An accelerated flutter speed optimization method based on aerodynamic stiffness coupling modal similarity degree

Abstract

The application discloses an acceleration flutter speed optimization method based on aerodynamic stiffness coupling modal similarity, which comprises the following steps: firstly, solving an aeroelastic control equation under a preset incoming flow speed condition to obtain a plurality of first-order aerodynamic coupling modal vectors; then, constructing a self-correlation modal execution criterion matrix based on the modal vectors, extracting the maximum value of non-diagonal line elements of the matrix, and defining the maximum value as an aerodynamic stiffness coupling modal similarity index; and finally, analyzing the mapping relationship between the to-be-optimized parameters and the similarity index, determining a parameter combination that makes the index reach a minimum value, and determining that the parameter combination corresponds to a structure or material design scheme with the maximum critical flutter speed. The application significantly reduces the calculation cost, greatly improves the optimization efficiency, is especially suitable for complex structure flutter boundary optimization design containing multiple degrees of freedom and multiple parameters, and provides an efficient calculation tool for aircraft aeroelastic design.

Description

Technical Field

[0001] This invention relates to the field of aerospace technology, specifically to an accelerated flutter velocity optimization method based on aerodynamic stiffness coupled modal similarity. Background Technology

[0002] Flutter, in the aerospace field, is a fluid-structure interaction vibration phenomenon that affects the structural stability and flight safety of aircraft. Given specific materials and aircraft structures, as the incoming flow velocity increases, the vibration amplitude of the aircraft gradually approaches infinity after a certain velocity, leading to material failure and structural damage. This velocity is known as the critical flutter velocity. During the aircraft design phase, optimizing the aircraft's material properties and structure to improve its critical flutter velocity and extend its safe flight envelope is of great significance.

[0003] In terms of flutter detection and engineering applications, time-domain analysis methods and methods such as the V-g method, harmonic balance method, or eigenvalue analysis based on velocity scanning are theoretically mature and reliable. However, their calculation process usually relies on point-by-point scanning of the incoming flow velocity to obtain the time history curve or eigenvalue at each velocity point, and to determine whether flutter occurs point by point. The critical flutter velocity is then obtained through interpolation methods.

[0004] In terms of material structure optimization for aircraft with critical flutter velocity, both traditional iterative algorithms and novel intelligent optimization algorithms require scanning the incoming flow velocity point by point and interpolating to calculate the critical flutter velocity in each optimization step. This method is well-suited for problems with low parameter space dimensions. However, in engineering design and optimization problems involving multi-layer laying angles, structural geometric parameters, and material uncertainties, the above methods often require a large number of repetitive calculations, leading to a sharp increase in computational costs. There is an urgent need to introduce a new, easily calculable index to describe the magnitude of the critical flutter velocity of the structure. Summary of the Invention

[0005] To overcome the shortcomings of existing calculation methods, which require multiple scans of the incoming flow velocity and result in excessive computation time, this invention proposes an accelerated flutter velocity optimization method based on aerodynamic stiffness coupled modal similarity. By calculating the confidence criteria between the various modes calculated after coupling the aerodynamic stiffness of the structure at a given incoming flow velocity, the aerodynamic stiffness coupled modal similarity is obtained. This similarity is used to approximately describe the ease with which the structure will flutter under aerodynamic loads. This transforms the multi-point velocity scan in traditional optimization algorithms into a single-point velocity calculation, significantly reducing the computational load and improving the computational speed.

[0006] This invention provides an accelerated flutter velocity optimization method based on aerodynamic stiffness coupled modal similarity, comprising: step S1, obtaining the aerodynamic stiffness coupled control equation of the structure to be analyzed through structural and aerodynamic modeling; step S2, determining the structural or material parameters to be optimized; step S3, taking values ​​for the parameters to be optimized within the optimization interval in steps and calculating the first few order modal vectors of the aerodynamic stiffness coupled control equation at a certain velocity; step S4, calculating the autocorrelation modal execution criterion between each order mode based on the obtained modal vectors; step S5, defining the maximum value of the off-diagonal elements in the autocorrelation modal execution criterion as the aerodynamic stiffness coupled modal similarity; step S6, taking the minimum value of the aerodynamic stiffness coupled modal similarity based on the relationship between the parameters to be optimized and the aerodynamic stiffness coupled modal similarity, and outputting the corresponding value of the parameters to be optimized, which is the structural or material parameter with the largest critical flutter velocity.

