A method, system, program product and storage medium for analyzing the flutter characteristics of a graphene-reinforced curved-wall panel under high-speed airflow

Abstract

The application provides a method, system, program product and storage medium for analyzing the flutter characteristics of graphene-reinforced curved wall panels under high-speed airflow, relating to the technical field of aviation-related equipment. The method no longer simplifies the research object into a homogeneous flat plate, but constructs a control equation with a curvature correction factor, which can reflect the geometric characteristics and stress state of the curved wall panels of the aircraft. The elastic modulus under different candidate distribution modes is introduced as the core variable, enabling the analysis model to evaluate the performance of functionally graded materials. Finally, by comparing the flutter critical boundaries and deformations under different modes, the method can output the optimal graphene arrangement configuration. This process solves the problem of analyzing the arrangement of functionally graded graphene-reinforced composites under high-speed airflow and curved structures, enabling the skin structure of new aircraft to have both lightweight and high anti-vibration performance.

Description

Technical Field

[0001] This application relates to the field of aviation-related equipment technology, and in particular to a method, system, program product and storage medium for analyzing the flutter characteristics of graphene-reinforced curved panels under high-speed airflow. Background Technology

[0002] Thin-walled structures of aircraft, such as fuselage skin and air intakes, must simultaneously meet the design requirements of lightweighting, high strength, and high vibration resistance. Among these, aeroelastic flutter, as a highly destructive vibration, is a risk point to be avoided in aircraft structural design.

[0003] In recent years, functionally graded graphene-reinforced composites with excellent mechanical properties have offered new possibilities for achieving lightweight, flutter-resistant designs for aircraft. By arranging graphene in composite materials according to a specific gradient, it is hoped that the stiffness and vibration resistance of the panels can be improved without increasing the structural weight.

[0004] However, the relevant technologies can only calculate planes. In real-world scenarios, the thin-walled structures of aircraft, especially the fuselage and air intakes, are generally curved surfaces with initial curvature, rather than ideal planes. Therefore, there is currently a lack of methods applicable to analyzing the flutter characteristics of functionally graded graphene-reinforced composite material arrangements under high-speed airflow and curved surface structures. Summary of the Invention

[0005] This application provides a method, system, program product, and storage medium for analyzing the flutter characteristics of graphene-reinforced curved panels under high-speed airflow, which solves the problem that related technologies cannot analyze the arrangement of functionally graded graphene-reinforced composite materials under high-speed airflow and curved structures.

[0006] In a first aspect, this application provides a method for analyzing the flutter characteristics of a graphene-reinforced curved panel under high-speed airflow, comprising: obtaining the initial physical parameters and environmental condition parameters of the target curved panel, and obtaining candidate distribution patterns; calculating the elastic modulus of each layer of the target curved panel under any candidate distribution pattern; constructing a control equation with a curvature correction factor based on the initial physical parameters, environmental condition parameters, and elastic modulus; solving the control equation, and calculating the elastic deformation and flutter critical boundary when the system state represented by the control equation becomes unstable according to a preset instability criterion; comparing the elastic deformation and flutter critical boundary corresponding to different candidate distribution patterns, and outputting the graphene arrangement configuration of the target curved panel.

[0007] By adopting the above technical solution, this method no longer simplifies the research object to a homogeneous flat plate. Instead, it constructs governing equations with curvature correction factors to reflect the geometric characteristics and stress state of the curved panels of an aircraft. Introducing the elastic modulus under different candidate distribution modes as core variables into the calculation enables the analysis model to evaluate the performance of functionally graded materials. Finally, by comparing the flutter critical boundary and deformation under different modes, this method can output the optimal graphene arrangement configuration. This process solves the problem that related technologies cannot analyze the arrangement of functionally graded graphene-reinforced composite materials under high-speed airflow and curved structures, enabling the skin structure of the new aircraft to possess both lightweight and high vibration resistance.

[0008] In conjunction with some embodiments of the first aspect, in some embodiments, the candidate distribution patterns include: a uniform distribution pattern, a surface enrichment distribution pattern, and a central enrichment distribution pattern.

[0009] By employing the aforementioned technical solution, this method identifies three representative candidate distribution patterns: uniform distribution, surface-enriched distribution, and central-enriched distribution. These three patterns correspond to three classic arrangement strategies of graphene reinforcing phases in the material matrix: overall reinforcement, strengthening surface flexural stiffness, and reinforcing core shear capacity. This allows computational resources to be focused on comparing the performance advantages and disadvantages of these configurations most likely to achieve engineering applications, thereby yielding conclusions with industrial guidance value.

[0010] In conjunction with some embodiments of the first aspect, in some embodiments, before calculating the elastic modulus of each layer of the target curved panel under the candidate distribution pattern, the method further includes: calling the target mass fraction distribution function corresponding to the candidate distribution pattern; the target mass fraction distribution function is defined as follows: for the uniform distribution pattern:

[0011] :

[0012] For the enrichment distribution pattern in the middle region:

[0013] In the formula, For the first Target mass fraction of the target curved wall panel. This represents the total mass fraction of graphene. The number of layers after discretization of the target curved panel. For the first Layered target curved wall panel, .

[0014] By adopting the above technical solution, three macroscopic and conceptual graphene distribution patterns are transformed into target quality fractions that can be quantified layer by layer.

