High-frequency modal intensive finite element model correction method based on load driving

Abstract

The invention discloses a high-frequency modal intensive finite element model correction method based on load driving, and aims to correct a system matrix by screening dominant modals under specified working conditions and improve the dynamic characteristic precision of a finite element model. The method comprises a load-driven modal selection strategy and a finite element model correction method based on matrix approximation. Firstly, a load-driven modal selection method is utilized to quantify the contribution degree of each order of modal to a current load, and a dominant modal is screened out for model correction. And then directly optimizing a mass matrix and a stiffness matrix through a matrix approximation method, so that the dynamic characteristics of the corrected model under a specified working condition are highly consistent with experimental data. And finally, through case verification of the helicopter tail beam structure, the effectiveness and practicability of the method are proved.

Description

Technical Field

[0001] The present invention relates to the field of finite element analysis, and in particular to a load-driven high-frequency modal intensive finite element model correction method. Background Art

[0002] Finite element analysis is an indispensable tool in modern engineering design and is widely used in many fields such as structural mechanics, thermodynamics, and fluid mechanics. However, due to the existence of modeling errors, parameter errors, and order errors, there is often a deviation between the dynamic characteristics of the finite element model and the actual structure. Therefore, finite element model correction becomes a key step to improve model accuracy and ensure the reliability of analysis results. Traditional modal selection methods are usually based on modal truncation methods, which simply select low-order modes as correction inputs. However, this method may not accurately reflect the key dynamic characteristics of the model under a specific actual working condition, and is not effective for correcting some finite element models working under relatively fixed working conditions. Summary of the Invention

[0003] The present invention provides a load-driven high-frequency modal-intensive finite element model correction method, which aims to improve the dynamic characteristics accuracy of the finite element model under specified working conditions by optimizing the system matrix and screening the dominant modes of the model under specified working conditions.

[0004] In order to achieve the above-mentioned object of the invention, the technical solution adopted by the present invention is:

[0005] A load-driven high-frequency modal-intensive finite element model updating method is provided, comprising the following steps:

[0006] First, a load-driven mode selection method is used to quantify the contribution of each mode of the structural finite element model to the structural response under a specified load, and the first few modes with the highest contribution are selected as the dominant modes.

[0007] Then, through the finite element model correction method based on matrix approximation, the original mass matrix and stiffness matrix of the system are directly adjusted so that the response results of the corrected finite element model under the specified load are consistent with the experimental data of the actual structure under the same load, and finally the correction of the structural finite element model is completed.

[0008] Furthermore, the load-driven mode selection method includes the following specific steps:

[0009] S11: Solve the first n modes of the finite element model and obtain the matrix Φ composed of n-order orthogonal normalized vibration mode column vectors m×n :

[0010]

[0011] m is the number of degrees of freedom of the model element nodes;

[0012] S12: Ignore the inertia and damping terms, decompose the excitation force under the actual working condition into a six-degree-of-freedom equivalent harmonic load, and then simplify the equivalent harmonic load into a static load acting on the structure. The static load is the amplitude of the equivalent harmonic load. Solve the finite element model under the static load F m×1 Static displacement under action △ m×1 ∈R m×1 :

[0013]

[0014] K is the elastic modulus;

[0015] S13: The static displacement △ m×1 Projected into the modal space, we get the generalized coordinate coefficients p of the first n modes. i The vector P n×1 , P n×1 ∈R n×1 :

[0016]

[0017] Coordinate coefficient p i p i The subscript i in represents the i-th mode;

[0018] S14: According to the absolute value of the generalized coordinate coefficient, select the first-order mode with the largest contribution as the dominant mode. Suppose the absolute values ​​of the generalized coordinate coefficients of each order mode are ranked from large to small as follows:

[0019] ∣p i ∣>∣p j ∣>∣p k ∣>∣p l ∣>…∣p m ∣>∣p n ∣

[0020] Then according to the first l coefficients p in the sort i The subscript of Φ is selected m×n The corresponding vibration mode column vectors in form a new matrix Φ m×l For model correction, denoted by Φ m×l .

[0021] Furthermore, the coordinate coefficient p i The absolute value represents the contribution of the current mode to the load response. The larger the absolute value, the greater the contribution.

[0022] Furthermore, the finite element model correction method based on matrix approximation includes the following specific steps:

[0023] S21: Modify the initial mass matrix M of the finite element model A , by minimizing the objective function And satisfy the first constraint, calculate the correction amount of the mass matrix:

[0024] ΔM=-M A Φ(Φ T M A Φ) -1 (Φ T M A Φ-I)(Φ T M A Φ) -1 Φ T M A

[0025] The corrected mass matrix is:

[0026] M=M A +△M;

[0027] S22: Modify the initial stiffness matrix K of the finite element model A , by minimizing the objective function And satisfy the second constraint condition, calculate the correction amount of the stiffness matrix: ΔK = -K A ΦΦ T M A -M A ΦΦ T K A +M A ΦΦ T K A ΦΦ T M A +M A ΦΛΦ T M A The corrected mass matrix is:

[0028] K=K A +△K

[0029] Where Λ is the diagonal matrix of the squares of the measured natural frequencies.

