Flow-induced vibration velocity effect frequency-division equivalent method

Abstract

The invention discloses a flow-induced vibration speed effect frequency-band-division equivalent method, and belongs to the field of aircraft structure dynamic strength optimization. On the basis of the length scaling factor, the thickness scaling factor is introduced, and the problem that the aerodynamic load frequency and the structure frequency are inconsistent due to the speed difference is compensated through the thickness factor; on the basis, the flow-induced vibration similarity law considering the flow velocity effect is deduced, prediction can be carried out in combination with actual working conditions, similarity theory prediction errors caused by velocity differences are further reduced, and the reliability of the flow-induced vibration equivalent method based on the scaling model is improved. According to the method, a curved plate structure flow-induced vibration similarity criterion expression is established in a frequency division mode by adopting a frequency division band method according to different structural mode types. Complex aircraft structure response prediction is simplified, the defects of the current flow-induced vibration similarity theory are overcome, the prediction reliability of the aircraft structure dynamic response similarity method can be improved, and improvement of the precision and efficiency of high-speed aircraft structure dynamic response assessment is facilitated.

Description

Technical Field

[0001] The invention belongs to the field of dynamic strength optimization of aircraft structures, and relates to a method for equivalent segmentation of the flow-induced vibration velocity effect. Background Technique

[0002] During the high-speed flight of an aircraft, a strong wall pulsating pressure load is generated on the surface of the aircraft by the high-speed airflow. The strong pulsating pressure is coupled with the skin structure of the aircraft to generate strong structural vibrations, which poses a certain test to the structural safety design of the aircraft. The pulsating pressure is transmitted from the skin structure into the instrument cabin through vibration, and it will also cause certain damage to the sound-sensitive equipment in the cabin. Conducting research on the wall pulsating pressure load and flow-induced vibration of high-speed aircraft, and developing reliable ground test simulation techniques for wall pulsating pressure environment and experimental evaluation techniques for flow-induced vibration response play an important supporting role in the structural safety design and refined design of high-speed aircraft.

[0003] The current experimental evaluation of flow-induced vibration is mainly based on noise experimental techniques. The implementation of this technique mainly includes two steps: Step 1, obtaining the equivalent sound pressure level of the pulsating pressure at typical positions on the surface of the aircraft through wind tunnel tests; Step 2, simulating the equivalent sound pressure level of the pulsating pressure obtained from the wind tunnel test through an air flow loudspeaker in a traveling wave tube or reverberation chamber, and then evaluating the structure. However, this flow-induced vibration evaluation technique has obvious deficiencies, which are specifically reflected in the following three aspects: it cannot simulate the spatial correlation of complex flows; it cannot simulate the pulsating pressure power spectrum generated by real flows; it cannot simulate extreme pulsating pressure loads. In view of the problem of insufficient simulation capabilities of traveling wave tubes and reverberation chambers for flow-induced actuation loads, wind tunnel technology has become one of the alternative solutions for flow-induced vibration assessment. However, the limitation of the wind tunnel size determines that a full-scale aircraft cannot be placed in the wind tunnel for assessment, and the aircraft must be scaled down. Therefore, establishing a reliable flow-induced vibration similarity law based on a scaled model is the key to solving the ground test assessment of flow-induced vibration.

[0004] However, although the existing research has preliminarily established a coupling similarity law for aerodynamic loads and structural responses based on the analytical method of flow-induced vibration response, this similarity law mainly focuses on the similarity of flow Mach number, structural vibration mode and characteristic frequency, and does not consider the influence of the change in flow velocity caused by the difference in local static temperature on the aerodynamic excitation frequency under ground test and flight conditions, resulting in a certain change in the matching characteristics of the aerodynamic load and structural characteristic frequency of the scaled model compared with the full-scale model, seriously affecting the prediction and evaluation accuracy of flow-induced vibration. Summary of the Invention

[0005] To solve the problem that the coefficients of the structural frequency and the aerodynamic excitation frequency are inconsistent due to the existence of the space-ground speed ratio, resulting in low prediction accuracy of fluid-induced vibration because scaling cannot be unified, the purpose of the present invention is to provide a method for equivalent sub-band of the fluid-induced vibration speed effect. Based on the scaling factor of the aircraft shape, a thickness scaling factor is introduced, and the thickness factor is used to compensate for the inconsistency between the aerodynamic load frequency and the structural frequency caused by the space-ground speed difference. On this basis, an equivalent sub-band method for fluid-induced vibration considering the flow velocity effect is derived, and further, according to different structural modal types, an equivalent sub-band method for fluid-induced vibration of a curved plate structure is established by frequency division, and the reliability of the prediction of the similarity method of the dynamic response of the aircraft structure is improved according to the equivalent sub-band method for fluid-induced vibration of the curved plate structure.

