Method, system and apparatus for evaluating periodic structural vibration fatigue properties of an aircraft

Abstract

The application discloses an aircraft periodic structure vibration fatigue characteristic evaluation method, system and equipment, relates to the high-speed aircraft structure vibration fatigue technical field, and comprises the following steps: a finite element model of a periodic structure characteristic cell is established, a characteristic value problem of a transfer matrix between cell sections is solved through dynamic condensation and periodic structure characteristics, and characteristic values and characteristic vectors of propagating waves are obtained; threshold screening of a wave base is utilized to remove rapidly attenuated waves, based on the propagation, reflection and superposition of remaining waves in a wave domain, physical domain mapping and finite element conversion are performed to obtain structural displacement and stress frequency response; input load power spectral density is utilized, combined with stress frequency response, to calculate structural dangerous point stress power spectral density response, and through a Dirlik model, a material S-N curve and a cumulative damage theory, the broadband vibration fatigue characteristics of the periodic structure are evaluated. The application realizes efficient and accurate evaluation of full-band vibration fatigue characteristics, and is suitable for performance verification and optimization design of high-speed aircraft periodic structures.

Description

Technical Field

[0001] This invention relates to the field of high-speed aircraft structural vibration fatigue technology, specifically to methods, systems, and equipment for evaluating the periodic structural vibration fatigue characteristics of aircraft. Background Technology

[0002] High-speed aircraft face harsh, broadband noise environments during service, with loads reaching 170 dB and frequencies ranging from 10 to 10,000 Hz. This causes severe broadband vibrations in the structure, leading to fatigue damage and even structural failure. Periodic structures are widely present in the fuselage, thermal protection systems, and load-bearing components of high-speed aircraft, and their unique dynamic characteristics and fatigue life directly determine the safety and reliability of the aircraft under extreme conditions. Therefore, conducting vibration fatigue characteristic assessments of periodic structures under broadband excitation is crucial for the performance verification and optimized design of aircraft structures.

[0003] Currently, the main methods for predicting the broadband vibration response of structures employ a frequency-band analysis strategy. In the low-frequency band, the finite element method is typically used, but as the frequency increases and the wavelength shortens, the computational cost rises sharply, leading to a significant increase in processing time. In the mid-to-high frequency band, statistical energy analysis or its hybrid methods are used; however, these methods can only obtain the average energy of the subsystem, making it difficult to accurately capture the local response of the structure, and the analysis process is complex and has limited applicability. Therefore, for the periodic structures of high-speed aircraft, existing methods suffer from low computational efficiency and inaccurate response predictions, making it difficult to meet the needs of practical engineering for reliability assessment of full-frequency vibration fatigue characteristics.

[0004] To this end, the present invention proposes a method, system and equipment for evaluating the fatigue characteristics of periodic structural vibrations of aircraft. Summary of the Invention

[0005] The purpose of this invention is to provide a method, system, and device for evaluating the vibration fatigue characteristics of periodic structures of aircraft. By constructing a periodic structural dynamic model suitable for full-band analysis, it can achieve efficient and accurate evaluation of the vibration fatigue characteristics of structures under broadband excitation, overcome the shortcomings of existing methods in terms of computational efficiency and accuracy, and assist in the performance verification and optimization design of periodic structures of high-speed aircraft under broadband excitation environment.

[0006] According to a first aspect of the present invention, in order to achieve the above-mentioned objective, the present invention provides the following technical solution: a method for evaluating the fatigue characteristics of periodic structural vibration of an aircraft, comprising the following steps: A finite element model of a periodic structural feature cell is constructed. By using dynamic condensation and periodic structural characteristics, the eigenvalue problem of the transfer matrix between the feature cell sections is solved, and the eigenvalues ​​and eigenvectors of the propagating wave are obtained. Based on eigenvalues ​​and eigenvectors, fast-decaying waves are filtered out using a wave basis threshold. Based on the propagation, reflection, and superposition of the remaining waves in the wave domain, the displacement and stress frequency response of the periodic structure are obtained through physical domain mapping and finite element transformation. Using the obtained stress frequency response and the input load power spectral density, the stress power spectral density response at the critical point of the structure is calculated. The broadband vibration fatigue characteristics of the periodic structure are evaluated by using the Dirlik model, the material SN curve, and the cumulative damage theory.

[0007] Furthermore, a finite element model of the periodic structural feature cell is constructed, as follows: The periodic structure's characteristic cells are modeled and meshed, and the corresponding mass matrix, stiffness matrix, and damping matrix are extracted. Introducing dynamic stiffness matrix D The dynamic equation of the characteristic cell is expressed as: (1) In the formula, , K , C , M These are the stiffness matrix, damping matrix, and mass matrix of the cell, respectively. q Let be the nodal displacement vector. f Let i be the nodal force vector, and i be the imaginary unit. ω is the angular frequency.