[0030] Furthermore, the first constraint condition is Φ T MΦ=I, the second constraint condition is KΦ=MΦΛ and K T =K.

[0031] Beneficial effects:

[0032] Finite element model modification does not pursue absolute accuracy of all modes. Instead, it balances computational efficiency, engineering requirements, and actual errors, and selects modes for modification based on load characteristics, allowing for greater focus on the key dynamic characteristics of the model under a specific actual working condition.

[0033] 1. Finite element model modification based on load-driven mode selection focuses on the key dynamic characteristics of the actual working conditions, avoiding redundant adjustments to irrelevant modes and preventing the introduction of new errors.

[0034] 2. Through the load-driven modal selection algorithm, modal parameters related to the load are preferentially selected for finite element model modification, which not only improves the model reliability under the target working conditions but also significantly reduces the computational cost, taking into account both accuracy and efficiency in engineering practice. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Figure 1 Flowchart of the finite element model updating method based on load-driven mode selection;

[0036] Figure 2 Schematic diagram of the beam model and the direction and position of the exciting force;

[0037] Figure 3 Simply take the first six modes for the response curve of the modified model under the specified working conditions;

[0038] Figure 4 The modes selected according to the method of the present invention are used for the response curve diagram of the modified model under the specified working conditions. DETAILED DESCRIPTION

[0039] In order to facilitate understanding by those skilled in the art, the present invention will be further described below with reference to embodiments and drawings. The contents mentioned in the embodiments are not intended to limit the present invention.

[0040] The technical solution adopted in the present invention is:

[0041] This application provides a load-driven high-frequency modal-intensive finite element model correction method, which includes the following main steps:

[0042] First, a load-driven modal selection method is used to quantify the contribution of each mode of the structural finite element model to the structural response under a specified load. The top modes with the highest contribution are selected as the dominant modes. Then, a finite element model correction method based on matrix approximation is used to directly adjust the system's original mass and stiffness matrices. This ensures that the response of the corrected finite element model under a specified load matches the experimental data of the actual structure under the same load, thus completing the correction of the structural finite element model.

[0043] Furthermore, the load-driven mode selection method includes the following specific steps:

[0044] S11: Solve the first n modes of the target finite element model and obtain the matrix Φ composed of n-order orthogonal normalized vibration mode column vectors m×n :

[0045]

[0046] m is the number of degrees of freedom of the model element nodes.

[0047] S12: Ignore the inertia and damping terms, decompose the excitation force under the actual working condition into a six-degree-of-freedom equivalent harmonic load, and then simplify the equivalent harmonic load into a static load acting on the structure. The magnitude of the static load is the amplitude of the equivalent harmonic load. Solve the model under the static load F m×1 Static displacement under action △ m×1 ∈R m×1 :

[0048]

[0049] K is the elastic modulus;

[0050] S13: The static displacement △ m×1 Projected into the modal space, we get the generalized coordinate coefficients p of the first n modes. i The vector P n×1 , P n×1 ∈R n×1 :

[0051]

[0052] Coefficient p i The subscript i represents the i-th order mode, and the absolute value of the coefficient represents the contribution of the current mode to the load response. The larger the absolute value, the greater the contribution.

[0053] S14: According to the absolute value of the generalized coordinate coefficient, select the first-order mode with the largest contribution as the dominant mode. Suppose the absolute values ​​of the generalized coordinate coefficients of each order mode are ranked from large to small as follows:

[0054] ∣p i ∣>∣p j ∣>∣p k ∣>∣p l ∣>…∣p m ∣>∣p n ∣

[0055] Then according to the first l coefficients p in the sort i The subscript of Φ is selected m×n The corresponding vibration mode column vectors in form a new matrix Φ m×l For model correction, denoted by Φ m×l .

[0056] Furthermore, the finite element model correction method based on matrix approximation includes the following specific steps:

[0057] S21: Modify the initial mass matrix M of the finite element model A , by minimizing the objective function

[0058] And satisfy the constraint Φ T MΦ=I, calculate the correction of mass matrix:

[0059] ΔM=-M A Φ(Φ T M A Φ) -1 (Φ T M A Φ-I)(Φ T M A Φ) -1 Φ T M A

[0060] The corrected mass matrix is:

[0061] M=M A +△M;

[0062] S22: Modify the initial stiffness matrix K of the finite element model A , by minimizing the objective function And satisfy the constraints KΦ=MΦΛ and K T =K, calculate the correction amount of the stiffness matrix:

[0063] ΔK=-K A ΦΦ T M A -M A ΦΦ T K A +M A ΦΦ T K A ΦΦ T M A +M A ΦΛΦ T M A The corrected mass matrix is:

[0064] K=K A +△K

[0065] Where Λ is the diagonal matrix of the squares of the measured natural frequencies.

[0066] In order to verify the effectiveness of the proposed method, this paper takes a beam structure as an example. Figure 2 , conduct a case analysis of modal selection and finite element model modification under a certain actual working condition. Perform modal analysis and transient analysis verification on the modified beam structure model.