[0006] The purpose of the present invention is achieved by the following technical solutions:

[0007] An equivalent sub-band method for fluid-induced vibration speed effect disclosed by the present invention includes the following steps:

[0008] Step 1: According to the flow velocity ratio between the true flight flow velocity V of the aircraft and the flow velocity in the ground test, determine the model length scaling factor σ and the thickness scaling factor σ t . The thickness scaling factor is obtained from the relationship between the length scaling factor and the flow velocity difference:

[0009]

[0010] Equivalent the geometric dimensions of the scaled model to: length width thickness radius of curvature to obtain the scaled model. Where "ˉ" represents the parameters related to the scaled model.

[0011] Step 2: Based on Step 1, perform modal identification on the scaled model, which is divided into three modes: flat plate-biased, curved plate-biased, and intermediate state.

[0012] Calculate the scaled mode of the scaled model and the true mode of the flat plate with the same dimensions, and compare the scaled mode with the true mode of the flat plate with the same dimensions to preliminarily identify the flat plate-biased mode and the non-flat plate mode.

[0013] Define the structural frequency ratio Rate:

[0014]

[0015] where, the flat plate frequency of the scaled model the curved plate frequency of the scaled model is the elastic modulus of the material of the scaled model; represents the density of the scaled model; represents the Poisson's ratio of the scaled model; is the characteristic frequency of the scaled model; m is the mode number in the a direction; n is the mode number in the b direction.

[0016] The magnitude of the Rate value divides the non-flat plate modes into two modes: the deflected plate and the intermediate state. When 5 < Rate < 100, it is the intermediate mode, and when Rate ≤ 5, it is the deflected plate mode.

[0017] Step 3: Based on Step 2, use the sub-band method to predict the structural response of the full-scale model through the scaled model.

[0018] The scaling relationship between the true full-scale model and the scaled model for the characteristic frequency of the deflected plate mode:

[0019]

[0020] where, is the material scaling parameter. Under the same material ω mn is the characteristic frequency of the full-scale model.

[0021] The relationship between the power spectral density of the structural velocity response and the structural characteristic frequency:

[0022]

[0023] where, S v (x A ,y A ,ω) represents the power spectral density of the velocity response; ω represents the angular frequency; ψ j (x A ,y A ) and ψ n (x A ,y A ) represent the vibration modes in the j and n directions; and Z n (ω) represent the impedances in the j and n directions; γ j and γ n represent the modal factors in the j and n directions; S pp (ω) represents the acoustic-vibration excitation; represents the constant coefficient.

[0024] Construct the scaling relationship between the power spectral density of the velocity response of the true full-scale model and the scaled model of the deflected plate structure according to Eqs. (3) and (4):

[0025]

[0026] where, q represents the dynamic pressure of the oncoming flow of the full-scale model, denotes the incoming flow dynamic pressure of the scaled model; ρ denotes the density of the full-scale model, denotes the density of the scaled model. (x A , y A ) denotes the arbitrary position coordinates of the relevant point. S v (x A , y A , ω) denotes the velocity response power spectral density of the real full-scale model, denotes the velocity response power spectral density of the scaled model.

[0027] Scaling relationship between the real full-scale model and the scaled model for the modal characteristic frequency of the deflected plate:

[0028]

[0029] Construct the scaling relationship of the velocity response power spectral density between the real full-scale model and the scaled model structure of the deflected plate mode according to Eqs. (4) and (6):

[0030]

[0031] Scaling relationship between the real full-scale model and the scaled model for the modal characteristic frequency of the intermediate state mode:

[0032]

[0033] Among them, is the interpolation coefficient, given by the interpolation result; is the characteristic frequency of the scaled model.

[0034] Construct the scaling relationship of the velocity response power spectral density between the real full-scale model and the scaled model structure of the intermediate state mode according to Eqs. (4) and (8):

[0035]

[0036] Based on the three modes of the flat plate, deflected plate, and intermediate state, the scaling relationship of the velocity response is obtained using the sub-band method, and the velocity effect of fluid-induced vibration is equivalently simulated in sub-bands according to the scaling relationship.