[0007] Further, step S1 includes: establishing a structural dynamics model based on the geometric parameters, material parameters, and boundary conditions of the structure to be analyzed; introducing an aerodynamic model to construct structural dynamics control equations containing aerodynamic stiffness and aerodynamic damping terms, wherein the aerodynamic stiffness term is used to characterize the influence of aerodynamic loads on the equivalent stiffness of the structure, and the aerodynamic damping term is used to characterize the influence of aerodynamic loads on the energy dissipation characteristics of the structure, thereby obtaining the aerodynamic stiffness coupled structural control equations, the formula of which is:

[0008]

[0009] In the formula, The system structure quality matrix, This is the aerodynamic damping matrix. Here is the structural stiffness matrix. Here is the aerodynamic stiffness matrix. For external load, For generalized coordinates.

[0010] Further, step S2 includes: determining the structural parameters or material parameters to be optimized according to the structural design requirements, wherein the parameters to be optimized include at least one of the material elastic parameters or the structural geometric parameters; setting the value range and value step size of each parameter to be optimized, and initializing the parameters to be optimized.

[0011] Further, step S3 includes: traversing the parameters to be optimized within the range of values ​​of the parameters to be optimized according to a preset step size; and, based on the aerodynamic stiffness coupling control equation at a preset incoming flow velocity, solving the first few orders of aerodynamic coupling modes of the structure at the corresponding parameter values ​​to obtain the mode vectors of each order of modes. The first few modes are low-order modes that have a major impact on flutter stability.

[0012] Further, step S4 includes: constructing a modal autocorrelation analysis matrix based on the modal vectors of each order obtained in step S3, and obtaining an autocorrelation mode execution criterion matrix to characterize the similarity of each order of modes by calculating the correlation between the modal vectors of different orders.

[0013] Further, step S5 includes: analyzing the autocorrelation modal execution criterion matrix, extracting the maximum value of the off-diagonal elements, and defining the maximum value as the aerodynamic stiffness coupling modal similarity index, with the following formula:

[0014]

[0015] In the formula, AMCA is the aerodynamic stiffness coupling modal similarity index, which is used to characterize the probability of different modes coupling or overlapping under the current incoming flow velocity and aerodynamic model conditions. Let i and j represent the mode vectors of the i-th and j-th aerodynamic coupling modes, respectively. They are usually column vectors, obtained by solving the aerodynamic stiffness coupling control equations under a preset inflow velocity; T is the transpose symbol; i and j represent different orders. This represents the maximum value of the normalized correlation among all different order pairs i≠j, which is the similarity between the two most similar modes.

[0016] Further, step S6 includes: selecting the minimum value of the aerodynamic stiffness coupling modal similarity index according to the correspondence between the parameter to be optimized and the aerodynamic stiffness coupling modal similarity index, and outputting the corresponding parameter value to be optimized as the combination of structural or material parameters with the largest critical flutter speed, thereby completing the accelerated optimization design of flutter speed.

[0017] According to one aspect of the present invention, a non-transitory computer-readable storage medium is provided, the non-transitory computer-readable storage medium storing computer instructions that cause the computer to execute the accelerated flutter velocity optimization method based on aerodynamic stiffness coupled modal similarity.