[0015] In conjunction with some embodiments of the first aspect, in some embodiments, the step of calculating the elastic modulus of each layer of the target curved panel under the candidate distribution mode specifically includes calculating the elastic modulus of each layer of the target curved panel under the candidate distribution mode based on the target mass fraction distribution function and initial physical parameters; wherein: the calculation function is:

[0016]

[0017]

[0018]

[0019]

[0020] In the formula, For the first The elastic modulus of the target curved wall panel. For the first Layered graphene , For geometric parameters, For geometric parameters, The length of the graphene. The width of the graphene is... The thickness of the graphene. The density is the polymer matrix. The density of graphene, This is the elastic attenuation reduction rate along the length direction. This is the elastic attenuation reduction rate in the width direction. for , This represents the elastic modulus of graphene.

[0021] By employing the aforementioned technical solution, the target mass fraction at the previous level is transformed into the elastic modulus that affects structural stiffness. Specifically, the formula converts the mass concept into a volume concept while incorporating the geometric parameters of graphene and the elastic decay reduction rate, simulating the mechanical response after the interaction between graphene and the matrix material. This series of formulas reflects the nonlinear changes in the internal stiffness of the material caused by the addition and distribution variations of graphene.

[0022] In conjunction with some embodiments of the first aspect, in some embodiments, the calculation function of the governing equation is:

[0023]

[0024] In the formula, For bending moment, For internal forces, For inertia, The lateral displacement of the target curved wall panel. These are the spatial coordinates along the length of the target curved panel. Let be the initial radius of curvature of the target curved wall panel. For time, The external aerodynamic load acting on the target curved wall plate.

[0025] By adopting the above technical solution, this equation connects the geometric nonlinearity of the structure, the gradient characteristics of the material, and the external dynamic load, and constructs a mathematical model that approximates the real physical process, providing a theoretical basis for accurately solving the flutter problem.

[0026] In conjunction with some embodiments of the first aspect, in some embodiments, after the step of constructing a control equation with a curvature correction factor based on initial physical parameters, environmental condition parameters, and elastic modulus, the method further includes: performing order reduction discretization processing on the control equation to generate a nonlinear differential equation system; solving the control equation; and calculating and obtaining the elastic deformation amount and flutter critical boundary when the system state represented by the control equation becomes unstable according to a preset instability criterion. Specifically, this includes: solving the nonlinear differential equation system; and calculating and obtaining the elastic deformation amount and flutter critical boundary when the system state represented by the nonlinear differential equation system becomes unstable according to a preset instability criterion.

[0027] By employing the above technical solution, the original governing equation is a complex partial differential equation, whose solution requires enormous computational resources and is difficult to converge. By performing a reduction-order discretization process, this equation can be transformed into a more manageable one. This transformation reduces the computational complexity and the demand for computational resources.

[0028] In conjunction with some embodiments of the first aspect, in some embodiments, the preset instability criterion is: the eigenvalues ​​of the governing equation change from negative real parts to positive real parts.

[0029] By employing the above technical solution, when the real parts of all eigenvalues ​​are negative, any small disturbance will decay over time, and the system will exhibit a stable state. However, once the real part of any eigenvalue crosses zero and becomes positive, the disturbance will be amplified, leading to increased amplitude, which physically corresponds to the occurrence of flutter. Therefore, using this criterion makes the judgment of instability no longer dependent on vague, subjective methods such as observing whether the time-domain response curve diverges, but rather becomes a precise and automatically identifiable mathematical event.

[0030] Secondly, this application provides a flutter characteristic analysis system for graphene-reinforced curved panels under high-speed airflow. The flutter characteristic analysis system for graphene-reinforced curved panels under high-speed airflow includes: one or more processors and a memory; the memory is coupled to one or more processors, the memory is used to store computer program code, the computer program code includes computer instructions, and one or more processors call the computer instructions to cause the flutter characteristic analysis system for graphene-reinforced curved panels under high-speed airflow to perform the method described in the first aspect and any possible implementation thereof.

[0031] Thirdly, this application provides a computer program product containing instructions that, when the computer program product is run on a flutter characteristic analysis system for graphene-reinforced curved panels under high-speed airflow, cause the flutter characteristic analysis system for graphene-reinforced curved panels under high-speed airflow to perform the method described in the first aspect and any possible implementation thereof.

[0032] Fourthly, this application provides a computer-readable storage medium including a computer program that, when executed by a processor, implements the method described in the first aspect and any possible implementation thereof.

[0033] One or more technical solutions provided in the embodiments of this application have at least the following technical effects or advantages:

[0034] This method no longer simplifies the research object to a homogeneous flat plate. Instead, it constructs governing equations with curvature correction factors to reflect the geometric characteristics and stress state of the curved panels of an aircraft. By introducing the elastic modulus under different candidate distribution modes as core variables into the calculation, the analysis model gains the ability to evaluate the performance of functionally graded materials. Finally, by comparing the flutter critical boundary and deformation under different modes, this method can output the optimal graphene arrangement configuration. This process solves the problem that related technologies cannot analyze the arrangement of functionally graded graphene-reinforced composite materials under high-speed airflow and curved structures, enabling the skin structure of novel aircraft to possess both lightweight and high vibration resistance. Attached Figure Description

[0035] Figure 1 This is a flowchart illustrating a method for analyzing the flutter characteristics of a graphene-reinforced curved panel under high-speed airflow in an embodiment of this application.