[0037] Step 4. Based on Step 3, apply the sub-band equivalent method.

[0038] The scaled model uses the sub-band equivalent method of the velocity effect of fluid-induced vibration to predict and calculate the structural response of the full-scale model. According to the equivalent method in Step 3, the acoustic-vibration response of the real aircraft can be equivalently obtained from the scaled model in the wind tunnel test in sub-bands, and more reliable acoustic-vibration responses can be obtained for different flow velocity ratios, improving the accuracy of the prediction results in wind tunnel test engineering and using the sub-band equivalent method to solve the related engineering problems caused by different flow velocity ratios in wind tunnel tests.

[0039] Beneficial effects:

[0040] 1. A method for equivalent sub - band of flow - induced vibration velocity effect disclosed by the present invention, on the basis of the length scale factor, introduces a thickness scale factor, and compensates for the problem that the aerodynamic load frequency and the structural frequency are inconsistent caused by velocity differences through the thickness factor; on this basis, the similarity law of flow - induced vibration considering the flow velocity effect is derived, which can be combined with actual working conditions for prediction, further reducing the prediction error of similarity theory caused by velocity differences, and improving the reliability of the flow - induced vibration equivalent method based on the scaled - down model.

[0041] 2. Compared with the traditional equivalent method of flow - induced vibration of the scaled - down model, the method for equivalent sub - band of flow - induced vibration velocity effect disclosed by the present invention uses the sub - band method to establish the similarity criterion expression of the flow - induced vibration of the curved plate structure by frequency division according to different structural modal types. It simplifies the prediction of the complex aircraft structure response, makes up for the deficiencies of the current flow - induced vibration similarity theory, and can improve the reliability of the prediction of the similarity method of the dynamic response of the aircraft structure, which helps to improve the accuracy and efficiency of the dynamic response assessment of the high - speed aircraft structure. Description of the drawings

[0042] Figure 1 It is a comparison diagram of the structural modes of the scaled - down model and the flat plate model of the same size;

[0043] Figure 2 It is a sub - band region diagram of the flat - biased, curved - biased, and intermediate - state modes;

[0044] Figure 3 It is a comparison curve of the prediction result of the scaled - down model using the similarity method considering the velocity effect and the structural response of the full - scale model;

[0045] Figure 4 Flowchart of the method for equivalent sub - band of flow - induced vibration velocity effect of the present invention. Detailed implementation manners

[0046] The following combines the drawings and embodiments to further describe the detailed implementation manners of the present invention. The following embodiments are only used to illustrate the technical solutions of the present invention more clearly, and cannot be used to limit the protection scope of the present invention.

[0047] In the following method, a curved plate with a = 0.3m, b = 1.5m, curvature radius R = 1.5m, and thickness h = 0.01m of the full - scale model and a scaled - down model with length - width scale factor σ = 0.5, thickness scale factor σ t = 0.454, and velocity ratio are taken. This method takes the curved plate model as an example to carry out the method for equivalent sub - band of flow - induced vibration velocity effect, as Figure 4As shown, a method for equivalent sub - banding of the flow - induced vibration velocity effect disclosed in this embodiment is specifically implemented as follows:

[0048] Step 1: Design of the scaled - down model. Scale down the structural dimensions of the aircraft's curved plate to establish a scaled - down model.

[0049] Construct the relationship between the thickness scale factor and the length scale factor to compensate for the flow velocity difference between the scaled - down model and the full - scale model caused by different sound speeds, as shown in formula (1):

[0050]

[0051] The structural dimensions consist of length a, width b, thickness h, and curvature radius R. Perform the following equivalent scaling on the structural dimensions:

[0052]

[0053] Step 2: Structural modal identification. Calculate the vibration mode of the scaled - down model and compare it with the vibration mode of a flat - plate model of the same size. The modal comparison is shown in Figure 1 . Through Figure 1 it is obtained that the scaled - down model is preliminarily identified as a flat - plate - like mode and a non - flat - plate mode. Then define the frequency ratio Rate, as shown in formula (2):

[0054]

[0055] According to the structural frequency ratio Rate, divide the non - flat - plate mode into a curved - plate - like mode and an intermediate mode. The relationship between the Rate ratio and the curved - plate - like, intermediate, and flat - plate - like regions is shown in Figure 2 . According to the relationship in Figure 2 , for the first mode, Rate < 5 is the curved - plate - like mode, for the second and third modes, 5 < Rate < 100 is the intermediate mode, and for the fourth and subsequent modes, Rate > 100 is the flat - plate mode. The modes of the scaled - down model are divided into three modes: flat - plate - like, curved - plate - like, and intermediate.