[0018] According to one aspect of the present invention, a flutter velocity optimization system based on aerodynamic stiffness coupled modal similarity is provided, comprising:

[0019] Based on the geometric parameters, material parameters, and boundary conditions of the structure to be analyzed, a finite element model of the structure is established, and an aerodynamic stiffness coupling control equation containing aerodynamic stiffness and aerodynamic damping terms is constructed by introducing an aerodynamic stiffness coupling control equation. The range and step size of the parameters to be optimized are set, and the parameters to be optimized are initialized. Under a preset inflow velocity, based on the aerodynamic stiffness coupling control equation, the first few orders of aerodynamic coupling modes of the structure are solved, and the corresponding mode vectors are output. Based on the mode vectors, the autocorrelation mode execution criterion matrix between each order of modes is calculated, and the maximum value of the off-diagonal elements is extracted as the aerodynamic stiffness coupling mode similarity index. Based on the correspondence between the parameters to be optimized and the aerodynamic stiffness coupling mode similarity index, the parameter value with the smallest aerodynamic stiffness coupling mode similarity index is selected. The structural parameter or material parameter corresponding to the minimum value of the aerodynamic stiffness coupling mode similarity index is taken as the optimization design result with the maximum critical flutter velocity.

[0020] The above technical solution establishes a structural dynamics finite element model that includes aerodynamic stiffness and aerodynamic damping, solves the aerodynamic coupling modes of the structure under a single incoming flow velocity, and constructs an aerodynamic stiffness coupling mode similarity index based on the correlation between modes to characterize the relative tendency of the structure to flutter under aerodynamic loads. This avoids the high computational cost caused by multiple scans of the incoming flow velocity in the traditional flutter optimization process and achieves accelerated computation of the flutter velocity optimization process.

[0021] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0022] (1) By introducing the aerodynamic stiffness coupled modal similarity index, the relative trend of structural flutter can be evaluated without the need for multi-flow velocity scanning, which significantly reduces the amount of computation in the flutter velocity optimization process.

[0023] (2) This invention transforms the traditional optimization objective that relies on critical flutter velocity into a single-velocity calculation index based on modal correlation, which is suitable for the rapid screening and optimization of high-dimensional design variables such as laminate ply parameters;

[0024] (3) This invention is applicable to various structural forms and aerodynamic models, and can be combined with existing finite element analysis methods to provide an effective engineering implementation scheme for the rapid design and optimization of flutter stability of aircraft structures. Attached Figure Description

[0025] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the accompanying drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the accompanying drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0026] Figure 1 The flowchart illustrates an accelerated flutter velocity optimization method based on aerodynamic stiffness coupled modal similarity, provided in an embodiment of the present invention.

[0027] Figure 2 The control surface structure model and boundary conditions provided for the examples of this invention.

[0028] Figure 3 The wall panel structure model and boundary conditions provided for the examples of this invention.

[0029] Figure 4 The curve provided for optimizing the boundary flutter velocity of the rudder face based on the laminate laying angle is provided as an example of the present invention.

[0030] Figure 5 The curve provided for optimizing the critical flutter velocity of the wall panel based on the laminate laying angle is provided as an example of the present invention. Detailed Implementation

[0031] Those skilled in the art should understand that this embodiment is only used to illustrate the technical concept of the present invention, and is not intended to limit the scope of protection of the present invention. The terms "comprising" and "having," and any variations thereof, in the specification, claims, and accompanying drawings of the present invention are intended to cover a non-exclusive inclusion, such as a process, method, system, product, or device that includes a series of steps or units, not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to these processes, methods, products, or devices.

[0032] The flowcharts shown in the accompanying drawings are merely illustrative and do not necessarily include all content and operations / steps, nor do they necessarily have to be performed in the described order. For example, some operations / steps can be broken down, while others can be combined or partially combined; therefore, the actual execution order may change depending on the specific circumstances.

[0033] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention. In addition, the technical features of the various embodiments or individual embodiments provided by the present invention can be arbitrarily combined to form new technical solutions. Such combinations are not bound by the order of steps and / or structural composition patterns, but must be based on the ability of those skilled in the art to implement them. When the combination of technical solutions is contradictory or cannot be implemented, it should be considered that such a combination of technical solutions does not exist and is not within the scope of protection claimed by the present invention.