[0036] Figure 2 This is a schematic diagram of a physical model of the target curved wall panel and its working conditions in an embodiment of this application;

[0037] Figure 3 This is a structural cross-sectional schematic diagram of three candidate distribution patterns in the embodiments of this application.

[0038] Figure 4 This is a schematic diagram of a simulation result of the effect of the static aerodynamic thermal load on the graphene distribution pattern in an embodiment of this application;

[0039] Figure 5 This is a schematic diagram of a simulation result of the effect of graphene mass fraction on static aerodynamic heat load in an embodiment of this application;

[0040] Figure 6 This is a schematic diagram of a simulation result of the static aerodynamic thermal load being affected by dimensionless temperature rise in an embodiment of this application;

[0041] Figure 7 This is a schematic diagram of a simulation result of the effect of initial curvature on the static aerodynamic thermal load in an embodiment of this application;

[0042] Figure 8 This is a schematic diagram of a simulation result of the static aerodynamic thermal load being affected by dimensionless dynamic pressure in an embodiment of this application.

[0043] Figure 9 This is a schematic diagram of a simulation result showing the effect of graphene mass fraction on static aeroelastic deformation in an embodiment of this application;

[0044] Figure 10 This is a schematic diagram of a simulation result of the effect of dimensionless temperature rise on the static aeroelastic deformation in an embodiment of this application;

[0045] Figure 11 This is a schematic diagram of a simulation result of the effect of initial geometric curvature on static aeroelastic deformation in an embodiment of this application;

[0046] Figure 12 This is a schematic diagram of a simulation result of the effect of dimensionless dynamic pressure on static aeroelastic deformation in an embodiment of this application.

[0047] Figure 13 This is a schematic diagram of the simulation results showing the influence of initial geometric curvature on the bifurcation characteristics of curved panels under three graphene distribution modes in the embodiments of this application.

[0048] Figure 14 This is a schematic diagram of a simulation result of the bifurcation diagram of the curved wall plate changing with dimensionless temperature rise under different distribution modes in the embodiments of this application.

[0049] Figure 15 This is an exemplary hardware structure diagram of a flutter characteristic analysis system for graphene-reinforced curved panels under high-speed airflow in an embodiment of this application. Detailed Implementation

[0050] The terminology used in the following embodiments of this application is for the purpose of describing particular embodiments only and is not intended to be limiting of this application. As used in the specification and appended claims of this application, the singular expressions “a,” “an,” “the,” “the,” “the,” and “this” are intended to include the plural expressions as well, unless the context clearly indicates otherwise. It should also be understood that the term “and / or” as used in this application refers to and includes any or all possible combinations of one or more of the listed items.

[0051] Hereinafter, the terms "first" and "second" are used for descriptive purposes only and should not be construed as implying or suggesting relative importance or implicitly indicating the number of indicated technical features. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature, and in the description of the embodiments of this application, unless otherwise stated, "multiple" means two or more.

[0052] Please see Figure 1 , Figure 1 This is a flowchart illustrating a method for analyzing the flutter characteristics of a graphene-reinforced curved panel under high-speed airflow in an embodiment of this application.

[0053] A method for analyzing the flutter characteristics of graphene-reinforced curved panels under high-speed airflow includes:

[0054] S101. Obtain the initial physical parameters and environmental operating condition parameters of the target curved wall panel, and obtain the candidate distribution pattern;

[0055] The initial physical parameters include the geometric dimensions of the target curved panel, such as length, width, and height; the initial geometry, such as initial arch height or initial radius of curvature; the total mass fraction, elastic modulus, density, and geometric dimensions (length, width, and height) of the graphene sheet; and the elastic modulus and density of the matrix material. Environmental parameters include airflow parameters, such as supersonic velocity and Mach number; air medium parameters, such as air density; and thermal environment parameters, such as temperature change.

[0056] Please see Figure 2 , Figure 2 This is a schematic diagram of a physical model of the target curved wall panel and its working conditions in an embodiment of this application;

[0057] In one specific embodiment, the target curved panel and its candidate distribution patterns are modeled. For example... Figure 2 As shown, the target curved panel is a two-dimensional model of a functionally graded graphene sheet reinforced composite (FG-GPLRC) curved panel. The geometric parameters of this model include: length... ,width and thickness The model's geometry has an initial arch height. The boundary condition of this model is simply supported at both ends.

[0058] During the analysis, the target curved panel was subjected to specific environmental operating parameters. For example... Figure 2 As shown, there is a line along the upper surface of the wall panel. A supersonic flow (i.e., along its length) has a velocity of... The air density of the incoming gas is Mach number is Meanwhile, it is assumed that there exists a temperature variation that is uniformly distributed along the thickness direction. .

[0059] In some specific embodiments, the candidate distribution patterns include: uniform distribution pattern, surface enrichment distribution pattern, and central enrichment distribution pattern.

[0060] Among them, the uniform distribution mode refers to the configuration in which the graphene reinforcing phase is uniformly distributed along the thickness direction in the matrix material; the surface enrichment distribution mode refers to the configuration in which the graphene density is highest on the upper and lower surface layers of the wall panel and decreases towards the center; and the central enrichment distribution mode refers to the configuration in which the graphene density is highest on the geometric mid-surface of the wall panel and decreases towards the surface layer.

[0061] Please see Figure 3 , Figure 3 This is a structural cross-sectional schematic diagram of three candidate distribution patterns in the embodiments of this application.

[0062] like Figure 3 As shown, this embodiment predetermines three specific candidate distribution patterns to characterize the arrangement of graphene within the target curved panel.

