Structural dynamic stiffness analysis method based on impedance coupling of substructure by frequency response function condensation

Abstract

The present application relates to the technical field of data processing, and more particularly to a structure dynamic stiffness analysis method based on frequency response function condensation substructure impedance coupling, comprising: obtaining node information, element connection relationship and material properties based on a global finite element model; defining a focus point set, a boundary point set and an internal point set according to the element connection relationship; obtaining block system matrices by blocking the global mass matrix, the stiffness matrix and the damping matrix; introducing an inertia compensation term to construct a transformation matrix based on the block system matrices and the highest analysis frequency of the system, condensing the system matrix to only retain the degrees of freedom of the focus point set and the boundary point set, and calculating the dynamic stiffness matrix in the frequency domain; and extracting the dynamic stiffness results of the focus point set by inverting the dynamic stiffness matrix, which significantly reduces the calculation scale through system matrix condensation, while strictly retaining the inertia effect and stiffness coupling effect of the far-field structure, effectively solving the contradiction between the low computational efficiency of the global model and the precision distortion of the local substructure method.

Description

Technical Field

[0001] This invention relates to the field of data processing technology, and in particular to a method for analyzing the dynamic stiffness of structures based on the impedance coupling of frequency response function condensation substructures. Background Technology

[0002] Frequency response function-based substructure impedance coupling is an analytical technique based on the dynamic substructure method, designed to efficiently predict the vibration characteristics of complex assemblies. Its principle involves decomposing the overall structure into several substructures, using the frequency response function to characterize the dynamic response behavior of each substructure in the frequency domain; impedance coupling, through the interfacial forces and motion coordination, accurately describes the energy transfer and interaction between substructures. The condensation process reduces the system's degrees of freedom by lowering the order of modes or physical coordinates, thereby improving solution efficiency while maintaining computational accuracy. This makes the method applicable to the dynamic design and optimization of large-scale engineering systems such as automobile bodies or wind turbine blades.

[0003] Dynamic stiffness analysis aims to assess the stiffness characteristics of a structure under dynamic load excitation. The dynamic stiffness value exhibits nonlinear behavior with frequency, thus significantly impacting the structure's vibration response and dynamic stability. Existing analysis procedures typically rely on numerical simulation methods, such as finite element simulation combined with experimental modal analysis, to quantify the dynamic stiffness distribution by identifying the structure's natural frequencies and mode shapes. This analysis allows engineers to predict the structure's dynamic performance under operating conditions, thereby optimizing design schemes to suppress resonance risks and enhance overall reliability.

[0004] Existing structural dynamic stiffness analysis techniques suffer from the following pain points: While global finite element model frequency response analysis methods can provide high-precision results, their computational efficiency is extremely low. This is because a full-band scan of the complete large-scale model is required for solution, involving response calculations for all degrees of freedom, resulting in enormous computational resource consumption and excessive time consumption. Local substructure separation methods, while significantly improving computational speed, suffer from severe accuracy distortion. This is because the artificial constraints applied at the cutting boundaries (such as fixed or free) do not match the complex dynamic boundary conditions in the actual assembly, completely ignoring the inertial and stiffness coupling effects of the far-field structure. Consequently, the calculation results cannot accurately reflect the dynamic impedance characteristics of the connection points. For example, in the dynamic stiffness analysis of automotive subframe mounting points, the global method may require several days to complete a single analysis, making it unsuitable for rapid design optimization cycles. The local method, due to simplified boundary conditions, results in overly rigid or flexible results, lacking engineering reliability. This creates an inherent contradiction in engineering practice where high accuracy and high efficiency are mutually exclusive. Summary of the Invention

[0005] To address the shortcomings of existing technologies, this invention provides a structural dynamic stiffness analysis method based on frequency response function condensation substructure impedance coupling. This invention solves the technical problem that existing dynamic stiffness analysis methods cannot simultaneously achieve high-precision and high-efficiency analysis in engineering practice due to the inherent contradiction between low global model calculation efficiency and accuracy distortion of local substructure methods.

[0006] To solve the above-mentioned technical problems, the specific contents of the present invention are as follows:

[0007] The present invention provides a structural dynamic stiffness analysis method based on frequency response function condensation substructure impedance coupling, comprising:

[0008] Step 1: Based on the global finite element model, obtain the node information, element connection relationships, and material properties of the global finite element model;

[0009] Step 2: Based on the element connection relationship, define the set of points of interest for which dynamic stiffness needs to be calculated, the set of boundary points coupled with the dynamics of the set of points of interest, and the set of internal points formed by the remaining nodes from all nodes of the global finite element model; wherein, the set of points of interest, the set of boundary points, and the set of internal points together constitute the complete node set of the global finite element model.

[0010] Step 3: Based on the defined set of points of interest, set of boundary points, and set of internal points, divide the global mass matrix, stiffness matrix, and damping matrix into blocks to obtain the block system matrix corresponding to the set of points of interest, set of boundary points, and set of internal points.

[0011] Step 4: Based on the node dynamics relationships represented by the block system matrix and the system's highest analysis frequency, an inertial compensation term related to the highest analysis frequency is introduced. This inertial compensation term is a global approximate inertial compensation operator, and its form is: Where I is the identity matrix, and Λ is a diagonal matrix with elements w 2 max The function is α, which is an empirical coefficient. A transformation matrix including an inertial compensation term is constructed. The original system matrix is ​​condensed to retain only the degrees of freedom of the set of points of interest and the set of boundary points using the transformation matrix. The dynamic stiffness matrix of the system in the frequency domain is calculated with only the degrees of freedom of the set of points of interest and the set of boundary points retained.

[0012] Step 5: Perform an inversion operation on the dynamic stiffness matrix of the polycondensation system calculated in Step 4. Extract the submatrix corresponding to the set of concerns from the inverted total impedance matrix as the dynamic stiffness result of the set of concerns, and output the dynamic stiffness result of the set of concerns.

[0013] Furthermore, in the structural dynamic stiffness analysis method based on frequency response function condensation substructure impedance coupling of the present invention, step 2 includes:

[0014] Step 21: Define the nodes or groups of nodes whose dynamic stiffness needs to be calculated as the set of points of interest;

[0015] Step 22: Based on the defined set of concerns, select nodes on units directly connected to the set of concerns that do not belong to the set of concerns, and classify them into the boundary point set;

[0016] Step 23: Based on the boundary point set obtained in Step 22, recursively select new nodes on the cells connected to the nodes in this boundary point set that have not yet been included in any node set, and expand the boundary point set.

[0017] Step 24: After defining the focus set and boundary point set, define all nodes in the global finite element model that are not included in the above node sets as internal point sets.

[0018] Furthermore, in the structural dynamic stiffness analysis method based on frequency response function condensation substructure impedance coupling of the present invention, step 4 includes:

[0019] Step 41: Based on the block system matrix obtained in Step 3, establish the displacement transformation relationship between the set of points of interest, the set of boundary points, and the set of internal points;

[0020] Step 42: Based on the displacement transformation relationship and the highest analysis frequency of the system in Step 4, an inertial compensation term related to the highest analysis frequency is introduced to construct the transformation matrix;

[0021] Step 43: Using the transformation matrix constructed in step 42, perform a reduction operation on the block system matrix obtained in step 3;

[0022] Step 44: Through the shrinking operation, obtain the reduced-order system matrix that includes only the degrees of freedom of the set of points of interest and the set of boundary points.