[0008] Furthermore, by utilizing the dynamic condensation and periodic structural characteristics, the eigenvalue problem of the transfer matrix between characteristic cell sections is solved, yielding the eigenvalues ​​and eigenvectors of the propagating wave, as detailed below: Dividing the nodes contained in a feature cell into three parts—left section, right section, and internal nodes—the dynamic equation of the cell is expressed as follows when the internal nodes are not subjected to external forces: (2) In the formula, the subscript L and R These represent the nodes on the left and right sides of the cell, respectively. I Represents nodes within a cell; By eliminating the degrees of freedom within the characteristic cell structure through dynamic condensation, equation MERGEFORMAT can be rewritten as: (3) in, , , , ; Because of the continuity of displacement and the balance of forces between adjacent cells in a periodic structure, the first... nThe right section of the cell and the first n The left cross section of +1 cell has the following relationship: (4) Introducing the transfer matrix T Equation (4) can be expressed in matrix form as follows: (5) Based on the transfer matrix obtained from the characteristic cells, the wave propagation in the structure is expressed through the eigenvalue problem, which is expressed as: (6) Where: eigenvalues It describes the amplitude attenuation and phase change of a free wave during propagation. k The wave number represents the free wave, and Δ represents the length of the structural feature cell in the direction of wave propagation.

[0009] Furthermore, based on eigenvalues ​​and eigenvectors, a wave basis threshold is used to filter out rapidly decaying waves, as follows: (7) In the formula, This represents the fundamental cutoff coefficient.

[0010] Furthermore, based on the propagation, reflection, and superposition of the remaining waves after screening in the wave domain, the displacement and stress frequency response of the periodic structure are obtained through physical domain mapping and finite element transformation, as follows: Based on the principles of the finite element method, the relationship between strain and displacement at element nodes is used to further derive the conversion relationship between stress and displacement at element nodes, thereby obtaining the stress response of each node in the structure: For a regular eight-node hexahedral element, the displacement of any point inside it can be written as: (8) in, u i , v i , w i Each node of the unit is located at x , y , z Component displacements on the axis N i For the first i The shape function corresponding to each node is expressed as follows: (9) In the formula, x c , yc , z c The value represents the coordinates of the center of the regular hexahedron. a , b , c Represent x , y , z Half the length of the unit side in the direction; By differentiating the displacement field in spatial coordinates, the relationship between strain and displacement at any point within the element can be obtained: (10) in, e x , e y , e z respectively along x , y , z Normal strain in the direction, c xy , c yz , c zx They are respectively xyz , yz , zx Shear strain on the coordinate plane; Based on the constitutive relation of materials, establish the relationship between stress and strain at any point within the element: (11) in, s x , s y , s z respectively along x , y , z Normal stress in the direction, t xy , t yz , t zx They are respectively xyz , yz , zx Shear stress on the coordinate plane. D t It is an elastic matrix, and its expression varies depending on the material properties.

[0011] Furthermore, using the obtained stress frequency response and combining it with the input load power spectral density, the stress power spectral density response at the structural critical point is calculated, as follows: The formula for calculating the structural stress power spectral density response is: (12) In the formula, G Y ( f ) represents the structural stress power spectral density response function matrix. H ( f () is the structural stress frequency response function matrix. G F ( f () represents the input load power spectral density function matrix. H Represents the conjugate transpose of a matrix; Based on the stress power spectral density response, by solving the root mean square value of the response curves of each node of the structure, the stress hazard points of the structure are found, and their corresponding stress power spectral density response curves are extracted. The formula for calculating the root mean square value of stress response is: (13) In the formula, s rms This represents the root mean square value of the nodal stress response. G x ( f ) represents the nodal stress power spectral density response function. f 1. f 2 represents the upper and lower limits of the frequency range for analysis.

[0012] Furthermore, the broadband vibration fatigue characteristics of the periodic structure were evaluated using the Dirlik model, material SN curves, and cumulative damage theory, as follows: Substituting the stress power spectral density response at the critical point into the Dirlik model, and combining the power-law material SN curve with Miner's linear cumulative damage theory, the broadband vibration fatigue characteristics of the periodic structure are calculated: The Dirlik model expression is: (14) in, S The stress amplitude, This is called the regularized stress amplitude. , , , , , , ,at the same time m 0、 m 1. m 2. mThe fourth is referred to as the zeroth, first, second, and fourth order spectral moments of the stress power spectral density. i The spectral moment of order is calculated using the following formula: (15) In the formula, f The vibration frequency, G ( f ) represents the load power spectral density response function; The power function formula is one of the commonly used forms of SN curves: (16) in, k , C For material constants, N This represents the number of loop iterations. By combining the SN curve of power-law materials with Miner's linear cumulative damage theory, the fatigue damage rate of critical structural components was calculated. for: (17) Among them fatigue damage rate The unit is damage per second. v p The mathematical expectation of the peak value per unit time is calculated from the spectral moments of the stress power spectral density function: (18) When the damage level reaches 1, the structure is considered to have experienced fatigue failure, and the fatigue life is... T The calculation formula is: (19) Among them fatigue life T The unit is seconds.