[0063] Specifically, Figure 3 (a) shows a uniform distribution (UD) mode, which indicates that the graphene reinforcing phase is uniformly distributed along the thickness direction within the plate, and the material properties of each layer are the same.

[0064] Figure 3 (b) shows the central enrichment distribution (O distribution) pattern, which indicates that the density of graphene gradually decreases from the geometric center of the plate in the direction of the upper and lower surface layers, so that the core layer of the wall panel has the highest stiffness.

[0065] Figure 3 (c) shows the surface enrichment distribution (X distribution) pattern, which indicates that the density of graphene gradually increases from the geometry of the plate to the upper and lower surface directions, resulting in the highest stiffness of the surface of the wall panel.

[0066] S102. For any candidate distribution pattern among the candidate distribution patterns, calculate the elastic modulus of each layer of the target curved wall panel under the candidate distribution pattern.

[0067] Among them, the elastic modulus is a physical quantity that characterizes the ability of a material to resist elastic deformation, and its value affects the stiffness of the structure.

[0068] In some embodiments, the process begins by invoking the target mass fraction distribution function corresponding to a specific candidate distribution pattern, substituting initial physical parameters such as the total mass fraction of graphene and the total number of wall layers to analyze the specific mass fraction of each discrete structural layer. Subsequently, the calculated mass fraction of each layer is transformed into an equivalent elastic modulus reflecting the macroscopic mechanical properties of that layer using a micromechanical hybrid law model. Finally, the calculation results for all layers are aggregated to form a sequence of elastic moduli that varies gradient along the wall thickness direction.

[0069] In some specific embodiments, for the surface enrichment distribution pattern, the layer indexes of the upper and lower surface layers and the middle layer of the panel are first determined during the calculation. Then, a higher mass fraction weight is assigned to the surface layer through a distribution function, and this weight is nonlinearly decreased towards the middle layer. This weight distribution is then converted into an elastic modulus distribution, which is not limited here. In other specific embodiments, for the central enrichment distribution pattern, the calculation logic is reversed. The highest mass fraction weight is assigned to the layers near the geometric mid-surface of the panel, and this weight is linearly or nonlinearly decreased towards the upper and lower surface layers. Then, the centrally enhanced mass distribution is mapped to the corresponding central high-stiffness elastic modulus distribution, which is not limited here.

[0070] In some embodiments, prior to the step of calculating the elastic modulus of each layer of the target curved panel under the candidate distribution pattern, the method further includes:

[0071] Invoke the target quality score distribution function corresponding to the candidate distribution pattern; the target quality score distribution function is defined as follows:

[0072] For a uniform distribution pattern:

[0073] :

[0074] For the enrichment distribution pattern in the middle region:

[0075] In the formula, For the first Target mass fraction of the target curved wall panel. This represents the total mass fraction of graphene. The number of layers after discretization of the target curved panel. For the first Layered target curved wall panel, .

[0076] The steps for calculating the elastic modulus of each layer of the target curved panel under candidate distribution patterns specifically include:

[0077] Based on the target mass fraction distribution function and initial physical parameters, the elastic modulus of each layer of the target curved panel under the candidate distribution mode is calculated; where:

[0078] The calculation function is:

[0079]

[0080]

[0081]

[0082]

[0083] In the formula, For the first The elastic modulus of the target curved wall panel. For the first Layered graphene , For geometric parameters, For geometric parameters, The length of the graphene. The width of the graphene is... The thickness of the graphene. The density is the polymer matrix. The density of graphene, This is the elastic attenuation reduction rate along the length direction. This is the elastic attenuation reduction rate in the width direction. for , The elastic modulus of graphene. For the first The target mass fraction of the target curved wall panel.

[0084] In one specific embodiment, in addition to calculating the elastic modulus of each layer, it is also necessary to determine other equivalent material properties of that layer in order to fully construct the governing equations. Specifically, for the functionally graded graphene sheet-reinforced two-dimensional curved panel... Layer, its equivalent Poisson's ratio equivalent density and equivalent thermal expansion coefficient It can be calculated using the mixing law. Its calculation function satisfies:

[0085]

[0086]

[0087]

[0088] In the formula, For the calculated first Volume fraction of layered graphene; These are Poisson's ratio, density, and coefficient of thermal expansion of the graphene material itself, obtained from the initial physical parameters. These are the Poisson's ratio, density, and coefficient of thermal expansion of the polymer matrix material itself, obtained from the initial physical parameters.

[0089] S103. Based on the initial physical parameters, environmental condition parameters and elastic modulus, construct the control equations with curvature correction factors;

[0090] Among them, the governing equation with curvature correction factor is a partial differential equation that can simultaneously describe the interaction between structural deformation, inertial force, elastic force, thermal stress and external aerodynamic force, and specifically takes into account the influence of the initial geometric curvature of the wall panel.

[0091] In one specific embodiment, the step of constructing the governing equations with curvature correction factors establishes the stress-strain relationship of the target curved panel, which satisfies the following formula:

[0092]

[0093]

[0094] In the formula, For in-plane stress, Along the thickness direction The changing elastic modulus; Poisson's ratio; For in-plane strain; Along the thickness direction The coefficient of thermal expansion changes; For temperature rise; and These are in-plane displacement and lateral displacement, respectively. Let be the initial radius of curvature.