[0023] Furthermore, in the structural dynamic stiffness analysis method based on frequency response function condensation substructure impedance coupling of the present invention, step 42 includes:

[0024] Step 421: Obtain the system's highest analysis frequency;

[0025] Step 422: Using the highest analysis frequency as the variable, calculate the relationship using the coefficients stored in the system beforehand, and solve for the inertia compensation coefficient;

[0026] Step 423: Construct a diagonal matrix as the inertia compensation term using the inertia compensation coefficient;

[0027] Step 424: Add the inertia compensation term to the transformation matrix constructed based on the displacement transformation relationship.

[0028] Furthermore, in the structural dynamic stiffness analysis method based on frequency response function condensation substructure impedance coupling of the present invention, step 5 includes:

[0029] Step 51: Set the frequency scan range and frequency step size with the highest analysis frequency of the system in Step 4 as the upper limit;

[0030] Step 52: Traverse each frequency point within the frequency scanning range, and calculate the system impedance matrix value at the current frequency point based on the dynamic stiffness matrix of the condensation system obtained in Step 4.

[0031] Step 53: Store each frequency point and its corresponding system impedance matrix value;

[0032] Step 54: Combine the system impedance matrix values ​​at all frequency points into a function of frequency, and use this as the result of the calculation of the condensation system impedance matrix.

[0033] Furthermore, in the structural dynamic stiffness analysis method based on frequency response function condensation substructure impedance coupling of the present invention, step 52 includes:

[0034] Read the current frequency point;

[0035] Based on the dynamic stiffness matrix of the polycondensation system obtained in step 4 and the current frequency point, calculate the system impedance matrix at the current frequency point.

[0036] Perform the inversion operation on the system impedance matrix;

[0037] From the matrix obtained after inversion, extract the values ​​of the submatrix corresponding to the set of concerns, and use them as the dynamic stiffness values ​​of the set of concerns at the current frequency.

[0038] Furthermore, in the structural dynamic stiffness analysis method based on frequency response function condensation substructure impedance coupling of the present invention, step 5 further includes:

[0039] Receive the dynamic stiffness results of the set of concerns output in step 5;

[0040] Convert dynamic stiffness results into graphics drawing instructions;

[0041] Execute the graphics drawing command to generate a curve showing the change of dynamic stiffness with frequency;

[0042] The graphs and dynamic stiffness results are transmitted to the user interface for display.

[0043] Furthermore, the structural dynamic stiffness analysis method based on frequency response function condensation substructure impedance coupling of the present invention also includes:

[0044] Based on the reduced-order system matrix obtained in step 4, modal verification is performed;

[0045] Modal parameters are extracted based on the reduced-order system matrix.

[0046] The modal parameters are compared with the modal parameters of the global finite element model;

[0047] Based on the comparison results, the modal confidence index is calculated;

[0048] A verification report is output based on the modal confidence index.

[0049] Furthermore, the structural dynamic stiffness analysis method based on frequency response function condensation substructure impedance coupling of the present invention also includes:

[0050] Based on the global finite element model and the definition method in step 2, multiple concerns are automatically processed.

[0051] Based on the global finite element model, multiple sets of points of interest for which dynamic stiffness needs to be calculated are defined in batches;

[0052] For each set of concerns, the shrinking process in step 4 and the dynamic stiffness extraction process in step 5 are executed in parallel to obtain the dynamic stiffness result of each set of concerns. The shrinking process in step 4 is to use a transformation matrix to shrink the original system matrix to retain only the degrees of freedom of the set of concerns and the boundary point set. The dynamic stiffness extraction process in step 5 is to perform an inversion operation on the shrinking system dynamic stiffness matrix calculated in step 4, extract the sub-matrix corresponding to the set of concerns from the inverted total impedance matrix, use it as the dynamic stiffness result of the set of concerns, and output the dynamic stiffness result of the set of concerns.

[0053] Collect the dynamic stiffness results for all sets of concerns;

[0054] A comprehensive analysis report is generated based on the collected dynamic stiffness results.

[0055] Furthermore, the structural dynamic stiffness analysis method based on frequency response function condensation substructure impedance coupling of the present invention also includes:

[0056] Integrate structural dynamic stiffness analysis methods into the CAE software platform;

[0057] Receives global finite element model files or parameters input by the user through a graphical user interface;

[0058] Call the finite element solver to parse the user-input model file or parameters and obtain the node information, element connection relationships and material properties of the global finite element model;

[0059] Based on the obtained node information, unit connection relationships, and material properties, proceed with steps 2 to 5;

[0060] The dynamic stiffness results of the focus set output in step 5 are transmitted to the user interface for visualization.

[0061] Beneficial effects of this invention;

[0062] This invention presents a structural dynamic stiffness analysis method based on frequency response function-based condensation of substructure impedance coupling. By defining sets of interest points, boundary points, and internal points, the global mass matrix, stiffness matrix, and damping matrix are divided into blocks. An inertial compensation term related to the highest analysis frequency of the system is introduced to construct a transformation matrix, thereby condensing the system matrix to retain only the degrees of freedom of the sets of interest points and boundary points. This significantly reduces the computational scale and improves analysis efficiency. The condensation process strictly preserves the inertial effects, stiffness coupling effects, and damping effects of the far-field structure, ensuring that the dynamic stiffness results of the sets of interest points extracted from the dynamic stiffness matrix of the condensed system are highly consistent with the global finite element model. This solves the accuracy distortion problem caused by the simplification of boundary conditions in the local substructure method, while avoiding computational redundancy in full-band scanning of the global model. The method supports automated processing of multiple sets of interest points and is integrated into CAE software platforms, providing an efficient and high-precision dynamic stiffness analysis solution for engineering practice. Attached Figure Description

[0063] To more clearly illustrate the technical solution of the present invention, the drawings used in the embodiments will be briefly introduced below. Obviously, for those skilled in the art, other drawings can be obtained based on the drawings without creative effort.

[0064] Figure 1 This is a flowchart of a structural dynamic stiffness analysis method based on frequency response function condensation substructure impedance coupling provided in an embodiment of the present invention.

[0065] Figure 2 This is a schematic diagram of the b-set node set definition method for the structural dynamic stiffness analysis method based on frequency response function condensation substructure impedance coupling provided in an embodiment of the present invention.

[0066] Figure 3 This is a schematic diagram of a subframe example of a structural dynamic stiffness analysis method based on frequency response function condensation substructure impedance coupling provided in an embodiment of the present invention.

[0067] Figure 4 The flowchart illustrates the dynamic stiffness calculation process of the structural dynamic stiffness analysis method based on frequency response function condensation substructure impedance coupling provided in this embodiment of the invention.

[0068] Figure 5 A comparison chart of calculation results for the structural dynamic stiffness analysis method based on frequency response function condensation substructure impedance coupling provided in the embodiments of the present invention. Detailed Implementation

[0069] To make the technical solution of the present invention clearer, the present invention will be clearly and completely described below with reference to specific embodiments and corresponding drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of them. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention. The present invention provided by various embodiments will be described in detail below with reference to the accompanying drawings. To better understand the purpose of the present invention, the present invention will be described in further detail below.

[0070] Please see Figure 1 The present invention provides a structural dynamic stiffness analysis method based on frequency response function condensation substructure impedance coupling, comprising:

[0071] Step 1: Based on the global finite element model, obtain the node information, element connection relationships, and material properties of the global finite element model;

[0072] Step 2: Based on the element connection relationship, define the set of points of interest for which dynamic stiffness needs to be calculated, the set of boundary points coupled with the dynamics of the set of points of interest, and the set of internal points formed by the remaining nodes from all nodes of the global finite element model; wherein, the set of points of interest, the set of boundary points, and the set of internal points together constitute the complete node set of the global finite element model.