[0013] According to a second aspect of the present invention, the present invention provides a system for evaluating the fatigue characteristics of periodic structural vibrations of an aircraft, for implementing the method for evaluating the fatigue characteristics of periodic structural vibrations of an aircraft described in the first aspect, comprising: The eigenvalue solving module is used to construct the finite element model of the periodic structural feature cell. Through dynamic condensation and periodic structural characteristics, it solves the eigenvalue problem of the transfer matrix between the cross sections of the feature cell, and obtains the eigenvalues ​​and eigenvectors of the propagating wave. The displacement and stress frequency response calculation module is used to filter out rapidly decaying waves based on eigenvalues ​​and eigenvectors using wave basis thresholds. Based on the propagation, reflection and superposition of the remaining waves in the wave domain, the displacement and stress frequency response of the periodic structure are obtained through physical domain mapping and finite element transformation. The fatigue characteristic assessment module is used to calculate the stress power spectral density response at the critical point of the structure by using the obtained stress frequency response and the input load power spectral density. It also evaluates the broadband vibration fatigue characteristics of the periodic structure by using the Dirlik model, the material SN curve and the cumulative damage theory.

[0014] According to a third aspect of the present invention, the present invention provides a terminal device, including a memory, a processor, and a computer program stored in the memory and capable of running on the processor, characterized in that the memory stores the computer program capable of running on the processor, and when the processor loads and executes the computer program, it employs the aircraft periodic structural vibration fatigue characteristic evaluation method described in the first aspect.

[0015] According to a fourth aspect of the present invention, the present invention provides a storage medium containing computer-executable instructions, which, when executed by a computer processor, are used to perform the method for evaluating the fatigue characteristics of periodic structural vibrations of an aircraft as described in the first aspect.

[0016] According to a fifth aspect of the present invention, the present invention provides a computer program product comprising a computer program, which, when executed by a processor, is used to load and execute the method for evaluating the fatigue characteristics of periodic structural vibrations of an aircraft as described in the first aspect.

[0017] Compared with the prior art, the present invention has the following beneficial effects: 1. Based on the wave finite element method and dynamic condensation technology, this invention constructs a periodic structural dynamic model applicable to full-band analysis. By solving the eigenvalue problem of the characteristic cell transfer matrix, the characteristic information of the propagating wave is accurately obtained. This invention overcomes the limitations of the traditional finite element method in high-frequency band calculation and the statistical energy analysis method in obtaining accurate local response, and realizes efficient and accurate prediction of structural displacement and stress frequency response.

[0018] 2. This invention effectively reduces the computational scale in wave domain analysis by filtering out rapidly decaying waves through wave basis thresholding. Combined with the wave propagation, reflection and superposition mechanisms in the structure, and through physical domain mapping and finite element transformation, it significantly improves the solution efficiency of the dynamic response of the structure under broadband excitation while ensuring computational accuracy.

[0019] 3. This invention combines stress frequency response with input load power spectral density, and establishes an integrated analysis process from load excitation to fatigue life assessment through the Dirlik model, material SN curves and Miner linear cumulative damage theory. This enables efficient and accurate assessment of broadband vibration fatigue characteristics of periodic structures, and provides reliable technical support for the performance verification and optimization design of periodic structures of high-speed aircraft under harsh broadband noise environments. Attached Figure Description

[0020] Figure 1 This is a flowchart illustrating the evaluation method described in this invention; Figure 2 This is a three-dimensional schematic diagram of the periodic structure of the aircraft in Embodiment 1 of the present invention; Figure 3 This is a schematic diagram of the periodic structural feature cell division in Embodiment 1 of the present invention; Figure 4 This is a graph of the input load power spectral density in Embodiment 1 of the present invention; Figure 5 This is the Mises stress root mean square response contour map of the structure in Embodiment 1 of the present invention; Figure 6 This is a stress power spectral density response curve of a structural critical point in Embodiment 1 of the present invention; Figure 7 This is a schematic diagram illustrating the contribution of each frequency band to damage at the critical points of the panel structure in Embodiment 1 of the present invention. Figure 8 This is a schematic diagram illustrating the contribution of each frequency band to damage at dangerous points in the load-bearing plate structure in Embodiment 1 of the present invention. Detailed Implementation

[0021] The technical solutions of the embodiments of this disclosure will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this disclosure, and not all embodiments. Based on the embodiments of this disclosure, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this disclosure.