[0095] Secondly, the bending moment Surface internal forces Inertial term and external aerodynamic forces By coupling the equations, the governing equations of the nonlinear curved plate are derived. The initial form of these equations is given by the formula, which satisfies the following formula:

[0096]

[0097] In the formula, For bending moment, For internal forces, For inertia, The lateral displacement of the target curved wall panel. These are the spatial coordinates along the length of the target curved panel. Let be the initial radius of curvature of the target curved wall panel. For time, The external aerodynamic load acting on the target curved wall plate.

[0098] , respectively composed of in-plane stress and material density It is obtained by integrating along the thickness.

[0099] Substitute each item into The expansion is performed to obtain the expanded form of the governing equations as follows;

[0100]

[0101] The calculation functions for the parameters included in the expanded governing equations are as follows:

[0102] Bending stiffness With equivalent tensile stiffness Defined as follows:

[0103]

[0104] In-plane forces generated by structural deformation Defined as follows:

[0105]

[0106] Thermal stress caused by temperature rise Defined as follows:

[0107]

[0108] External aerodynamic loads Defined by the following formula:

[0109] In the formula, and The first The elastic modulus and Poisson's ratio of the layer; Total number of floors; For the length of the wall panel, This refers to the wall panel thickness. It is the equivalent thermal expansion coefficient; This is the initial deflection height; The pressure of the fluid is determined by the air density. and incoming flow velocity Calculated; The factor is calculated from the Mach number. Calculated.

[0110] In some preferred embodiments, the governing equations are subjected to order reduction discretization to generate nonlinear differential equations;

[0111] In some specific embodiments,

[0112]

[0113] In the formula, the dimensionless parameters contained in the dimensionless differential equation and their correspondence with the original physical quantities are as follows: These are the dimensionless parameters corresponding to lateral displacement, coordinates, time, and initial deflection, respectively. The initial geometric curvature parameter can also be obtained from the initial arch height. and plate thickness The ratio was calculated to obtain, It is a dimensionless dynamic pressure; It is a dimensionless thermal stress; These are aerodynamic parameters related to Mach number; It is a dimensionless surface internal force.

[0114] In a further embodiment, in order to further simplify the above nonlinear differential equations, a system of nonlinear differential equations is obtained;

[0115] The specific steps are as follows:

[0116] First, to satisfy the boundary conditions of simply supported ends of the wall panel, a linear combination of sine functions is used to represent the dimensionless displacement function of the wall panel, as shown in the following formula:

[0117]

[0118] Substituting the displacement function into the dimensionless differential equation obtained in the previous example and performing integration, we obtain a time-dependent, reduced-order matrix equation, as shown below:

[0119]

[0120] Among them, nonlinear terms and Defined by the following general definition:

[0121]

[0122] To facilitate numerical solutions, the above second-order matrix equations are transformed into a system of four-dimensional first-order nonlinear ordinary differential equations through variable substitution, i.e., a system of nonlinear differential equations, as shown in the following formulas:

[0123]

[0124] in the formula It is a dimensionless displacement function; Dimensionless spatial coordinates; Time is dimensionless.

[0125] and For generalized coordinates, represent the contribution of different modes to the total displacement; Its first-order time derivative; Its second-order time derivative; These are intermediate variables used for the transformation, respectively equal to and ; It is a dimensionless dynamic pressure; These are aerodynamic parameters related to Mach number; It is a dimensionless thermal stress; These are the initial geometric curvature parameters.

[0126] S104. Solve the governing equations and, based on the preset instability criteria, calculate and obtain the elastic deformation and flutter critical boundary when the system state represented by the governing equations becomes unstable.

[0127] In some embodiments, the stability of the equation set is analyzed by gradually increasing the dynamic pressure or temperature rise in the environmental operating parameters and continuously monitoring the eigenvalues ​​of the Jacobian matrix of the system. Once a preset instability criterion is triggered, for example, when the real part of the eigenvalue changes from a negative value to a positive value by crossing the imaginary axis, the dynamic pressure and frequency at this moment are recorded as the flutter critical boundary, and the maximum static deformation of the system before instability is calculated at the same time.

[0128] In some embodiments, in the dimensionless differential equation, the time-invariant load term generated by the combined action of the initial geometry and the incoming dynamic pressure is defined as the static aerodynamic load. .

[0129] First, by determining the dimensionless initial geometric height Taking the derivative, we obtain the following formula:

[0130]

[0131] Then, the result of the above equation is compared with the dimensionless dynamic pressure. Coupling yields static aerodynamic loads. The calculation function;

[0132] In dimensionless differential equations, the load term generated by the combined action of thermal stress and initial geometric curvature, which also does not change with time, is defined as the static thermal load. Its calculation function is shown below:

[0133]

[0134] The above static aerodynamic load With static thermal load The total static aerodynamic heat load is obtained by superimposing the loads. Its calculation function is shown in the formula:

[0135]

[0136] In the formula, The initial geometric height is dimensionless; Dimensionless spatial coordinates; The initial arch height of the target curved wall panel; The thickness of the target curved wall panel; It is a dimensionless dynamic pressure;

[0137] The temperature rise is dimensionless, calculated from the actual temperature rise. With critical buckling temperature rise The ratio is worth getting.

[0138] S105. Compare the elastic deformation and flutter critical boundary corresponding to different candidate distribution patterns, and output the graphene arrangement configuration of the target curved wall plate.