[0073] Step 3: Based on the defined set of points of interest, set of boundary points, and set of internal points, divide the global mass matrix, stiffness matrix, and damping matrix into blocks to obtain the block system matrix corresponding to the set of points of interest, set of boundary points, and set of internal points.

[0074] Step 4: Based on the node dynamics relationships represented by the block system matrix and the system's highest analysis frequency, an inertial compensation term related to the highest analysis frequency is introduced. This inertial compensation term is a global approximate inertial compensation operator, and its form is: Where I is the identity matrix, and Λ is a diagonal matrix with elements w 2 max The function is α, which is an empirical coefficient. A transformation matrix including an inertial compensation term is constructed. The original system matrix is ​​condensed to retain only the degrees of freedom of the set of points of interest and the set of boundary points using the transformation matrix. The dynamic stiffness matrix of the system in the frequency domain is calculated with only the degrees of freedom of the set of points of interest and the set of boundary points retained.

[0075] Step 5: Perform an inversion operation on the dynamic stiffness matrix of the polycondensation system calculated in Step 4. Extract the submatrix corresponding to the set of concerns from the inverted total impedance matrix as the dynamic stiffness result of the set of concerns, and output the dynamic stiffness result of the set of concerns.

[0076] Step 1 obtains node information, element connection relationships, and material properties based on the global finite element model. The underlying technical solution involves reading the global finite element model data through a computer-aided engineering software interface, specifically analyzing node coordinate information, element types, and node connection topology, while extracting material property parameters such as elastic modulus, Poisson's ratio, and density. This step is the fundamental data preparation stage of the method, providing input for subsequent node classification and matrix construction. Node information defines the model's geometry, element connection relationships describe the relationships between mechanical components, and material properties are used to derive the system matrix. The output of Step 1 directly serves the node set definition in Step 2.

[0077] Step 2 defines the focus set, boundary point set, and internal point set from all nodes in the global finite element model based on element connectivity. The underlying technical solution first designates specific nodes or node groups for which dynamic stiffness needs to be calculated as the focus set. Based on the focus set, nodes on directly connected elements that do not belong to the focus set are categorized into the boundary point set. The boundary point set is recursively expanded, adding new nodes from elements connected to nodes in the boundary point set. After defining the focus set and boundary point set, all remaining nodes are defined as the internal point set. This step classifies nodes by analyzing element connectivity; the focus set identifies the analysis focus, the boundary point set captures adjacent dynamic coupling regions, and the internal point set represents far-field nodes. The logic of Step 2 is based on the element connectivity in Step 1, and the output node classification lays the foundation for the matrix partitioning in Step 3.

[0078] Step 3 divides the global mass matrix, stiffness matrix, and damping matrix into blocks based on the defined sets of interest points, boundary points, and interior points. The lower-level technical solution divides the global matrix into corresponding sub-matrices according to the node set index, such as sub-matrices corresponding to the sets of interest points, boundary points, and interior points, including cross-coupling sub-matrices. This step reduces the system dimensionality through matrix partitioning while preserving the dynamic coupling relationships between different node sets. The partitioned system matrix represents the mechanical interactions between the sets of interest points, boundary points, and interior points. Step 3 directly utilizes the node set output from Step 2, and the generated partitioned system matrix provides input for the condensation operation in Step 4.

[0079] Step 4 introduces an inertial compensation term and constructs a transformation matrix based on the nodal dynamics represented by the block system matrix and the system's highest analysis frequency. The transformation matrix is ​​then used to shrink the original system matrix to retain only the degrees of freedom of the sets of points of interest and boundary points, and the dynamic stiffness matrix in the frequency domain is calculated. The next step is to first establish the displacement transformation relationship between the sets of points of interest, boundary points, and internal points. Using the system's highest analysis frequency as a variable, the inertial compensation coefficients are solved using predefined coefficients, and a diagonal matrix is ​​constructed as the inertial compensation term. This inertial compensation term is added to the transformation matrix constructed from the displacement transformation relationship. The transformation matrix is ​​then used to shrink the block system matrix, obtaining a reduced-order system matrix containing only the degrees of freedom of the sets of points of interest and boundary points. This step enhances the accuracy of existing shrinkage methods in the mid-to-high frequency range through the inertial compensation term. The transformation matrix approximates the dynamic effects of the internal point sets, and the system matrix size is reduced after shrinkage but is equivalent to a global model. Step 4, relying on the block matrix and the highest analysis frequency from Step 3, outputs the shrunken system dynamic stiffness matrix for Step 5.

[0080] Step 5 inverts the dynamic stiffness matrix of the condensed system calculated in Step 4, extracts the corresponding subset matrix of the set of interests from the inverted total impedance matrix as the dynamic stiffness result, and outputs it. The lower-level technical solution sets the frequency scanning range and frequency step size with the highest analysis frequency of the system as the upper limit. It iterates through each frequency point within the frequency scanning range, calculating the system impedance matrix value at that frequency point based on the dynamic stiffness matrix of the condensed system. It inverts the system impedance matrix, extracts the corresponding subset matrix value of the set of interests from the inverse matrix as the dynamic stiffness value at the current frequency point. All frequency points and their corresponding dynamic stiffness values ​​are stored and combined into a function of frequency as the final output. This step decouples the local dynamic stiffness through frequency domain solution, and the output result characterizes the impedance characteristics of the set of interests in the global system. Step 5 uses the condensed matrix from Step 4 to perform frequency scanning and matrix operations, completing the dynamic stiffness analysis process.

[0081] Overall, the steps are logically interconnected: Step 1 provides the raw data, Step 2 classifies the nodes, Step 3 performs matrix partitioning, Step 4 performs dynamic reduction, and Step 5 extracts the dynamic stiffness results. The method improves computational efficiency while maintaining accuracy through progressive data reduction and equivalent modeling.

[0082] Specifically, in the structural dynamic stiffness analysis method based on frequency response function condensation substructure impedance coupling of the present invention, step 2 includes:

[0083] Step 21: Define the nodes or groups of nodes whose dynamic stiffness needs to be calculated as the set of points of interest;

[0084] Step 22: Based on the defined set of concerns, select nodes on units directly connected to the set of concerns that do not belong to the set of concerns, and classify them into the boundary point set;

[0085] Step 23: Based on the boundary point set obtained in Step 22, recursively select new nodes on the cells connected to the nodes in this boundary point set that have not yet been included in any node set, and expand the boundary point set.

[0086] Step 24: After defining the focus set and boundary point set, define all nodes in the global finite element model that are not included in the above node sets as internal point sets.

[0087] Step 21: Using the user interface or program instructions of computer-aided engineering software, explicitly define the specific nodes or groups of nodes whose dynamic stiffness needs to be analyzed as the set of concerns. This operation is usually based on the physical location or functional attributes of the nodes, such as structural connection points or load application points. Step 22: Based on the element connection relationships of the finite element model, identify all elements directly connected to the nodes in the set of concerns, and extract the nodes on these elements that do not belong to the set of concerns, classifying them into the boundary point set. This step ensures that nodes directly adjacent to the set of concerns are included in the analysis scope. Step 23: Expand the boundary point set using a recursive algorithm. Based on the nodes in the current boundary point set, continue to find new nodes on connected elements that have not yet been included in any node set, and add them to the boundary point set. The recursive operation is usually performed at several levels to ensure that a sufficiently wide range of dynamic coupling regions is covered. Step 24: After completing the definition of the set of concerns and the boundary point set, classify all remaining nodes in the global finite element model into the internal point set. The internal point set represents the far-field region with weaker dynamic coupling to the set of concerns, and its dynamic effects will be equivalently processed through subsequent clustering algorithms. The entire node classification process establishes a hierarchical coupling relationship from local concerns to the global system, providing a structural foundation for subsequent dynamic clustering.