[0034] The following specific embodiments further illustrate the accelerated flutter velocity optimization method based on aerodynamic stiffness coupled modal similarity proposed in this invention.

[0035] Please refer to the appendix for details. Figure 1 The following section will further introduce the accelerated flutter velocity optimization method based on aerodynamic stiffness coupled modal similarity. The specific steps are as follows:

[0036] Step S1: Through structural and aerodynamic modeling, obtain the coupled aerodynamic stiffness control equations for the structure to be analyzed. Specifically, see attached... Figure 2 Appendix Figure 3 As shown, the rudder structure is a double-layer T700 carbon fiber reinforced resin matrix composite material with a bottom length of 300 mm, an upper bottom length of 150 mm, and a height of 300 mm. The middle 1 / 3 section (100 mm long) of the bottom bottom is a fixed-support boundary condition. The wall panel structure is a double-layer T700 carbon fiber reinforced resin matrix composite material with an equal side length of 1000 mm and simply supported on all four sides. Based on the geometric dimensions, material parameters, and boundary conditions of the structure to be analyzed, a finite element model of the structure is established. During the structural modeling process, an aerodynamic model is introduced to construct an aerodynamic stiffness coupled control equation that includes structural mass, structural stiffness, aerodynamic stiffness, and aerodynamic damping terms. .

[0037] Step S2: Determine the structural or material parameters to be optimized. In this embodiment, for the rudder surface and wall panel of the embodiment object, a double-layer laminated plate structure is adopted. Under the premise of fixing the laying angle of plate No. 1 and the properties of the laminated material, the laying angle of layer No. 2 is selected as the parameter to be optimized, and the value range of the parameter to be optimized is set to 0 to 180° and the value step is 2°.

[0038] Step S3: Under a preset incoming flow velocity, calculate the aerodynamic coupling modes corresponding to the parameters to be optimized. Specifically, within the range of values ​​of the parameters to be optimized, traverse the parameters to be optimized according to a preset step size; under a preset incoming flow velocity, based on the aerodynamic stiffness coupling control equation obtained in step S1, neglecting its damping term, solve for the first few orders of aerodynamic coupling modes of the structure to obtain the corresponding mode vectors. The first few orders of modes are preferably low-order bending modes and torsional modes that have a major influence on flutter stability.

[0039] Step S4: Calculate the autocorrelation mode execution criteria among different modes. Specifically, based on the mode vectors obtained in step S3, construct the mode autocorrelation matrix. By calculating the correlation between mode vectors of different orders, obtain the autocorrelation mode execution criterion matrix used to characterize the similarity of different modes.

[0040] Step S5: Determine the aerodynamic stiffness coupling modal similarity index. Specifically, analyze the autocorrelation mode execution criterion matrix, extract the maximum value of the off-diagonal elements, and define the maximum value as the aerodynamic stiffness coupling modal similarity index. The aerodynamic stiffness coupling modal similarity index is used to characterize the probability of different order modes coupling or overlapping under the current incoming flow velocity and aerodynamic model conditions.

[0041] Step S6: Accelerate the optimization of flutter velocity based on the aerodynamic stiffness coupled modal similarity index. Specifically, according to the correspondence between the parameters to be optimized and the aerodynamic stiffness coupled modal similarity index, the minimum value of the aerodynamic stiffness coupled modal similarity index is selected, and the corresponding value of the parameter to be optimized is output as the combination of structural or material parameters with the highest critical flutter velocity, thereby achieving accelerated optimization design of flutter velocity. (See attached...) Figure 4 and attached Figure 5 As shown, the dashed lines represent the aerodynamic stiffness coupling modal similarity indices for the control surface and the wall panel under different optimization parameters. Their minimum values ​​correspond precisely to the maximum critical flutter velocities of the control surface and the wall panel, respectively. For the control surface in this embodiment, its second plate reaches the maximum critical flutter velocity at a 118° laying direction; for the wall panel in this embodiment, its second plate reaches the maximum critical flutter velocity at a 152° laying direction. Each aerodynamic stiffness coupling modal similarity index can be obtained with only one inflow velocity calculation, greatly improving the optimization solution speed.