[0139] Among them, the graphene arrangement configuration refers to the optimal graphene distribution pattern and its corresponding total mass fraction and other parameters determined to meet specific design goals (such as maximum flutter resistance or minimum static deformation).

[0140] This step involves normalizing and comparing multiple sets of performance indicators calculated for different candidate distribution patterns in the previous steps, and finally selecting the design scheme with the best overall performance.

[0141] In one specific embodiment, to verify the effectiveness of the analysis method and optimization scheme, a series of numerical examples were used to analyze the static aerodynamic heat load under different parameters.

[0142] First, please refer to Figure 4 , Figure 4 This is a schematic diagram of a simulation result showing the influence of graphene distribution pattern on static aerodynamic heat load in an embodiment of this application; the purpose of this study is to investigate the influence of graphene distribution pattern on static aerodynamic heat load. A total mass fraction was set... It is 0.3%, dimensionless dynamic pressure. The initial curvature to thickness ratio is 200. The temperature rise is 0.2. Under the condition of 10, the static aerodynamic heat loads were calculated under three modes: uniform distribution (UD), central enrichment distribution (O), and surface enrichment distribution (X). Along dimensionless coordinates The distribution of . (By ) Figure 4 It can be seen that at all locations, the X distribution pattern corresponds to the smallest absolute value of static aerodynamic heat load, followed by the UD distribution pattern, and the O distribution pattern has the largest value. This indicates that the X distribution pattern is the optimal distribution pattern for reducing the static aerodynamic heat load of the curved wall panel.

[0143] Secondly, please refer to Figure 5 , Figure 5 This is a schematic diagram of a simulation result showing the effect of graphene mass fraction on static aerodynamic heat load in an embodiment of this application; the purpose of this study was to investigate the effect of graphene mass fraction on static aerodynamic heat load. A fixed X distribution pattern was adopted, and... =200, =0.2, Under the condition of =10, the total mass fraction was compared. Static aerodynamic heat loads at 0%, 0.1%, 0.2%, and 0.3%, respectively. .Depend on Figure 5 It can be seen that as the mass fraction of graphene increases, the static aerodynamic heat load decreases, but the impact is relatively small.

[0144] Further, please refer to Figure 6 , Figure 7 and Figure 8 , Figure 6 This is a schematic diagram of a simulation result of the static aerodynamic thermal load being affected by dimensionless temperature rise in an embodiment of this application; Figure 7 This is a schematic diagram of a simulation result of the effect of initial curvature on the static aerodynamic thermal load in an embodiment of this application; Figure 8 This is a schematic diagram of a simulation result showing the effect of dimensionless dynamic pressure on the static aerodynamic thermal load in an embodiment of this application. The influence of other environmental parameters on the static aerodynamic thermal load was studied using the X-distribution mode. Please refer to... Figure 6 In fixed =200, =0.2, Under the condition of 0.3%, static aerodynamic heat load It increases with increasing dimensionless temperature rise. Please refer to [reference needed]. Figure 7 In fixed =200, =2, Under the condition of 0.3%, static aerodynamic heat load With initial geometric curvature The growth trend is consistent, and the greater the curvature, the greater the absolute value of the load. Please refer to... Figure 8In fixed =0.2, =2, Under the condition of 0.3%, static aerodynamic heat load It increases with the increase of dimensionless dynamic pressure, and the load distribution is approximately symmetrical about the midpoint of the wall panel. Specifically, when... When > 0, the static aerodynamic thermal load exerts a positive pressure on the plate; when When <0, the static aerodynamic heat load exerts a negative pressure on the plate.

[0145] In a specific embodiment, to verify the effectiveness of the analysis method and provide a basis for the final configuration optimization, a series of numerical examples were used to discuss and analyze the static aeroelastic deformation under different parameters. Under static aerodynamic thermal load, functionally graded graphene sheet-reinforced two-dimensional curved panels undergo time-independent static aeroelastic deformation. In this embodiment, the static aeroelastic deformation is obtained by setting all time-dependent derivative terms in the nonlinear differential equation system obtained in the previous steps to zero and solving it using the differential evolution algorithm.

[0146] First, under the conditions of a total mass fraction of 0.3%, a dimensionless dynamic pressure of 100, an initial curvature-to-thickness ratio of 2, and a dimensionless temperature rise of 1, the static aeroelastic deformation values ​​corresponding to three different graphene distribution modes were calculated. The calculation results show that among all candidate distribution modes, the surface-enriched distribution (X distribution) mode has the smallest static aeroelastic deformation value of 0.105450; the uniform distribution (UD distribution) mode is second; and the central-enriched distribution (O distribution) mode has the largest value. This demonstrates that the X distribution mode performs best in suppressing static deformation.