[0088] Specifically, in the structural dynamic stiffness analysis method based on frequency response function condensation substructure impedance coupling of the present invention, step 4 includes:

[0089] Step 41: Based on the block system matrix obtained in Step 3, establish the displacement transformation relationship between the set of points of interest, the set of boundary points, and the set of internal points;

[0090] Step 42: Based on the displacement transformation relationship and the highest analysis frequency of the system in Step 4, an inertial compensation term related to the highest analysis frequency is introduced to construct the transformation matrix;

[0091] Step 43: Using the transformation matrix constructed in step 42, perform a reduction operation on the block system matrix obtained in step 3;

[0092] Step 44: Through the shrinking operation, obtain the reduced-order system matrix that includes only the degrees of freedom of the set of points of interest and the set of boundary points.

[0093] Based on the block system matrix obtained in step 3, step 41 establishes the displacement transformation relationship between the set of points of interest, the set of boundary points, and the set of internal points. This displacement transformation relationship is expressed by the linear mapping relationship between the displacement of the internal point set and the displacement of the set of points of interest and the set of boundary points, providing a mathematical basis for the subsequent construction of the transformation matrix.

[0094] Step 42 introduces an inertial compensation term related to the highest analysis frequency of the system, based on the displacement transformation relationship and the highest analysis frequency, and constructs a transformation matrix. The inertial compensation term calculates the inertial compensation coefficients using the highest analysis frequency of the system and constructs a diagonal matrix form to correct the insufficient accuracy of existing static condensation methods in the mid-to-high frequency region. The transformation matrix, combined with the displacement transformation relationship and the inertial compensation term, forms a reduced-order transformation operator that can accurately characterize the dynamic properties of the system.

[0095] Step 43 uses the transformation matrix constructed in step 42 to perform a reduction operation on the block system matrix obtained in step 3. The reduction operation reduces the system's degrees of freedom from the complete set to only include the set of points of interest and the set of boundary points through matrix operations between the transformation matrix and the original system matrix, while preserving the dynamic characteristics of the original system.

[0096] Step 44 uses a condensation operation to obtain a reduced-order system matrix that includes only the degrees of freedom of the sets of points of interest and boundary points. The reduced-order system matrix includes a condensed form of the mass matrix, stiffness matrix, and damping matrix, which is used for subsequent frequency domain dynamic stiffness calculations, significantly improving computational efficiency while maintaining computational accuracy.

[0097] Specifically, in the structural dynamic stiffness analysis method based on frequency response function condensation substructure impedance coupling of the present invention, step 42 includes:

[0098] Step 421: Obtain the system's highest analysis frequency;

[0099] Step 422: Using the highest analysis frequency as the variable, calculate the relationship using the coefficients stored in the system beforehand, and solve for the inertia compensation coefficient;

[0100] Step 423: Construct a diagonal matrix as the inertia compensation term using the inertia compensation coefficient;

[0101] Step 424: Add the inertia compensation term to the transformation matrix constructed based on the displacement transformation relationship.

[0102] In the structural dynamic stiffness analysis method based on frequency response function-based impedance coupling of condensation substructures, step 42 involves the construction and integration of inertial compensation terms, specifically including four sub-steps. Step 421 obtains the highest analysis frequency of the system from the system configuration or user input. This frequency defines the upper limit of the analysis band and is the fundamental parameter for subsequent calculations. Step 422 uses the highest analysis frequency as the input variable and solves for the inertial compensation coefficients using pre-stored coefficient calculation formulas in the system. These formulas are designed based on dynamic principles and are used to quantify the influence of inertial effects during the condensation process. Step 423 uses the solved inertial compensation coefficients to construct a diagonal matrix as the inertial compensation term. The dimension of this matrix corresponds to the degrees of freedom of the internal point set, and the element values ​​reflect the amount of inertial compensation at the highest analysis frequency. Step 424 adds the inertial compensation term to the transformation matrix constructed based on the displacement transformation relationship, achieving integration through matrix operations, thereby enhancing the transformation matrix's ability to approximate the dynamic behavior of the internal point set. These steps are sequentially connected: step 421 provides key inputs, step 422 derives compensation parameters, step 423 formalizes the compensation entity, and step 424 finally refines the transformation matrix. Together, they enable the condensation process to maintain accuracy in the frequency domain without having to solve the global model. The entire process relies on the system's highest analysis frequency to drive the compensation mechanism, logically progressing layer by layer, ultimately supporting the efficient calculation of the dynamic stiffness matrix.

[0103] Specifically, in the structural dynamic stiffness analysis method based on frequency response function condensation substructure impedance coupling of the present invention, step 5 includes:

[0104] Step 51: Set the frequency scan range and frequency step size with the highest analysis frequency of the system in Step 4 as the upper limit;

[0105] Step 52: Traverse each frequency point within the frequency scanning range, and calculate the system impedance matrix value at the current frequency point based on the dynamic stiffness matrix of the condensation system obtained in Step 4.

[0106] Step 53: Store each frequency point and its corresponding system impedance matrix value;

[0107] Step 54: Combine the system impedance matrix values ​​at all frequency points into a function of frequency, and use this as the result of the calculation of the condensation system impedance matrix.

[0108] Step 5, in the structural dynamic stiffness analysis method based on the impedance coupling of the condensation substructure using the frequency response function, is responsible for extracting the dynamic stiffness results of the set of points of interest from the dynamic stiffness matrix of the condensation system. This step calculates and outputs the dynamic stiffness through frequency domain scanning and matrix operations. Step 5 executes the core calculation process of frequency response analysis based on the dynamic stiffness matrix of the condensation system obtained in Step 4 and the highest analysis frequency of the system.

[0109] Step 51 sets the frequency scan range and frequency step size, using the highest analysis frequency of the system as the upper limit. The frequency scan range typically starts from zero Hz and extends to the highest analysis frequency of the system, covering the entire frequency band of interest. The frequency step size is determined based on the required analysis accuracy; a smaller step size increases resolution but computational load, while a larger step size improves efficiency but may miss details. This step ensures reasonable setting of frequency parameters, providing input conditions for subsequent calculations.

[0110] Step 52 iterates through each frequency point within the frequency scanning range and calculates the system impedance matrix value at each frequency point based on the dynamic stiffness matrix of the condensation system obtained in Step 4. For each frequency point, first, the current frequency value is read, and then the system impedance matrix at that frequency is constructed using the dynamic stiffness matrix of the condensation system. This system impedance matrix characterizes the complex impedance characteristics of the condensation system in the frequency domain. Next, the system impedance matrix is ​​inverted to obtain the total impedance matrix. Finally, the submatrix values ​​corresponding to the set of interests are extracted from the total impedance matrix and used as the dynamic stiffness values ​​of the set of interests at the current frequency point. This process achieves the discrete-point solution of dynamic stiffness in the frequency domain through iterative calculation.