[0067] Taking an actual working condition of the beam structure as an example, firstly, the first 30 modal analyses of the beam model are performed in the finite element analysis software. Figure 2 When the six-degree-of-freedom equivalent harmonic load is in the direction and position shown in , the amplitude of the six-degree-of-freedom equivalent harmonic load generated is Fx=86.24N, Fy=68.77N, Fz=519.88N, Mx=36.35N·m, My=92.11N·m, and Mz=91.72N·m. It is taken as a static load and brought into the load-driven modal selection method proposed in the present invention for calculation. It can be obtained that the 3rd, 5th, 7th, 11th, 24th, and 26th order modes should be used for correction at this time, and then the first 6 order modes are simply taken for correction to obtain two corrected finite element models.

[0068] The exciting force is applied to the original node of the two modified finite element models, and the fitting of the response curve of the node in the six degrees of freedom direction with the response curve measured in the actual test is observed. Figure 3 In order to simply take the first six modes for the response curve of the modified model under the specified working conditions, it can be seen from the figure that δ x , δ y and θ z The response curves of the revised model and the original model have a poor fit in three degrees of freedom; Figure 4 The response curve of the model selected by the method of the present invention for the modified model under the specified working condition is shown in the figure. x Except for the insufficient fit between the response curve of the modified model and the original model in the direction of the degree of freedom, the fit is very good in the other degrees of freedom.

[0069] The results show that a load-driven high-frequency modal-intensive finite element model correction method has better correction effect than the traditional method of simply selecting low-order modes for correction.

[0070] The present invention has many specific application paths. The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements can be made without departing from the principles of the present invention. These improvements should also be considered as the scope of protection of the present invention.

Claims

1. A load-driven high-frequency modal intensive finite element model correction method, characterized in that: The following steps are involved: First, a load-driven mode selection method is used to quantify the contribution of each mode of the structural finite element model to the structural response under a specified load, and the first few modes with the highest contribution are selected as the dominant modes. Then, through the finite element model correction method based on matrix approximation, the original mass matrix and stiffness matrix of the system are directly adjusted so that the response results of the corrected finite element model under the specified load are consistent with the experimental data of the actual structure under the same load, and finally the correction of the structural finite element model is completed.

2. The load-driven high-frequency modal intensive finite element model correction method according to claim 1, characterized in that: The load-driven mode selection method includes the following specific steps: S11: Solve the first n modes of the finite element model and obtain the matrix Φ composed of n-order orthogonal normalized vibration mode column vectors m×n : m is the number of degrees of freedom of the model element nodes; S12: Ignore the inertia and damping terms, decompose the excitation force under the actual working condition into a six-degree-of-freedom equivalent harmonic load, and then simplify the equivalent harmonic load into a static load acting on the structure. The static load is the amplitude of the equivalent harmonic load. Solve the finite element model under the static load F m×1 Static displacement under action △ m×1 ∈R m×1 : K is the elastic modulus; S13: The static displacement △ m×1 Projected into the modal space, we get the generalized coordinate coefficients p of the first n modes. i The vector P n×1 , P n×1 ∈R n×1 : Coordinate coefficient p i p i The subscript i in represents the i-th mode; S14: According to the absolute value of the generalized coordinate coefficient, select the first-order mode with the largest contribution as the dominant mode. Suppose the absolute values ​​of the generalized coordinate coefficients of each order mode are ranked from large to small as follows: ∣p i ∣>∣p j ∣>∣p k ∣>∣p l ∣>…∣p m ∣>∣p n ∣ Then according to the first l coefficients p in the sort i The subscript of Φ is selected m×n The corresponding vibration mode column vectors in form a new matrix Φ m×l For model correction, denoted by Φ m×l .

3. The load-driven high-frequency modal intensive finite element model correction method according to claim 1, characterized in that: The coordinate coefficient p i The absolute value represents the contribution of the current mode to the load response. The larger the absolute value, the greater the contribution.

4. The load-driven high-frequency modal intensive finite element model correction method according to claim 1, characterized in that: The finite element model correction method based on matrix approximation includes the following specific steps: S21: Modify the initial mass matrix M of the finite element model A , by minimizing the objective function And satisfy the first constraint, calculate the correction amount of the mass matrix: ΔM=-M A F(F T M A F) -1 (F T M A Φ-I)(Φ T M A F) -1 F T M A The corrected mass matrix is: M=M A +△M; S22: Modify the initial stiffness matrix K of the finite element model A , by minimizing the objective function And satisfy the second constraint, calculate the correction of the stiffness matrix quantity: ΔK=-K A ΦΦ T M A -M A ΦΦ T K A +M A ΦΦ T K A ΦΦ T M A +M A ΦΛΦ T M A The corrected mass matrix is: K=K A +△K Where Λ is the diagonal matrix of the squares of the measured natural frequencies.

5. A high-frequency modal intensive finite element based on load drive according to claim 1 The metamodel modification method is characterized by: The first constraint condition is Φ T MΦ=I, The second constraint condition is KΦ=MΦΛ and K T =K.

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