[0022] Example 1: Please see Figure 1-Figure 8 The present invention provides a technical solution: a method for evaluating the fatigue characteristics of periodic structural vibrations of an aircraft, comprising: S1. Establish a finite element model of the periodic structural characteristic cell. Through dynamic condensation and periodic structural characteristics, solve the eigenvalue problem of the transfer matrix between cell sections to obtain the eigenvalues ​​and eigenvectors of the propagating wave, as detailed below: S11. Model and mesh the characteristic cells of the periodic structure, and extract the mass matrix, stiffness matrix and damping matrix corresponding to the model; Introducing dynamic stiffness matrix D The dynamic equation of the characteristic cell can be written as: (1) In the formula, , K , C , MThese are the stiffness matrix, damping matrix, and mass matrix of the cell, respectively. q Let be the nodal displacement vector. f Let i be the nodal force vector, and i be the imaginary unit. Angular frequency; S12. By utilizing the dynamic condensation and periodic structural characteristics, the eigenvalue problem of the transfer matrix between characteristic cell sections is solved to obtain the eigenvalues ​​and eigenvectors of the propagating wave, as detailed below: Dividing the nodes contained in a feature cell into three parts—left section, right section, and internal nodes—the dynamic equation of the cell can be written as follows when the internal nodes are not subjected to external forces: (2) In the formula, the subscript L and R These represent the nodes on the left and right sides of the cell. I Represents nodes within a cell; By eliminating the degrees of freedom within the characteristic cell structure through dynamic condensation, equation (2) can be written as: (3) in, , , , ; Because of the continuity of displacement and the balance of forces between adjacent cells in a periodic structure, the first... n The right section of the cell and the first n The left cross section of +1 cell has the following relationship: (4) Introducing the transfer matrix T The matrix form of equation (4) can be expressed as: (5) Based on the transfer matrix obtained from the characteristic cells, the propagation of waves in the structure can be described by the eigenvalue problem, which can be expressed as: (6) Where: eigenvalues It describes the amplitude attenuation and phase change of a free wave during propagation. k The wave number represents the free wave, and Δ represents the length of the structural feature cell in the direction of wave propagation. S2. By using a wavebase threshold to filter out rapidly decaying waves, and based on the propagation, reflection, and superposition of the residual waves in the wave domain, through physical domain mapping and finite element transformation, the displacement and stress frequency response of the structure are obtained accurately and efficiently, as follows: S21. In actual calculations, rapidly decaying waves have minimal impact on the overall vibration response of the structure. By using eigenvalues ​​to filter waves, rapidly decaying waves can be effectively eliminated. (7) In the formula, Indicates the fundamental cutoff coefficient; S22. Mapping the propagation, reflection, and superposition of residual waves in the wave domain to the physical domain allows for efficient and accurate acquisition of the structure's displacement response in the physical domain: Based on the relevant principles of finite element method, the relationship between strain and displacement of element nodes is used to further obtain the conversion relationship between stress and displacement of element nodes, thereby accurately obtaining the stress response of each node of the structure. For a regular eight-node hexahedral element, the displacement of any point inside it can be written as: (8) in, u i , v i , w i Each node of the unit is located at x , y , z Component displacements on the axis N i For the first i The shape function corresponding to each node is expressed as follows: (9) In the formula, x c , y c , z c The value represents the coordinates of the center of the regular hexahedron. a , b , c Represent x , y , z Half the length of the unit side in the direction; By differentiating the displacement field in spatial coordinates, the relationship between strain and displacement at any point within the element can be obtained: (10) in, e x , e y , e z respectively along x , y ,z Normal strain in the direction, c xy , c yz , c zx They are respectively xyz , yz , zx Shear strain on the coordinate plane; Based on the constitutive relation of materials, the relationship between stress and strain at any point within an element can be established: (11) in, s x , s y , s z respectively along x , y , z Normal stress in the direction, t xy , t yz , t zx They are respectively xyz , yz , zx Shear stress on the coordinate plane, D t It is an elastic matrix, and its expression varies depending on the material properties; S3. By utilizing the input load power spectral density and combining it with the stress frequency response, the stress power spectral density response at the structural critical point is calculated. Using the Dirlik model, material SN curves, and cumulative damage theory, the broadband vibration fatigue characteristics of periodic structures are efficiently and accurately evaluated, as detailed below: S31. Using the obtained stress frequency response and the input load power spectral density, the stress power spectral density response at the structural critical point is calculated as follows: Based on the stress frequency response and load power spectral density, the formula for calculating the structural stress power spectral density response is as follows: (12) In the formula, G Y ( f ) represents the structural stress power spectral density response function matrix. H ( f () is the structural stress frequency response function matrix. G F ( f () represents the input load power spectral density function matrix. H Represents the conjugate transpose of a matrix; Based on the stress power spectral density response, by solving the root mean square value of the response curves of each node of the structure, the stress hazard points of the structure can be found and their corresponding stress power spectral density response curves can be extracted. The formula for calculating the root mean square value of stress response is: (13) In the formula, s rms This represents the root mean square value of the nodal stress response. G x ( f ) represents the nodal stress power spectral density response function. f 1. f 2 represents the upper and lower limits of the analysis frequency range; S32. Substitute the stress power spectral density response at the critical point into the Dirlik model, and combine the power function material SN curve with Miner's linear cumulative damage theory to calculate the broadband vibration fatigue characteristics of the periodic structure: The Dirlik model is based on 70 forms of power spectral density function. It proposes a method that uses an exponential distribution and two Rayleigh distributions to approximate the probability density function of rainflow cycle counting amplitude. Its expression is: (14) in, S The stress amplitude, This is called the regularized stress amplitude. , , , , , , ,at the same time m 0、 m 1. m 2. m The fourth is referred to as the zeroth, first, second, and fourth order spectral moments of the stress power spectral density. i The spectral moment of order is calculated using the following formula: (15) In the formula, f The vibration frequency, G ( f ) represents the load power spectral density response function; The SN curve of a material describes the relationship between stress level and the number of cycles. It is one of the basic data for characterizing the fatigue performance of materials and is also the basis for predicting vibration fatigue life. The power function formula is one of the commonly used forms of the SN curve. (16) in, k , C For material constants, N This represents the number of loop iterations. By combining the SN curve of power-law materials with Miner's linear cumulative damage theory, the fatigue damage rate of critical structural components was calculated. for: (17) Among them fatigue damage rate The unit is damage per second. v p The mathematical expectation of the peak value per unit time can be calculated from the spectral moments of the stress power spectral density function: (18) When the damage level reaches 1, the structure is considered to have experienced fatigue failure, and the fatigue life is... T The calculation formula is: (19) Among them fatigue life T The unit is seconds.