[0147] Secondly, please refer to Figure 9 , Figure 10 , Figure 11 and Figure 12 , Figure 9 This is a schematic diagram of a simulation result showing the effect of graphene mass fraction on static aeroelastic deformation in an embodiment of this application; Figure 10 This is a schematic diagram of a simulation result of the effect of dimensionless temperature rise on the static aeroelastic deformation in an embodiment of this application; Figure 11 This is a schematic diagram of a simulation result of the effect of initial geometric curvature on static aeroelastic deformation in an embodiment of this application; Figure 12 This is a schematic diagram of a simulation result of the effect of dimensionless dynamic pressure on static aeroelastic deformation in an embodiment of this application. It studies the influence of different physical parameters on the static aeroelastic deformation curve under the X-distribution mode. Please refer to... Figure 9 In fixed =150, =1, Under the condition of =2, the dimensionless displacement of static aeroelastic deformation decreases with increasing total graphene mass fraction. Please refer to... Figure 10 In fixed =0.3%, Under the operating conditions of 150°C and H / h = 2, the dimensionless displacement increases with increasing dimensionless temperature rise. Please refer to... Figure 11 Under fixed operating conditions, the dimensionless displacement increases with increasing initial geometric curvature. Please refer to [reference needed]. Figure 12 In fixed =0.3%, =2, Under the condition of 1=0.5, the dimensionless displacement decreases as the dimensionless dynamic pressure increases. The dimensionless displacement is distributed along a dimensionless coordinate system, and its peak value characterizes the severity of static aeroelastic deformation.

[0148] In a specific embodiment, to verify the effectiveness of the analysis method and provide a basis for the final configuration optimization, the flutter characteristics under different parameters were analyzed through a series of numerical examples. Specifically, the bifurcation characteristics of the system were analyzed by solving the nonlinear differential equations obtained in the previous steps.

[0149] In this embodiment, the fourth-order Runge-Kutta method is used to solve the nonlinear differential equation system, and the displacement response and valley value at a specific location in the direction of the incoming flow are extracted to draw a bifurcation diagram.

[0150] First, please refer to Figure 13 , Figure 13 This is a schematic diagram of the simulation results of the effect of initial geometric curvature on the bifurcation characteristics of curved panels under three graphene distribution modes in the embodiments of this application. The study investigated the effect of initial geometric curvature on the bifurcation characteristics of curved panels under different graphene distribution modes.

[0151] Under the conditions of a dimensionless temperature rise of 1, a dimensionless dynamic pressure of 100, and a total mass fraction of 0.3%, the response of lateral displacement to changes in initial curvature and thickness ratio was analyzed. Figure 13 (a) shows a bifurcation diagram under the uniform distribution (UD) pattern; Figure 13 (b) shows a bifurcation diagram under the surface enrichment distribution (X distribution) pattern; Figure 13 (c) shows the bifurcation diagram under the central enrichment distribution (O distribution) pattern. Figure 13 It can be seen that before the initial geometric curvature reaches a critical value, the curved panel undergoes stable flutter motion (manifested as finite, regular amplitude). When Beyond this critical value, the motion of the panel enters a chaotic state (manifested as irregular fluctuations in amplitude over a very large range). Comparing the three modes, the X distribution mode can withstand the largest critical initial geometric curvature before entering chaotic motion, followed by the O distribution mode, and the UD distribution mode has the smallest. This indicates that the X distribution mode has a wider stable operating range.

[0152] Secondly, please refer to Figure 14 The influence of dimensionless temperature rise on the bifurcation characteristics of curved panels under different graphene distribution patterns was investigated. =1, It is 130. Under the condition of 0.3%, the response of lateral displacement to dimensionless temperature rise was analyzed. Figure 14 (a) shows the bifurcation diagram under the UD distribution pattern; Figure 14 (b) shows the bifurcation diagram under the X distribution pattern; Figure 14 (c) shows the bifurcation diagram under the O distribution pattern. Figure 14 It can also be seen that as the dimensionless temperature rise increases, the curved plate under all three distribution modes will transition from stable vibration to chaotic motion, while the X distribution mode can withstand the highest critical dimensionless temperature rise, showing the best dynamic stability under thermal conditions.

[0153] The following describes an exemplary flutter characteristic analysis system 1500 for graphene-reinforced curved panels under high-speed airflow provided in an embodiment of this application. Figure 15 This is an exemplary hardware structure diagram of the flutter characteristic analysis system 1500 for graphene-reinforced curved panels under high-speed airflow provided in this application embodiment.

[0154] In some embodiments, the flutter characteristic analysis system 1500 for graphene-reinforced curved panels under high-speed airflow is a computer device or includes a computer device in the system. The computer device includes a processor, memory, and a network interface connected via a system bus. The processor of the computer device provides computing and control capabilities. The memory of the computer device includes a non-volatile storage medium and internal memory. The non-volatile storage medium stores an operating system, computer programs, and a database. The internal memory provides an environment for the operation of the operating system and computer programs in the non-volatile storage medium. The database of the computer device stores data. The network interface of the computer device is used to communicate with other external terminals or servers via a network connection. In some embodiments, the network interface can be a wired network interface; in some embodiments, the network interface can also be a wireless network interface. When the computer program is executed by the processor, it implements the methods in the embodiments of this application.

[0155] Those skilled in the art will understand that Figure 15 The structure shown is merely a block diagram of a portion of the structure related to the present application and does not constitute a limitation on the computer device to which the present application is applied. Specific computer devices may include more or fewer components than those shown in the figure, or combine certain components, or have different component arrangements.

[0156] The above-described embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit it. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of this application.

[0157] As used in the above embodiments, depending on the context, the term "when..." can be interpreted as meaning "if...", "after...", "in response to determining...", or "in response to detecting...". Similarly, depending on the context, the phrase "when determining..." or "if (the stated condition or event) is interpreted as meaning "if determining...", "in response to determining...", "when (the stated condition or event) is detected", or "in response to detecting (the stated condition or event)".