[0042] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention 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 or all of the technical features therein; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the technical solutions of the embodiments of the present invention.

Claims

1. A method for optimizing flutter velocity based on aerodynamic stiffness coupled modal similarity, characterized in that, Includes the following steps: S1. Through structural and aerodynamic modeling, the aerodynamic stiffness coupling control equation of the structure to be analyzed is obtained. The control equation includes structural mass term, structural stiffness term, and aerodynamic stiffness term introduced by aerodynamic load. S2, determine the structural or material parameters to be optimized, and set the value range of the parameters to be optimized; S3, under a preset incoming flow velocity, for different values ​​of the parameter to be optimized, solve the first few aerodynamic coupling modes of the structure based on the aerodynamic stiffness coupling control equation to obtain the corresponding mode vector; S4. Based on the modal vector, calculate the autocorrelation mode execution criterion between each order of modes and construct the modal autocorrelation matrix; S5, extract the maximum value of the off-diagonal elements in the modal autocorrelation matrix and define it as the aerodynamic stiffness coupling modal similarity index; S6. Based on the correspondence between the parameters to be optimized and the aerodynamic stiffness coupling modal similarity index, the minimum value of the aerodynamic stiffness coupling modal similarity index is selected according to the optimization algorithm, and the corresponding value of the parameters to be optimized is output as the combination of structural or material parameters with the largest critical flutter velocity.

2. The method according to claim 1, characterized in that, The aerodynamic stiffness coupling control equation is a structural dynamics equation that includes the following terms: structural mass matrix, structural stiffness matrix, and aerodynamic stiffness matrix formed by aerodynamic equivalence.

3. The method according to claim 1 or 2, characterized in that, The aerodynamic stiffness term is obtained from piston flow theory, linearized aerodynamic models, or other aerodynamic models applicable to high-speed airflow conditions.

4. The method according to claim 1, characterized in that, The first few aerodynamic coupling modes mentioned in step S3 are low-order modes that affect the flutter stability of the structure.

5. The method according to claim 1, characterized in that, The aerodynamic stiffness coupling modal similarity index is calculated based on the correlation between modal vectors of different orders, and the formula is as follows: This is used to characterize the likelihood of different modes coupling or overlapping at the current incoming flow velocity; Let represent the mode vectors of the i-th and j-th aerodynamic coupling modes, respectively, obtained by solving the aerodynamic stiffness coupling control equations under a preset incoming flow velocity; T is the transpose symbol; i and j represent different orders; This represents the maximum value of the normalized correlation among all different order pairs i≠j, which is the similarity between the two most similar modes.

6. The method according to claim 1, characterized in that, The parameters to be optimized include at least one of the following: structural geometric parameters, material elastic parameters, laminate layup angle, layup sequence, and any parameters that affect the mechanical properties and flutter boundary of the structure.

7. A flutter velocity optimization system based on aerodynamic stiffness coupled modal similarity for implementing the method as described in any one of claims 1-6, characterized in that, include: The modeling module is used to build a structural model based on the structural geometric parameters, material parameters and boundary conditions, and to construct the aerodynamic stiffness coupling control equations that include aerodynamic stiffness terms. The modal solving module is used to solve the first few aerodynamic coupling modes of the control equations under a preset incoming flow velocity; The similarity calculation module is used to calculate the modal autocorrelation matrix based on the aerodynamic coupling modes and extract the aerodynamic stiffness coupling mode similarity index. The optimization and filtering module is used to filter out the parameter values ​​with the largest corresponding critical flutter speed based on the relationship between the parameter to be optimized and the aerodynamic stiffness coupling mode similarity index.

8. A non-transitory computer-readable storage medium storing computer instructions thereon, wherein when executed by a processor, the computer instructions cause the processor to perform the accelerated flutter velocity optimization method based on aerodynamic stiffness coupled modal similarity as described in any one of claims 1 to 6.

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