[0023] The technical solution of this embodiment will be further explained below with reference to specific examples: This embodiment uses Figure 2 The periodic structure of the aircraft shown is used as an example for illustration. Figure 2 The periodic structure shown consists of a sandwich structure bonded to a metal load-bearing plate, through which... Figure 2 The structure shown is divided into characteristic cells, which can be used to obtain... Figure 3 The cell partitioning results shown, based on the eigenvalue problem of the transfer matrix derived from the characteristic cells, can calculate the eigenvalues ​​and eigenvectors of the propagating wave: Where: eigenvalues It describes the amplitude attenuation and phase change of a free wave during propagation. k The wave number represents the free wave, and Δ represents the length of the structural feature cell in the direction of wave propagation. Based on the eigenvalues ​​and eigenvectors of propagating waves, fast-decaying waves are filtered out using wave basis thresholding. Based on the propagation, reflection and superposition of residual waves in the wave domain, the displacement and stress frequency response of the structure are obtained accurately and efficiently through physical domain mapping and finite element transformation. use Figure 4 The stress power spectral density response of the structure can be calculated from the input load power spectral density shown. In the formula, G Y( f ) represents the structural stress power spectral density response function matrix. H ( f ) is the structural stress frequency response function matrix. G F ( f () represents the input load power spectral density function matrix. H Represents the conjugate transpose of a matrix; Based on the stress power spectral density response, we can obtain Figure 5 The stress root mean square response contour plot of the structure shown is for... Figure 5 The cloud map shown can identify the stress hazard points of the structure and extract [the relevant data]. Figure 6 The stress power spectral density response curve of the structure shown is shown. By substituting the stress power spectral density response at the critical point into the Dirlik model, and combining the SN curve of power-law materials with Miner's linear cumulative damage theory, it is possible to calculate... Figure 7 and Figure 8 The broadband vibration fatigue characteristics of the periodic structure shown are as follows. The Dirlik model expression is: in, S The stress amplitude, This is called the regularized stress amplitude. , , , , , , ,at the same time m 0、 m 1. m 2. m The fourth is referred to as the zeroth, first, second, and fourth order spectral moments of the stress power spectral density. i The spectral moment of order is calculated using the following formula: In the formula, f The vibration frequency, G ( f ) is the load power spectral density response function.