[0111] Step 53 stores each frequency point and its corresponding system impedance matrix value or dynamic stiffness value. The storage method adopts an array or database structure, with the frequency point as the index and the value stored in complex form, including the real part and the imaginary part, for subsequent processing and combination; the storage operation is performed in real time during the calculation process to avoid data loss and support interruption recovery.

[0112] Step 54 combines the system impedance matrix values ​​or dynamic stiffness values ​​at all frequency points into a function of frequency. Combination methods include linear interpolation or direct tabulation, generating continuous or discrete frequency response curves; the final output is the calculated result of the condensed system impedance matrix, used for graphical display or further analysis. This step completes the integration and output of the dynamic stiffness results.

[0113] Step 5 consists of tightly integrated sub-steps: Step 51 sets the frequency parameters, Step 52 performs the core calculations, Step 53 persists the data, and Step 54 generates the final result. The entire process achieves efficient extraction and visualization of dynamic stiffness.

[0114] Specifically, in the structural dynamic stiffness analysis method based on frequency response function condensation substructure impedance coupling of the present invention, step 52 includes:

[0115] Read the current frequency point;

[0116] Based on the dynamic stiffness matrix of the polycondensation system obtained in step 4 and the current frequency point, calculate the system impedance matrix at the current frequency point.

[0117] Perform the inversion operation on the system impedance matrix;

[0118] From the matrix obtained after inversion, extract the values ​​of the submatrix corresponding to the set of concerns, and use them as the dynamic stiffness values ​​of the set of concerns at the current frequency.

[0119] During frequency scanning, the system first sequentially reads the current frequency point value from a preset frequency list. This operation traverses and analyzes every discrete frequency value within the frequency band. The current frequency point value is then used as an input parameter for subsequent calculation steps.

[0120] Based on the dynamic stiffness matrix of the polycondensation system obtained in step 4, the system substitutes the current frequency value into the frequency domain expression of the dynamic stiffness matrix to calculate the numerical representation of the system impedance matrix at that frequency. The system impedance matrix characterizes the complex impedance characteristics of the polycondensation system at a specific frequency, and its construction depends on the mass, stiffness, and damping block matrices included in the dynamic stiffness matrix of the polycondensation system.

[0121] The system impedance matrix is ​​numerically inverted using the LU decomposition algorithm to obtain the total impedance matrix. The total impedance matrix represents the system frequency response function, including the dynamic response information of all degrees of freedom of the set of points of interest and the boundary point set.

[0122] From the total impedance matrix, the system extracts the values ​​of a submatrix by indexing the degrees of freedom corresponding to the set of points of interest. These submatrix values ​​are directly used as the dynamic stiffness results for the set of points of interest at the current frequency. The dynamic stiffness results are stored in complex form, including real and imaginary parts, and are used for subsequent frequency response combinations.

[0123] Specifically, in the structural dynamic stiffness analysis method based on frequency response function condensation substructure impedance coupling of the present invention, step 5 further includes:

[0124] Receive the dynamic stiffness results of the set of concerns output in step 5;

[0125] Convert dynamic stiffness results into graphics drawing instructions;

[0126] Execute the graphics drawing command to generate a curve showing the change of dynamic stiffness with frequency;

[0127] The graphs and dynamic stiffness results are transmitted to the user interface for display.

[0128] The system receives the dynamic stiffness results of the set of interest output in step 5. These dynamic stiffness results are stored in array form, including complex values ​​corresponding to each frequency point within the frequency scanning range, which characterize the impedance characteristics of the set of interest. The receiving process reads the result data from the calculation module through the data interface and verifies the data integrity to prevent transmission errors or data loss, thus providing an input basis for subsequent graphics processing.

[0129] The dynamic stiffness results are then converted into graphical drawing instructions. The conversion process involves parsing the real and imaginary parts of the dynamic stiffness data, calculating the amplitude or phase information, and calling the graphics library API to generate drawing commands. The graphical drawing instructions include setting the coordinate axis range, defining the curve style, labeling frequency points and stiffness values, and configuring legends and titles to ensure that the graphical elements conform to engineering analysis standards.

[0130] Next, the graphics rendering instructions are executed to generate a curve showing the dynamic stiffness as a function of frequency. The execution process is handled by the graphics rendering engine, which creates the curve in memory according to the instructions, applies data interpolation or smoothing algorithms to optimize the curve display, and outputs it in a common image format. The curve visually shows the trend of dynamic stiffness as a function of frequency, making it easier for engineers to identify resonant frequencies and stiffness characteristics.

[0131] Finally, the curves and dynamic stiffness results are transmitted to the user interface for display. The transmission mechanism is implemented through GUI components, such as embedded image controls and data tables, supporting user interaction operations such as zooming, saving, and exporting. The user interface updates the displayed content in real time, providing visualization analysis and report generation functions for dynamic stiffness results, enhancing the practicality of the method and the user experience.

[0132] Specifically, the structural dynamic stiffness analysis method based on frequency response function condensation substructure impedance coupling of the present invention further includes:

[0133] Based on the reduced-order system matrix obtained in step 4, modal verification is performed;

[0134] Modal parameters are extracted based on the reduced-order system matrix.

[0135] The modal parameters are compared with the modal parameters of the global finite element model;

[0136] Based on the comparison results, the modal confidence index is calculated;

[0137] A verification report is output based on the modal confidence index.

[0138] Based on the reduced-order system matrix obtained in step 4, modal verification is performed. This verification process is achieved by solving the eigenvalue problem of the reduced-order system matrix. The eigenvalue solution uses the Lanczos algorithm or a similar iterative method to calculate the natural frequencies and mode shapes of the reduced-order system, thereby evaluating the retention of dynamic characteristics of the model after condensation. Modal verification aims to confirm whether the reduced-order system matrix accurately represents the modal behavior of the original global system, providing a foundation for subsequent accuracy evaluation.

[0139] Based on the reduced-order system matrix, modal parameters are extracted, including natural frequencies, damping ratios, and mode shape vectors. The extraction method involves performing eigenvalue decomposition on the reduced-order system matrix to obtain eigenvalues ​​and eigenvectors. The eigenvalues ​​correspond to the squares of the system's natural frequencies, and the eigenvectors represent the mode shapes. These parameters are used to describe the free vibration characteristics of the system.

[0140] The extracted modal parameters are compared with the modal parameters of the global finite element model. The modal parameters of the global finite element model are obtained through modal analysis of the complete finite element model, including global natural frequencies and global mode shapes. The comparison operation includes frequency deviation calculation and mode shape correlation analysis. Frequency deviation is evaluated by percentage difference, and mode shape correlation is performed by vector dot product or similarity measure.

[0141] Based on the comparison results, the modal confidence index is calculated. The modal confidence index adopts the Modal Assurance Criterion or similar statistical index to quantify the consistency between the reduced-order model mode shape and the global model mode shape. The calculation process involves the normalization of mode shape vectors and inner product operation. The index value ranges from 0 to 1, and the higher the value, the better the consistency.

[0142] Based on the modal confidence index, a verification report is output, which includes comparative data, index values, and graphical results, such as frequency deviation tables and mode shape comparison diagrams. The report is generated through automated scripts or software modules, and the output format is a text file or a visual interface, which is used by engineers to evaluate the reliability and accuracy of the condensation model.

[0143] Specifically, the structural dynamic stiffness analysis method based on frequency response function condensation substructure impedance coupling of the present invention further includes:

[0144] Based on the global finite element model and the definition method in step 2, multiple concerns are automatically processed.