[0158] In the above embodiments, implementation can be achieved entirely or partially through software, hardware, firmware, or any combination thereof. When implemented using software, it can be implemented entirely or partially as a computer program product. The computer program product includes one or more computer instructions. When the computer program instructions are loaded and executed on a computer, all or part of the processes or functions described in the embodiments of this application are generated. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The computer instructions can be stored in a computer-readable storage medium or transmitted from one computer-readable storage medium to another. For example, the computer instructions can be transmitted from one website, computer, server, or data center to another website, computer, server, or data center via wired (e.g., coaxial cable, fiber optic, digital subscriber line) or wireless (e.g., infrared, wireless, microwave, etc.) means. The computer-readable storage medium can be any available medium that a computer can access or a data storage device such as a server or data center that integrates one or more available media. The available medium can be a magnetic medium (e.g., floppy disk, hard disk, magnetic tape), an optical medium (e.g., DVD), or a semiconductor medium (e.g., solid-state drive), etc.

[0159] Those skilled in the art will understand that all or part of the processes in the methods of the above embodiments can be implemented by a computer program instructing related hardware. This program can be stored in a computer-readable storage medium, and when executed, it can include the processes described in the above method embodiments. The aforementioned storage medium includes various media capable of storing program code, such as ROM or random access memory (RAM), magnetic disks, or optical disks.

Claims

1. A method for analyzing the flutter characteristics of a graphene-reinforced curved panel under high-speed airflow, characterized in that, include: Obtain the initial physical parameters and environmental conditions of the target curved wall panel, and acquire candidate distribution patterns; For any of the candidate distribution patterns, calculate the elastic modulus of each layer of the target curved panel under the candidate distribution pattern; Based on the initial physical parameters, the environmental operating condition parameters, and the elastic modulus, a control equation with a curvature correction factor is constructed. Solve the control equations and, based on the preset instability criterion, calculate the elastic deformation and flutter critical boundary when the system state represented by the control equations becomes unstable. By comparing the elastic deformation amount corresponding to different candidate distribution patterns with the flutter critical boundary, the graphene arrangement configuration of the target curved wall panel is output.

2. The method according to claim 1, characterized in that, The candidate distribution patterns include: uniform distribution pattern, surface enrichment distribution pattern, and central enrichment distribution pattern.

3. The method according to claim 2, characterized in that, Before the step of calculating the elastic modulus of each layer of the target curved wall panel under the candidate distribution pattern, the method further includes: The target quality score distribution function corresponding to the candidate distribution pattern is invoked; the target quality score distribution function is defined as follows: For the uniform distribution pattern: ： For the aforementioned enrichment distribution pattern in the middle region: In the formula, For the first Target mass fraction of the target curved wall panel. This represents the total mass fraction of graphene. The number of layers after discretization of the target curved panel. For the first Layered target curved wall panel, .

4. The method according to claim 3, characterized in that, The step of calculating the elastic modulus of each layer of the target curved panel under the candidate distribution pattern specifically includes: Based on the target mass fraction distribution function and the initial physical parameters, the elastic modulus of each layer of the target curved panel under the candidate distribution pattern is calculated; wherein: The calculation function is: In the formula, For the first The elastic modulus of the target curved wall panel. For the first Layered graphene , For geometric parameters, For geometric parameters, The length of the graphene. The width of the graphene is... The thickness of the graphene. The density is the polymer matrix. The density of graphene, This is the elastic attenuation reduction rate along the length direction. This is the elastic attenuation reduction rate in the width direction. for , This represents the elastic modulus of graphene.

5. The method according to claim 4, characterized in that, The calculation function for the governing equation is: In the formula, For bending moment, For internal forces, For inertia, The lateral displacement of the target curved wall panel. These are the spatial coordinates along the length of the target curved panel. Let be the initial radius of curvature of the target curved wall panel. For time, The external aerodynamic load acting on the target curved wall plate.

6. The method according to claim 1, characterized in that, After the step of constructing the control equation with curvature correction factor based on the initial physical parameters, the environmental condition parameters, and the elastic modulus, the method further includes: The governing equations are discretized by reducing their order to generate a system of nonlinear differential equations. The steps of solving the governing equations and calculating the elastic deformation and flutter critical boundary when the system state represented by the governing equations becomes unstable, based on a preset instability criterion, specifically include: The nonlinear differential equations are solved, and based on a preset instability criterion, when the system state represented by the nonlinear differential equations becomes unstable, the elastic deformation and flutter critical boundary are calculated and obtained.

7. The method according to claim 1, characterized in that, The preset instability criterion is: the eigenvalues ​​of the governing equation change from negative real parts to positive real parts.

8. A flutter characteristic analysis system for graphene-reinforced curved panels under high-speed airflow, characterized in that, The flutter characteristic analysis system for graphene-reinforced curved wall panels under high-speed airflow includes: one or more processors and a memory; the memory is coupled to the one or more processors, the memory is used to store computer program code, the computer program code includes computer instructions, and the one or more processors call the computer instructions to cause the flutter characteristic analysis system for graphene-reinforced curved wall panels under high-speed airflow to perform the method as described in any one of claims 1-7.

9. A computer program product containing instructions, characterized in that, When the computer program product is run on the flutter characteristic analysis system for graphene-reinforced curved panels under high-speed airflow, the flutter characteristic analysis system for graphene-reinforced curved panels under high-speed airflow performs the method as described in any one of claims 1-7.

10. A computer-readable storage medium comprising a computer program, characterized in that, The method as described in any one of claims 1-7 is implemented when the computer program instructions are executed by the processor.

Images