[0024] The SN curve of a material describes the relationship between stress level and the number of cycles. It is one of the fundamental data for characterizing the fatigue performance of materials and is also the basis for predicting vibration fatigue life. The power function formula is one of the commonly used forms of the SN curve: in, k , C For material constants,N This represents the number of loop iterations. By combining the SN curve of power-law materials with Miner's linear cumulative damage theory, the fatigue damage rate of critical structural components was calculated. for: Among them fatigue damage rate The unit is damage per second. v p The mathematical expectation of the peak value per unit time can be calculated from the spectral moments of the stress power spectral density function: When the damage level reaches 1, the structure is considered to have experienced fatigue failure, and the fatigue life is... T The calculation formula is: When the damage level reaches 1, the service life of the sandwich structure at the critical point calculated by this invention is 11,584 seconds, and the service life of the load-bearing plate at the critical point is 83,434 seconds.

[0025] In summary, this invention, based on the wave finite element method and dynamic condensation technology, constructs a dynamic model of periodic structures suitable for full-band analysis. By solving the eigenvalue problem of the characteristic cell transfer matrix, it accurately obtains the characteristic information of propagating waves and filters out rapidly decaying waves using wave basis thresholding, effectively reducing the computational scale in wave domain analysis and achieving efficient and accurate prediction of structural displacement and stress frequency response. Furthermore, combining stress frequency response and input load power spectral density, and using the Dirlik model, material SN curves, and Miner's linear cumulative damage theory, an integrated analysis process from load excitation to fatigue life assessment is established. This enables efficient and accurate evaluation of the broadband vibration fatigue characteristics of periodic structures, meeting the performance verification and optimization design requirements of periodic structures in high-speed aircraft under harsh broadband noise environments.

[0026] Example 2: This invention provides a system for evaluating the fatigue characteristics of periodic structural vibrations of aircraft, used to implement the method for evaluating the fatigue characteristics of periodic structural vibrations of aircraft described in Embodiment 1, comprising: The eigenvalue solving module is used to construct the finite element model of the periodic structural feature cell. Through dynamic condensation and periodic structural characteristics, it solves the eigenvalue problem of the transfer matrix between the cross sections of the feature cell, and obtains the eigenvalues ​​and eigenvectors of the propagating wave. The displacement and stress frequency response calculation module is used to filter out rapidly decaying waves based on eigenvalues ​​and eigenvectors using wave basis thresholds. Based on the propagation, reflection and superposition of the remaining waves in the wave domain, the displacement and stress frequency response of the periodic structure are obtained through physical domain mapping and finite element transformation. The fatigue characteristic assessment module is used to calculate the stress power spectral density response at the critical point of the structure by using the obtained stress frequency response and combining it with the input load power spectral density. It also evaluates the broadband vibration fatigue characteristics of the periodic structure by using the Dirlik model, the material SN curve and the cumulative damage theory.

[0027] Example 3: The present invention provides a terminal device, including a memory, a processor, and a computer program stored in the memory and capable of running on the processor. The memory stores the computer program capable of running on the processor. When the processor loads and executes the computer program, it adopts the method for identifying radiation-conducting heat transfer parameters of thermal protection structures described in Embodiment 1.

[0028] It should be noted that the terminal device can be a computer device such as a desktop computer, a laptop computer, or a cloud server, and the terminal device includes, but is not limited to, a processor and a memory. For example, the terminal device may also include input / output devices, network access devices, and buses.

[0029] Furthermore, the processor can be a central processing unit (CPU). Of course, depending on the actual use, other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), off-the-shelf programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. can also be used. The general-purpose processor can be a microprocessor or any conventional processor, etc., and this application does not limit it in this regard.

[0030] Example 4: The present invention provides a storage medium containing computer-executable instructions, which, when executed by a computer processor, are used to perform the method for evaluating the fatigue characteristics of periodic structural vibrations of an aircraft as described in Embodiment 1.

[0031] The computer program can be stored in a computer-readable medium. The computer program includes computer program code, which can be in the form of source code, object code, executable file, or certain middleware. The computer-readable medium includes any entity or device capable of carrying computer program code, recording media, USB flash drive, portable hard drive, magnetic disk, optical disk, computer memory, read-only memory (ROM), random access memory (RAM), electrical carrier signals, telecommunication signals, and software distribution media, etc. It should be noted that the computer-readable medium includes, but is not limited to, the above-mentioned components.

[0032] Example 5: The present invention provides a computer program product, which includes a computer program. When the computer program is executed by a processor, it is used to load and execute the method for evaluating the fatigue characteristics of periodic structural vibration of an aircraft as described in Embodiment 1.