[0145] Based on the global finite element model, multiple sets of points of interest for which dynamic stiffness needs to be calculated are defined in batches;

[0146] For each set of concerns, the shrinking process in step 4 and the dynamic stiffness extraction process in step 5 are executed in parallel to obtain the dynamic stiffness result of each set of concerns. The shrinking process in step 4 is to use a transformation matrix to shrink the original system matrix to retain only the degrees of freedom of the set of concerns and the boundary point set. The dynamic stiffness extraction process in step 5 is to perform an inversion operation on the shrinking system dynamic stiffness matrix calculated in step 4, extract the sub-matrix corresponding to the set of concerns from the inverted total impedance matrix, use it as the dynamic stiffness result of the set of concerns, and output the dynamic stiffness result of the set of concerns.

[0147] Collect the dynamic stiffness results for all sets of concerns;

[0148] A comprehensive analysis report is generated based on the collected dynamic stiffness results.

[0149] Based on the global finite element model and the node set definition method defined in step 2, the system automatically processes multiple points of interest. This process uses a computer-aided engineering software interface to read the user-input information on the locations or node groups of multiple points of interest, and applies the node classification logic from step 2 to achieve batch identification and processing of multiple points of interest. The automated processing relies on predefined scripts or algorithms to parse the global finite element model data and automatically iterate on each point of interest without manual intervention.

[0150] Based on a global finite element model, the system defines multiple sets of points of interest for which dynamic stiffness needs to be calculated in batches. For each point of interest, the system automatically identifies and defines its corresponding set of points of interest, boundary points, and internal points, according to the rules in step 2. The definition of the boundary points follows either the geometric range principle or the connection path principle. The geometric range principle selects nodes within physical distance of the point of interest, while the connection path principle selects nodes connected to the point of interest through element connection relationships. The internal point set consists of the remaining nodes, completely covering the global model node set. The batch definition process is implemented through loop or parallel algorithms, efficiently handling multiple points of interest in a large-scale model.

[0151] For each defined set of concerns, the system executes the contraction process in step 4 and the dynamic stiffness extraction process in step 5 in parallel. The contraction process constructs a transformation matrix based on the block system matrix, introduces an inertial compensation term, and reduces the system matrix to retain only the degrees of freedom of the sets of concerns and boundary points. The dynamic stiffness extraction process calculates the system impedance matrix through frequency scanning, performs inversion operations, and extracts the sub-matrices of the sets of concerns. Parallel computing utilizes multi-core processors or a distributed computing environment to process multiple sets of concerns simultaneously, significantly improving computational efficiency and shortening analysis time.

[0152] The system collects the dynamic stiffness results of all interest point sets and stores the dynamic stiffness values ​​of each interest point set in the frequency domain in a centralized database or file system. The storage format includes frequency point indices and corresponding complex dynamic stiffness values, supporting subsequent data retrieval and processing. The collection process is implemented through a data aggregation algorithm, automatically summarizing the results of parallel computations to ensure data integrity and consistency.

[0153] Based on the collected dynamic stiffness results, the system generates a comprehensive analysis report. The report generation module converts the dynamic stiffness values ​​into visual charts, including dynamic stiffness versus frequency curves, comparison curves for multiple points of interest, and data tables. The report content covers the dynamic stiffness characteristic analysis of all sets of points of interest, a summary of numerical values ​​at key frequencies, and an overall performance evaluation. The generated report can be displayed through a graphical user interface or exported to a standard document format, providing engineers with support for design optimization and decision-making.

[0154] Specifically, the structural dynamic stiffness analysis method based on frequency response function condensation substructure impedance coupling of the present invention further includes:

[0155] Integrate structural dynamic stiffness analysis methods into the CAE software platform;

[0156] Receives global finite element model files or parameters input by the user through a graphical user interface;

[0157] Call the finite element solver to parse the user-input model file or parameters and obtain the node information, element connection relationships and material properties of the global finite element model;

[0158] Based on the obtained node information, unit connection relationships, and material properties, proceed with steps 2 to 5;

[0159] The dynamic stiffness results of the focus set output in step 5 are transmitted to the user interface for visualization.

[0160] Integrating structural dynamic stiffness analysis methods into a CAE software platform involves implementing the algorithm as a software module and interacting with the platform's core functions through an application programming interface (API). The integration process includes coding the algorithm logic, designing data interfaces, and embedding user interface elements, enabling the method to seamlessly integrate into the CAE software's analysis workflow and utilize the platform's existing pre-processing and post-processing tools.

[0161] The system receives global finite element model files or parameters from users through a graphical user interface (GUI). The GUI provides file upload controls and parameter input forms. Users can select model files via dialog boxes (common formats include INP or CDB files) or directly input node coordinates, element types, and material property values. After verifying the completeness of the input data, the interface transmits the data to the backend processing module.

[0162] The system invokes an integrated or external finite element solver, such as NASTRAN or ABAQUS, to parse the user-input model file or parameters. The parsing process reads the geometric and property information of the model file, extracts node numbers, coordinate data, element connection topology, and material parameters such as elastic modulus and density, and converts this information into an internal data structure for subsequent analysis.

[0163] Based on the acquired node information, element connection relationships, and material properties, steps 2 through 5 are executed. The system automatically performs node set definition, identifying the sets of points of interest, boundary points, and internal points according to the element connection relationships. Subsequently, the system matrix is ​​partitioned, generating block-based forms of the mass matrix, stiffness matrix, and damping matrix. A transformation matrix is ​​applied for dynamic condensation to obtain the reduced-order dynamic stiffness matrix of the system. Finally, frequency scanning and matrix operations are used to extract the dynamic stiffness values ​​of the sets of points of interest. The entire process is automated, improving analysis efficiency.

[0164] The dynamic stiffness results of the focus set output in step 5 are transmitted to the user interface for visualization. The dynamic stiffness data is transmitted to the graphical user interface in array form. The interface calls the visualization engine to generate a curve of dynamic stiffness changing with frequency, such as an amplitude-frequency response curve or a phase-frequency response curve, and renders it in the display panel. Users can interact with the interface to view curve details, adjust the display range, or export the results data to complete the analysis process.

[0165] This invention addresses the inherent contradiction between the low computational efficiency of the global model and the accuracy distortion of the local substructure method in existing dynamic stiffness analysis methods. It proposes a highly efficient analysis scheme based on frequency response function reduction and substructure impedance coupling. Existing global frequency response methods require full-band scanning of the complete model, involving response calculations for all degrees of freedom, resulting in enormous computational resource consumption and excessive time consumption. While the local substructure separation method improves speed, the artificial constraints of the cut boundaries do not match the actual dynamic boundary conditions, neglecting the inertial and stiffness coupling effects of the far-field structure, leading to severe accuracy distortion. This invention resolves this contradiction through two core stages: system-level dynamic reduction and dynamic stiffness decoupling.

[0166] In the system-level dynamic reduction stage, this invention first explicitly defines three types of node sets in the global finite element model: the set of points of interest, the set of boundary points, and the set of internal points. The set of points of interest includes nodes or groups of nodes whose dynamic stiffness needs to be calculated; the set of boundary points is automatically selected through element connection relationships, starting from the nodes directly connected to the set of points of interest, and recursively expanding 1-2 layers to capture adjacent dynamic coupling regions and retain key dynamic influences.

