complete fitting process of the branch fitting mode shape.

[0053] The following description, in conjunction with the accompanying drawings and preferred embodiments, provides further details:

[0054] In the current embodiment, a method for fitting the mode shape of the internal load branch is presented, which can realize the identification of modal parameters in the case of unconditional measurement of the mode shape of the internal load during the modal test of the aircraft, and provides important support for improving the attitude control design capability of the aircraft.

[0055] Step 1: Simplify the aircraft shell into a main beam structure with elastic beams connected in series and concentrated mass, and simplify the internal load into a branch beam structure with elastic beams connected in series and concentrated mass.

[0056] Step 2: Simplify the weak connection structure between the internal load and the aircraft into linear springs and torsion springs connecting the main beam and the branch beam;

[0057] Step 3: Establish the system dynamic equations, solve the homogeneous dynamic equations, and obtain the initial calculated modal parameters;

[0058] Step 4: In the modal test of the aircraft system, record the position information of the measuring points on the outer surface of the aircraft shell and obtain the test mode shape of the main beam (there are no measuring points for the part of the load installed inside the aircraft, that is, the mode shape of the load inside the aircraft cannot be obtained);

[0059] Step 5: Correct the main beam structure based on the test modal parameters (frequency, main beam mode shape) and resolve the modal parameters;

[0060] Step 6: Extract the axial coordinates of the branch beam with the largest calculated vibration mode and the axial coordinates of the connection between the branch beam and the main beam as key positions. Set the vibration mode of the branch beam at the key positions as control points and perform spline interpolation function calculation. Adjust the size of the control point vibration mode to generate a fitted branch beam vibration mode that satisfies the two conditions of zero total inertial force and zero total inertial moment of elastic vibration.

[0061] Step 7: Evaluate the correlation between the calculated mode shape and the fitted mode shape of the branch beam. If the MAC value is above 80%, record the calculated mode shape of the main beam. If the MAC value is below 80%, correct the stiffness of the spring connection between the branch beam structure and the main beam structure in the calculation model, and resolve the modal parameters.

[0062] Step 8: Evaluate the correlation between the calculated mode shape and the experimental mode shape of the main beam. If the MAC value is below 95%, return to step 5. If the MAC value is between 95% and 100%, and the difference between the calculated frequency and the experimental frequency is no more than 5%, then the calculated mode shape of the main beam is considered to be consistent with the experimental mode shape, and the calculated mode shape of the branch beam is determined to be the final fitted mode shape.

[0063] The built-in load-branched mode shape fitting system includes modeling units, solution and model correction units, and comparison units, among which:

[0064] The modeling unit is used to build the aircraft system model, and simplifies the aircraft shell into a main beam structure, the internal load of the aircraft into a branch beam structure, and the connection structure between the aircraft shell and the internal load into a spring connector.

[0065] The solution and model correction unit establishes the dynamic equations and calculates the system modal parameters; based on the experimental modal parameters (frequency, main beam mode shape), the main beam structure is initially corrected, and the modal parameters are solved again; the axial coordinates of the largest calculated mode shape of the branch beam and the axial coordinates of the connection between the branch beam and the main beam are extracted as key positions, the mode shapes of the branch beam at the key positions are set as control points, and spline interpolation function calculations are carried out. The mode shape size of the control point is adjusted to generate a fitted branch beam mode shape that meets the inertial equilibrium requirements;

[0066] The comparison unit will evaluate the correlation between the calculated mode shape and the fitted mode shape of the branch beam. If the correlation is high, the calculated mode shape of the main beam will be recorded. If the correlation is low, the stiffness of the spring connection between the branch beam structure and the main beam structure in the calculation model will be corrected, and the modal parameters will be solved again. Then, the correlation between the calculated mode shape and the experimental mode shape of the main beam will be evaluated. If the correlation reaches 95% to 100%, the calculated mode shape of the branch beam will be determined as the final fitted mode shape. Otherwise, the unit will return to the step of correcting the main beam according to the experimental modal parameters until the calculated mode shape and the experimental mode shape of the main beam are consistent.

[0067] like Figure 1 , Figure 2 , Figure 3 The figures shown are schematic diagrams comparing the calculated and experimental mode shapes for the first and second order pitch bending modes of the aircraft system. The system modal calculation model consists of an equivalent main beam for the aircraft shell and branch beams equivalent to the internal loads. Measuring points are installed on the outer surface of the aircraft shell during modal testing. The apex of the aircraft is taken as the zero point of the coordinate system, and the internal loads are connected to the aircraft compartments at 4.5m and 6.6m.