[0033] It should be noted that, in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such process, method, article, or apparatus.

[0034] For those skilled in the art, the specific meaning of the above terms in this invention can be understood according to the specific circumstances. When an element is referred to as "assembled on," "mounted on," "fixed on," or "set on" another element, it can be directly expressed and does not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples.

Claims

1. A method for evaluating the fatigue characteristics of periodic structural vibrations in aircraft, characterized in that, Includes the following steps: A finite element model of a periodic structural feature cell is constructed. By using dynamic condensation and periodic structural characteristics, the eigenvalue problem of the transfer matrix between the feature cell sections is solved, and the eigenvalues ​​and eigenvectors of the propagating wave are obtained. Based on eigenvalues ​​and eigenvectors, fast-decaying waves are filtered out using a wave basis threshold. Based on the propagation, reflection, and superposition of the remaining waves in the wave domain, the displacement and stress frequency response of the periodic structure are obtained through physical domain mapping and finite element transformation. Using the obtained stress frequency response and the input load power spectral density, the stress power spectral density response at the critical point of the structure is calculated. The broadband vibration fatigue characteristics of the periodic structure are evaluated by using the Dirlik model, the material SN curve, and the cumulative damage theory.

2. The method for evaluating the fatigue characteristics of periodic structural vibration of an aircraft according to claim 1, characterized in that: The finite element model of the periodic structural feature cell is constructed as follows: The periodic structure's characteristic cells are modeled and meshed, and the corresponding mass matrix, stiffness matrix, and damping matrix are extracted. Introducing dynamic stiffness matrix D The dynamic equation of the characteristic cell is expressed as: （1） In the formula, , K , C , M These are the stiffness matrix, damping matrix, and mass matrix of the cell, respectively. q Let be the nodal displacement vector. f Let i be the nodal force vector, and i be the imaginary unit. ω is the angular frequency.

3. The method for evaluating the fatigue characteristics of periodic structural vibration of an aircraft according to claim 1, characterized in that: By utilizing the dynamic condensation and periodic structural characteristics, the eigenvalue problem of the transfer matrix between characteristic cell sections is solved, yielding the eigenvalues ​​and eigenvectors of the propagating wave, as detailed below: Dividing the nodes contained in a feature cell into three parts—left section, right section, and internal nodes—the dynamic equation of the cell is expressed as follows when the internal nodes are not subjected to external forces: （2） In the formula, the subscript L and R These represent the nodes on the left and right sides of the cell, respectively. I Represents nodes within a cell; By eliminating the degrees of freedom within the characteristic cell structure through dynamic condensation, equation (2) can be rewritten as: （3） in, , , , ; Because of the continuity of displacement and the balance of forces between adjacent cells in a periodic structure, the first... n The right section of the cell and the first n The left cross section of +1 cell has the following relationship: （4） Introducing the transfer matrix T Equation (4) can be expressed in matrix form as follows: （5） Based on the transfer matrix obtained from the characteristic cells, the wave propagation in the structure is expressed through the eigenvalue problem, which is expressed as: （6） Where: eigenvalues It describes the amplitude attenuation and phase change of a free wave during propagation. k The wave number represents the free wave, and Δ represents the length of the structural feature cell in the direction of wave propagation.

4. The method for evaluating the fatigue characteristics of periodic structural vibration of an aircraft according to claim 1, characterized in that: Based on eigenvalues ​​and eigenvectors, a wave basis threshold is used to filter out rapidly decaying waves, as follows: （7） In the formula, This represents the fundamental cutoff coefficient.

5. The method for evaluating the fatigue characteristics of periodic structural vibration of an aircraft according to claim 1, characterized in that: Based on the propagation, reflection, and superposition of the residual waves in the wave domain after screening, the displacement and stress frequency response of the periodic structure are obtained through physical domain mapping and finite element transformation, as follows: Based on the principles of the finite element method, the relationship between strain and displacement at element nodes is used to further derive the conversion relationship between stress and displacement at element nodes, thereby obtaining the stress response of each node in the structure: For a regular eight-node hexahedral element, the displacement of any point inside it can be written as: （8） in, u i , v i , w i Each node of the unit is located at x , y , z Component displacements on the axis N i For the first i The shape function corresponding to each node is expressed as follows: （9） In the formula, x c , y c , z c The value represents the coordinates of the center of the regular hexahedron. a , b , c Represent x , y , z Half the length of the unit side in the direction; By differentiating the displacement field in spatial coordinates, the relationship between strain and displacement at any point within the element can be obtained: （10） in, ε x , ε y , ε z respectively along x , y , z Normal strain in the direction, γ xy , γ yz , γ zx They are respectively xy , yz , zx Shear strain on the coordinate plane; Based on the constitutive relation of materials, establish the relationship between stress and strain at any point within the element: （11） in, σ x , σ y , σ z respectively along x , y , z Normal stress in the direction, τ xy , τ yz , τ zx They are respectively xy , yz , zx Shear stress on the coordinate plane, D t It is an elastic matrix, and its expression varies depending on the material properties.