[0167] The internal point set, including the remaining nodes, represents the far-field region. Based on the node set definition, the global mass matrix, stiffness matrix, and damping matrix are partitioned into blocks. Then, an improved Guyan-Irons reduction algorithm is introduced to construct a transformation matrix including an inertial compensation term. The inertial compensation term is related to the system's highest analysis frequency, and an empirical coefficient range of 0.25-0.5 is used to approximate the inertial dynamic effects, improving accuracy in the mid-to-high frequency range. The transformation matrix is ​​used to reduce the original system matrix to a reduced-order model that retains only the degrees of freedom of the sets of points of interest and boundary points. The degrees of freedom are drastically reduced from millions to tens or hundreds, thus significantly improving computational efficiency.

[0168] In the dynamic stiffness decoupling stage, the dynamic stiffness results of the set of concerns are directly extracted from the dynamic stiffness matrix of the reduced-order system through frequency scanning and matrix inversion. The dynamic stiffness matrix of the reduced-order system is constructed in the frequency domain. For each frequency point, the system impedance matrix is ​​calculated and inverted. The submatrix corresponding to the set of concerns is extracted from the total impedance matrix as the dynamic stiffness output. This process mathematically preserves all dynamic influences of the far-field structure on the points of concern, including inertia, stiffness, and damping effects. Therefore, the calculation results are highly consistent with the global model analysis, avoiding accuracy distortion.

[0169] Ultimately, this invention achieves a balance between efficiency and accuracy by reducing computational redundancy through dynamic condensation technology and ensuring the reliability of results through impedance coupling theory, making it suitable for rapid iterative and optimization design in engineering practice.

[0170] The specific embodiments of this invention are as follows: The core idea of ​​this invention is to mathematically transform a large global finite element model into a small system that retains only the points of interest and their dynamic boundaries. Then, the dynamic stiffness of the points of interest is directly solved from the impedance matrix of this condensed system. The entire process consists of two core stages: system condensation and dynamic stiffness decoupling, with the specific steps as follows:

[0171] System-level power reduction;

[0172] The goal of this stage is to accurately project the dynamic characteristics of the global system model into a reduced-order model consisting of key degrees of freedom. First, three types of node sets are explicitly defined in the global finite element model:

[0173] a-set (Attention Set): The node or group of nodes whose dynamic stiffness needs to be calculated. For example, a mounting point on the subframe.

[0174] Boundary Set (b-set): Neighboring nodes strongly coupled to the dynamics of the point of interest. These nodes are key channels for transmitting the dynamic effects of the far-field structure and are typically selected as follows: Identify all elements directly connected to nodes in the a-set; all nodes on these elements that do not belong to the a-set should be automatically included in the b-set. Recursively, identify elements connected to nodes in the current b-set and include any new nodes on them in the b-set, extending this process 1-2 layers. Figure 2 As shown in the figure: the nodes within the red circle are the nodes whose dynamic stiffness needs to be calculated, defined as a-set, and the nodes outside the red circle but inside the yellow circle are the nodes that need to be defined as b-set.

[0175] o-set (Omit Set): All other nodes in the model except for a-set and b-set.

[0176] Based on this definition, the global mass matrix M, stiffness matrix K, and damping matrix C are divided into blocks.

[0177] ;

[0178] ;

[0179] ;

[0180] This invention employs an improved Guyan-Irons condensation method. Its transformation matrix T not only includes static condensation information but also introduces a first-order inertial compensation term to improve accuracy in the mid-to-high frequency range. The specific construction process of the transformation matrix T is as follows:

[0181] To account for dynamic effects, we analyze the system's dynamic equations as follows:

[0182] ;

[0183] In the formula:

[0184] K is the global stiffness matrix;

[0185] M is the global quality matrix;

[0186] w is the angular frequency when the load is applied;

[0187] U is the displacement response vector;

[0188] F is the load vector.

[0189] Expand it by node:

[0190] ;

[0191] In the formula:

[0192] K aa M aa These are the stiffness matrix and mass matrix of the point of interest, respectively;

[0193] K bb M bb These are the stiffness matrix and mass matrix of the boundary points, respectively;

[0194] K oo M oo These are the stiffness matrix and mass matrix of the interior points, respectively;

[0195] K aa Maa These are the stiffness matrix and mass matrix of the point of interest, respectively;

[0196] K ab K ba The stiffness matrix is ​​the coupling between the point of interest and the boundary points;

[0197] K ao K oa The stiffness matrix is ​​the coupling between the point of interest and the internal points;

[0198] K bo K ob This is the stiffness matrix for the coupling between boundary points and interior points;

[0199] M ab M ba The quality matrix is ​​the coupling between the points of interest and the boundary points;

[0200] M ao M oa The quality matrix is ​​the coupling between the point of interest and the internal points;

[0201] M bo M ob The mass matrix is ​​the coupling between boundary points and interior points;

[0202] U a U b U o These are the displacement response vectors of the point of interest, the boundary point, and the interior point, respectively.

[0203] F a F b and are the load vectors of the points of interest and boundary points, respectively.

[0204] Expanding the third line of the equation, we get:

[0205] ;

[0206] Moving the terms including Uo to one side, we get:

[0207] ;

[0208] Introduce a global approximate inertial compensation operator:

[0209] ;

[0210] Here, I is the identity matrix, and Λ is a diagonal matrix with elements w. 2 max The function (w) 2 maxThe highest analysis frequency of interest is used to approximate the dynamic effect of the inertial term. This is a key improvement over existing static condensation polymerization. α is an empirical coefficient. Through a large number of numerical experiments, its value in the range of 0.25-0.5 can achieve the best results in most engineering problems. Its physical meaning can be understood as an equivalent estimate of the maximum inertial force.

[0211] Therefore, we can obtain the final expression for the displacement of the internal point:

[0212] ;

[0213] make:

[0214] ;

[0215] Therefore, the complete displacement transformation relationship is:

[0216] ;

[0217] In the formula, T oa T is the displacement transformation matrix between internal points and points of interest; ob The displacement transformation matrix between interior points and boundary points; I is the identity matrix.

[0218] Finally, the transformation matrix T is:

[0219] ;

[0220] Using the transformation matrix T, the original system matrix is ​​reduced to include only the a-set and b-set degrees of freedom:

[0221] ;

[0222] In the formula, M r K r and C r These are the mass matrix, stiffness matrix, and damping matrix of the model after order reduction, respectively.

[0223] Thus, we have obtained a reduced-order model that is extremely small in scale but accurately includes global dynamic information.

[0224] Dynamic stiffness decoupling and extraction;

[0225] The purpose of this stage is to calculate the dynamic stiffness of the point of interest from the reduced-order model. For a given frequency ω, the dynamic stiffness matrix of the reduced-order system is:

[0226] ;

[0227] In the formula, Z r Here is the dynamic stiffness matrix of the reduced-order system;

[0228] M r K r and C r These are the mass matrix, stiffness matrix, and damping matrix of the reduced-order system, respectively.

[0229] i is the imaginary unit.

[0230] The physical meaning of this matrix is: the complex impedance exhibited by the system after condensation in the a-set and b-set degrees of freedom.

[0231] The key point is that the dynamic stiffness matrix of the a-set is precisely the inverse of the impedance matrix of the entire reduced-order system, i.e.:

[0232] ;

[0233] Where: K d (w) is the dynamic stiffness matrix of the point of interest at the given frequency w;

[0234] Z r (w) is the impedance matrix of the reduced-order system at a given frequency w;

[0235] For single-point excitation, the diagonal elements of this matrix represent the dynamic stiffness at that point. This formula directly decouples the impedance properties of a local point from the dynamic response of the global system.