[0068] The specific parameters for this embodiment are as follows:

[0069] Taking the second-order bending mode as an example, the modal parameters were calculated through several iterations based on the first two-order results of the modal test, after correcting the stiffness of the main beam structure and the connection stiffness between the branch beam and the main beam. The results are compared with the modal test results, as shown in Table 1. In the initial model, the stiffness of the two connection points was set to 1e15 N / m. The main beam model was modified according to the test results, and the modal parameters were calculated. The vibration modes at the connection points between the branch beam and the main beam were extracted as control points, and the maximum vibration mode of the branch beam was adjusted. The vibration mode fitting of the branch beam that meets the inertial balance requirements was carried out (the inertial balance requirements are quite strict. In this example, the inertial force and inertial moment at each station were calculated according to formula (5). The inertial balance requirement is that it does not exceed 10% of the sum of all positive values). The first-order modal branch beam fitting vibration mode has a high correlation with the calculated vibration mode. The correlation between the calculated vibration mode of the main beam and the test vibration mode exceeds 95%. The first-order modal fitting results meet the requirements, but the second-order modal branch beam fitting vibration mode differs greatly from the calculated vibration mode. The first iteration was entered. In the first iteration, the stiffness of the connection between the branch beam and the main beam was changed to 1e8. The modal parameters were calculated using N / m, and the branch beam vibration modes were fitted. The first-order modal of the branch beam showed a high correlation with the calculated vibration mode, while the correlation between the calculated vibration mode and the experimental vibration mode of the main beam exceeded 95%. The first-order modal fitting results met the requirements. The correlation between the second-order modal of the branch beam and the calculated vibration mode was approximately 80%, while the correlation between the calculated vibration mode and the experimental vibration mode of the main beam was between 90% and 95%. The second iteration was then used to correct the main beam model. In the second iteration, the correlation between the branch beam's fitted vibration mode and the calculated vibration mode, as well as the correlation between the main beam's calculated vibration mode and the experimental vibration mode, both met the specified requirements, thus determining the branch beam fitted vibration modes for the first two modes.

[0070] Table 1

[0071]

[0072]

[0073] Although the present invention has been disclosed above with reference to preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art can make possible changes and modifications to the technical solutions of the present invention by utilizing the methods and techniques disclosed above without departing from the spirit and scope of the present invention. Therefore, any simple modifications, equivalent changes and alterations made to the above embodiments based on the technical essence of the present invention without departing from the content of the technical solutions of the present invention shall fall within the protection scope of the technical solutions of the present invention.

[0074] The contents not described in detail in this specification are common knowledge to those skilled in the art.

Claims

1. A method for fitting mode shapes of internally loaded branch modes, characterized in that... include: The aircraft shell is simplified into a main beam structure, and the internal load of the aircraft is simplified into a branch beam structure. The connection structure between the aircraft shell and the internal load is simplified to an equivalent stiffness spring connector; Establish the system dynamic equations, solve the homogeneous dynamic equations, and obtain the initial calculated modal parameters; Record the location information of measuring points on the outer surface of the aircraft shell during the modal test of the aircraft system, and obtain the test vibration mode of the main beam; The main beam structure was modified based on the frequency and mode shape parameters of the experimental modal parameters, and the modal parameters were re-solved. The axial coordinates of the branch beam with the largest calculated vibration mode and the axial coordinates of the connection between the branch beam and the main beam are extracted as key positions. The vibration modes of the branch beam at the key positions are set as control points and spline interpolation function calculations are carried out. The vibration mode sizes of the control points are adjusted to generate the fitted branch beam vibration mode that meets the requirements of inertial equilibrium. The correlation between the calculated mode shape and the fitted mode shape of the branch beam is evaluated. If the correlation is higher than the preset standard, the calculated mode shape of the main beam is recorded. If the correlation is lower than the preset standard, the stiffness of the spring connection between the branch beam structure and the main beam structure in the calculation model is corrected, and the test modal parameters are solved again. The correlation between the calculated mode shape and the experimental mode shape of the main beam is evaluated. If the correlation meets the standard and the difference between the calculated frequency and the experimental frequency does not exceed the predetermined standard, then the calculated mode shape of the branch beam is determined as the final fitted mode shape.

2. The method for fitting mode shapes of internally loaded branch modes according to claim 1, characterized in that: The main beam structure is a model structure consisting of elastic beams connected in series with concentrated mass from the aircraft shell, and the branch beam structure is a model structure consisting of elastic beams connected in series with concentrated mass from the internal load. The main beam structure and the branch beam structure together form the model structure of the aircraft system.

3. The method for fitting mode shapes of internally loaded branch modes according to claim 2, characterized in that: The spring connectors include linear springs and torsion springs, both of which are used to connect the main beam structure and the branch beam structure under the model structure.

4. The method for fitting mode shapes of internally loaded branch modes according to claim 3, characterized in that: The dynamic equations of the aircraft system are as follows: (1) In the formula, For the quality matrix, Here is the stiffness matrix. It is an external force vector. and These are displacement and acceleration vectors; The specific method for calculating the modal parameters is as follows: The displacements of a system with degrees of freedom can be expressed by the modal displacements of each order as follows: (2) In the formula, For the mode shape matrix, , It is the first First-order modal displacement; Simultaneous dynamic equations and Displacement of the system with degrees of freedom: (3) To determine the natural frequencies and mode shapes of the aircraft system, the external forces in equation (3) are set to zero, and the generalized eigenvalue equations of the system are obtained: (4) Solving equation (4) yields the natural frequency parameters and mode parameters of the system.