6. The method for evaluating the fatigue characteristics of periodic structural vibration of an aircraft according to claim 1, characterized in that: Using the obtained stress frequency response and the input load power spectral density, the stress power spectral density response at the structural critical point is calculated, as follows: The formula for calculating the structural stress power spectral density response is: （12） In the formula, G Y ( f ) represents the structural stress power spectral density response function matrix. H ( f ) is the structural stress frequency response function matrix. G F ( f () represents the input load power spectral density function matrix. H Represents the conjugate transpose of a matrix; Based on the stress power spectral density response, by solving the root mean square value of the response curves of each node of the structure, the stress hazard points of the structure are found, and their corresponding stress power spectral density response curves are extracted. The formula for calculating the root mean square value of stress response is: （13） In the formula, σ rms This represents the root mean square value of the nodal stress response. G x ( f ) represents the nodal stress power spectral density response function. f 1. f 2 represents the upper and lower limits of the analysis frequency range.

7. The method for evaluating the fatigue characteristics of periodic structural vibration of an aircraft according to claim 1, characterized in that: The broadband vibration fatigue characteristics of periodic structures are evaluated using the Dirlik model, material SN curves, and cumulative damage theory, as detailed below: Substituting the stress power spectral density response at the critical point into the Dirlik model, and combining the power-law material SN curve with Miner's linear cumulative damage theory, the broadband vibration fatigue characteristics of the periodic structure are calculated: The Dirlik model expression is: （14） in, S The stress amplitude, This is called the regularized stress amplitude. , , , , , ,at the same time m 0、 m 1. m 2. m The fourth is referred to as the zeroth, first, second, and fourth order spectral moments of the stress power spectral density. i The spectral moment of order is calculated using the following formula: （15） In the formula, f The vibration frequency, G ( f ) represents the load power spectral density response function; The power function formula is one of the commonly used forms of SN curves: （16） in, k , C For material constants, N This represents the number of loop iterations. By combining the SN curve of power-law materials with Miner's linear cumulative damage theory, the fatigue damage rate of critical structural components was calculated. for: （17） Among them fatigue damage rate The unit is damage per second. v p The mathematical expectation of the peak value per unit time is calculated from the spectral moments of the stress power spectral density function. （18） When the damage level reaches 1, the structure is considered to have experienced fatigue failure, and the fatigue life is... T The calculation formula is: （19） Among them fatigue life T The unit is seconds.

8. A system for evaluating the fatigue characteristics of periodic structural vibrations of an aircraft, used to implement the method for evaluating the fatigue characteristics of periodic structural vibrations of an aircraft as described in any one of claims 1 to 7, characterized in that, include: The eigenvalue solving module is used to construct the finite element model of the periodic structural feature cell. Through dynamic condensation and periodic structural characteristics, it solves the eigenvalue problem of the transfer matrix between the cross sections of the feature cell, and obtains the eigenvalues ​​and eigenvectors of the propagating wave. The displacement and stress frequency response calculation module is used to filter out rapidly decaying waves based on eigenvalues ​​and eigenvectors using wave basis thresholds. Based on the propagation, reflection and superposition of the remaining waves in the wave domain, the displacement and stress frequency response of the periodic structure are obtained through physical domain mapping and finite element transformation. The fatigue characteristic assessment module is used to calculate the stress power spectral density response at the critical point of the structure by using the obtained stress frequency response and the input load power spectral density. It also evaluates the broadband vibration fatigue characteristics of the periodic structure by using the Dirlik model, the material SN curve and the cumulative damage theory.

9. A terminal device, comprising a memory, a processor, and a computer program stored in the memory and capable of running on the processor, characterized in that, The memory stores a computer program that can run on a processor. When the processor loads and executes the computer program, it employs the method for evaluating the fatigue characteristics of periodic structural vibration of an aircraft as described in any one of claims 1 to 7.

10. A storage medium containing computer-executable instructions, characterized in that, The computer-executable instructions, when executed by a computer processor, are used to perform the method for evaluating the fatigue characteristics of periodic structural vibrations of an aircraft as described in any one of claims 1 to 7.

11. A computer program product, characterized in that, The computer program product includes a computer program that, when executed by a processor, is used to load and execute the method for evaluating the fatigue characteristics of periodic structural vibrations of an aircraft as described in any one of claims 1 to 7.

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