[0236] Numerical examples for verification;

[0237] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention will be clearly and completely described below in conjunction with specific examples and corresponding drawings.

[0238] The following is a subframe calculation example, such as Figure 3 As shown.

[0239] The dynamic stiffness curve of a certain rear mounting point of the subframe is to be calculated, with the node settings of a-set and b-set as follows. Figure 2 As shown, the remaining nodes are set to o-set, the frequency sweep range is set to 1-300Hz, and the dynamic stiffness is solved following the procedure below, as follows: Figure 4 As shown.

[0240] The calculation results are as follows Figure 5 As shown:

[0241] Table 1 Comparison of Calculation Time

[0242]

[0243] From Figure 5As shown in Table 1, the calculation results of this invention are highly consistent with the solution results of the global finite element model. The curves of the solution results of the global finite element model and the curves of the calculation results of this invention coincide, further proving the correctness and efficiency of the method.

Claims

1. A method for structural dynamic stiffness analysis based on impedance coupling of substructures with frequency response function condensation, characterized in that, The method comprises the following steps: Step 1, based on a global finite element model, obtaining node information, element connection relationship and material properties of the global finite element model; Step 2, according to the element connection relationship, defining a point set of interest for calculating dynamic stiffness, a boundary point set coupled with the point set of interest for calculating dynamic stiffness and an internal point set composed of the remaining nodes from all nodes of the global finite element model; wherein the point set of interest, the boundary point set and the internal point set together constitute a complete node set of the global finite element model; Step 3, based on the defined point set of interest, boundary point set and internal point set, performing block processing on the global mass matrix, stiffness matrix and damping matrix to obtain block system matrices corresponding to the point set of interest, boundary point set and internal point set; Step 4, based on the node dynamic relationship represented by the block system matrix and the highest analysis frequency of the system, an inertia compensation term related to the highest analysis frequency is introduced, which is a global approximate inertia compensation operator, and its form is where I is a unit matrix, and A is a diagonal matrix whose elements are functions of w 2 max , and a is an empirical coefficient, and a transformation matrix including the inertia compensation term is constructed, and the original system matrix is condensed to only retain the degrees of freedom of the set of points of interest and the set of boundary points using the transformation matrix, and the dynamic stiffness matrix of the system retaining only the degrees of freedom of the set of points of interest and the set of boundary points in the frequency domain is calculated; Step 5, performing inverse operation on the condensed system dynamic stiffness matrix obtained in step 4, extracting a sub-matrix corresponding to the point set of interest from the full impedance matrix obtained after the inverse operation, taking the sub-matrix as the dynamic stiffness result of the point set of interest, and outputting the dynamic stiffness result of the point set of interest; Based on the global finite element model and the definition method of step 2, multiple points of interest are automatically processed; Based on the global finite element model, multiple point sets of interest for calculating dynamic stiffness are defined in batches; For each point set of interest, the condensation process of step 4 and the dynamic stiffness extraction process of step 5 are executed in parallel to obtain the dynamic stiffness result of each point set of interest, wherein the condensation process of step 4 is to use a transformation matrix to condense the original system matrix to only retain the degrees of freedom of the point set of interest and the boundary point set, and the dynamic stiffness extraction process of step 5 is to perform inverse operation on the condensed system dynamic stiffness matrix obtained in step 4, extract a sub-matrix corresponding to the point set of interest from the full impedance matrix obtained after the inverse operation, take the sub-matrix as the dynamic stiffness result of the point set of interest, and output the dynamic stiffness result of the point set of interest; Collect the dynamic stiffness results of all point sets of interest; Based on the collected dynamic stiffness results, generate a comprehensive analysis report.

2. The method for structural dynamic stiffness analysis based on impedance coupling of condensed substructure according to the frequency response function as claimed in claim 1, characterized in that, Step 2 comprises: Step 21: define a node or node group for calculating dynamic stiffness as a point set of interest; Step 22: based on the defined point set of interest, select nodes not belonging to the point set of interest on the elements directly connected to the point set of interest and classify them into a boundary point set; Step 23: based on the boundary point set obtained in step 22, recursively select new nodes not yet included in any node set from the elements connected to the nodes in the boundary point set to expand the boundary point set; Step 24: after defining the point set of interest and the boundary point set, define all nodes in the global finite element model that are not included in the above node sets as an internal point set.

3. The method according to claim 2, wherein, Step 4 comprises: Step 41: based on the block system matrix obtained in step 3, establish a displacement transformation relationship among the point set of interest, the boundary point set and the internal point set; Step 42: based on the displacement transformation relationship and the highest analysis frequency of step 4, introduce an inertia compensation term related to the highest analysis frequency to construct a transformation matrix; Step 43: using the transformation matrix constructed in step 42, perform condensation operation on the block system matrix obtained in step 3; Step 44: through the condensation operation, obtain a reduced-order system matrix including only the degrees of freedom of the point set of interest and the boundary point set.

4. The method according to claim 3, wherein, Step 42 comprises: Step 421: Obtain the highest analysis frequency of the system; Step 422: Calculate the inertia compensation coefficient by a pre-stored coefficient calculation relationship with the highest analysis frequency as the variable; Step 423: Construct a diagonal matrix as the inertia compensation term using the inertia compensation coefficient; Step 424: Add the inertia compensation term to the transformation matrix constructed based on the displacement transformation relationship.

5. The method according to claim 4, wherein, Step 5 includes: Step 51: Set the frequency scanning range and frequency step with the highest analysis frequency of the system in step 4 as the upper limit; Step 52: Traverse each frequency point in the frequency scanning range, and calculate the system impedance matrix value at the current frequency point based on the condensed system dynamic stiffness matrix obtained in step 4; Step 53: Store each frequency point and its corresponding system impedance matrix value; Step 54: Combine the system impedance matrix values of all frequency points into a function of frequency as the calculation result of the condensed system impedance matrix.

6. The method according to claim 5, wherein, Step 52 includes: Read the current frequency point; Calculate the system impedance matrix at the current frequency point based on the condensed system dynamic stiffness matrix obtained in step 4 and the current frequency point; Perform an inverse operation on the system impedance matrix; Extract the sub-matrix value corresponding to the set of interest points from the matrix obtained after the inverse operation as the dynamic stiffness value of the set of interest points at the current frequency point.

7. The method according to claim 6, wherein, Step 5 also includes: Receive the dynamic stiffness result of the set of interest points output by step 5; Convert the dynamic stiffness result into a graph drawing instruction; Execute the graph drawing instruction to generate a curve graph of dynamic stiffness varying with frequency; Transfer the curve graph and the dynamic stiffness result to the user interface for display.

8. The method according to claim 7, wherein, Also includes: Perform modal verification based on the reduced system matrix obtained in step 4; Extract modal parameters based on the reduced system matrix; Compare the modal parameters with the modal parameters of the global finite element model; Calculate the modal confidence index based on the comparison result; Output a verification report based on the modal confidence index.

9. The method according to claim 8, wherein, Also includes: Integrate the structural dynamic stiffness analysis method into the CAE software platform; Receive the global finite element model file or parameters input by the user through the graphical user interface; Call the finite element solver to analyze the model file or parameters input by the user to obtain the node information, element connection relationship, and material properties of the global finite element model; Based on the obtained node information, element connection relationship, and material properties, execute steps 2 to 5; Transfer the dynamic stiffness result of the set of interest points output by step 5 to the user interface for visual display.

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