5. The method for fitting mode shapes of internally loaded branch modes according to claim 4, characterized in that: The modal test specifically refers to the modal test conducted after the aircraft has completed final assembly. The purpose is to obtain the modal parameters of the aircraft structure in the lateral, longitudinal, and torsional directions, namely the modal frequencies, mode shapes, and damping ratios, to provide information for the design of the flight control system. The measurement point location information is arranged on the outer surface of the aircraft shell according to the principle that the geometric configuration reflects the highest-order mode shape to be tested. Since the modal test cannot attach measurement points to the internal load, it is impossible to obtain the mode shape of the load inside the aircraft. When the load is partially exposed to the outside, measurement points are placed on the surface as the basis for fitting the branch mode shape.

6. The method for fitting mode shapes of internally loaded branch modes according to claim 5, characterized in that: The spline interpolation function is specifically: The branch beam is divided into several key locations. each interval , For the first Axial coordinates of key locations, For branch beams in The calculated mode shape at that location is obtained by using Control points ( The mode shape curve of the branch beam in each interval is represented as a cubic function: ( In the formula For the branch beam in the first Mode shape function for each interval, Let be the constant term in the function, and be the unknown variable to be solved. For axial geometric coordinates; The method for calculating the spline curve for each interval is as follows: Solve for the four unknowns in each interval, totaling One unknown, based on the continuous control points ( , , ), control point first derivative continuity ( , ), control point second derivative continuity ( , ), boundary constraints at both ends ( , ),Establish Solving the equations yields... Given several unknowns, the branch beams between each pair of adjacent key locations are fitted with cubic spline curves based on the obtained unknowns.

7. The method for fitting mode shapes of internally loaded branch modes according to claim 6, characterized in that: The inertial balance requirements are specifically as follows: The total inertial force and total inertial moment of the elastic vibration system consisting of the main beam and branch beams are zero, as follows: (5) In the formula, This indicates the number of positions for the main beam. Main beam The axial coordinates of the station. Main beam The quality of the position. Main beam Test vibration modes at the station location; This indicates the number of positions for the branch beam. For the branch beam The axial coordinates of the station. For the branch beam The quality of the position. For the branch beam Calculation of vibration modes based on station position; By adjusting the control points The value is determined so that equation (5) holds, and the corresponding fitted branch mode shape under this process is recorded.

8. The method for fitting mode shapes of internally loaded branch modes according to claim 7, characterized in that: The Modal Confidence Criterion (MAC) is used to evaluate the geometric correlation between two mode shape vectors. The calculation formula is as follows: (6) In the formula, , Let be the two mode shape vectors whose correlation is to be determined; when the MAC value calculated by equation (6) is close to 1, the two mode shape vectors describe the mode shape of the same mode; If the MAC value between the calculated mode shape and the fitted mode shape of the branch beam is above 80%, it is considered to have a high degree of correlation. If the MAC value between the calculated mode shape and the experimental mode shape of the main beam in the model is between 95% and 100%, it indicates that the two mode shapes of the main beam are consistent, and the final fitted mode shape of the branch beam is determined.

9. A built-in load-branched mode shape fitting system, characterized in that: It includes modeling units, solution and model correction units, and comparison units, among which: The modeling unit is used to build the aircraft system model, and simplifies the aircraft shell into a main beam structure, the internal load of the aircraft into a branch beam structure, and the connection structure between the aircraft shell and the internal load into a spring connector. The solution and model correction unit establishes the dynamic equations and calculates the system modal parameters; based on the frequency of the experimental modal parameters and the main beam vibration mode parameters, the main beam structure is initially corrected, and the modal parameters are solved again; the axial coordinates of the largest calculated vibration mode of the branch beam and the axial coordinates of the connection between the branch beam and the main beam are extracted as key positions, the vibration mode of the branch beam at the key positions is set as control points, and spline interpolation function calculation is carried out. The size of the vibration mode of the control point is adjusted to generate a fitted branch beam vibration mode that meets the requirements of inertial equilibrium. The comparison unit will evaluate the correlation between the calculated mode shape and the fitted mode shape of the branch beam. If the correlation is high, the calculated mode shape of the main beam will be recorded. If the correlation is low, the stiffness of the spring connection between the branch beam structure and the main beam structure in the calculation model will be corrected, and the modal parameters will be solved again. Then, the correlation between the calculated mode shape and the experimental mode shape of the main beam will be evaluated. If the correlation reaches 95%~100% and the difference between the calculated frequency and the experimental frequency does not exceed 5%, the calculated mode shape of the branch beam will be determined as the final fitted mode shape. Otherwise, the unit will return to the step of correcting the main beam according to the experimental modal parameters until the calculated mode shape and the experimental mode shape of the main beam are consistent.

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