[0056] Step 3: Calculation of the full - scale structure response. Based on the three modes of the scaled - down model, establish a structural response scaling relationship using the sub - band method and predict and calculate the response of the full - scale structure.

[0057] The structural response power spectrum of the scaled - down model can be directly obtained through numerical calculation and wind - tunnel tests. The structural response of the full - scale model is calculated by back - calculation based on the structural response data of the scaled - down model and the similarity law established by the sub - band method.

[0058] First, for the flat - plate - like mode (the fourth mode):

[0059] The scaling relationship of the characteristic frequency of the flat - plate - like mode is shown in formula (3)

[0060]

[0061] Partial flat plate modal impedance Z j The scaling relationship is shown in Equation (11).

[0062]

[0063] Wherein, Z j represents the impedance of the full-scale model; represents the impedance of the scaled model; ω is the analysis frequency of the structure.

[0064] Based on the structural size scaling in Step 1 and the modal identification in Step 2, the relationship between the velocity response power spectral density of the scaled model and the full-scale model is obtained, as shown in Equation (5).

[0065] Velocity response:

[0066]

[0067] Secondly, for the partial curved plate mode (the first mode):

[0068] The scaling relationship of the partial curved plate modal characteristic frequency is shown in Equation (6)

[0069]

[0070] Partial curved plate modal impedance Z j The scaling relationship is shown in Equation (12).

[0071]

[0072] Based on the structural size scaling in Step 1 and the modal identification in Step 2, the relationship between the velocity response power spectral density of the scaled model and the full-scale model is obtained, as shown in Equation (7).

[0073] Velocity response:

[0074]

[0075] Finally, for the intermediate modes (the second and third modes):

[0076] The scaling relationship of the intermediate state modal characteristic frequency is shown in Equation (8):

[0077]

[0078] Based on the structural size scaling in Step 1 and the modal identification in Step 2, the size of is obtained by interpolation, and the relationship between the velocity response power spectral density of the scaled model and the full-scale model is obtained, as shown in Equation (9).

[0079]

[0080] Step 4. Based on Step 3, apply the equivalent method for different frequency bands.

[0081] The curve of the power spectral density function of the structural velocity response is shown in Figure 3 . Compare and analyze Figure 3 the prediction results of with the full-scale model results obtained from finite element calculations. It is concluded that the equivalent method for different frequency bands of the flow-induced vibration velocity effect can successfully predict the response results of the full-scale model while considering the velocity difference phenomenon. According to the equivalent method in Step 3, the acoustic and vibration responses of the real aircraft can be equivalently obtained from the scaled model in the wind tunnel test for different frequency bands, and more reliable acoustic and vibration responses can be obtained for different flow velocity ratios, improving the accuracy of the prediction results in wind tunnel test engineering. The equivalent method for different frequency bands is used to solve the related engineering problems caused by different flow velocity ratios in wind tunnel tests.

[0082] When conducting the ground test of the aircraft flow-induced vibration, when using the equivalent method for different frequency bands of the velocity effect of this patent to predict the structural response, in order to ensure that the deviation of the final structural response result is reduced, the same material is preferably selected for the scaled model and the full-scale model. Generally, if models with different materials are to be selected, materials with similar material parameters are selected for scaling. Therefore, while ensuring the scaling of material dimensions, the similarity of material properties must also be ensured to ensure the best agreement between the ground test and the actual situation.

[0083] The current similarity laws for the ground test of aircraft flow-induced vibration focus on the similarity of the flow Mach number and the structural characteristic frequency, and do not consider the influence of the change in flow velocity caused by the difference in local static temperature on the aerodynamic excitation frequency under ground test and flight conditions. However, to ensure the similarity laws of aerodynamics and structural modes, the flow velocities of the scaled model and the full-scale model must be the same. In fact, due to the different local sound speeds, the flow velocities of the full-scale model and the scaled model are always different, and the structural response prediction similarity method that does not consider the flow velocity difference is inaccurate, seriously affecting the prediction and evaluation accuracy of flow-induced vibration. The equivalent method for different frequency bands of the flow-induced vibration velocity effect proposed by the present invention not only makes up for the deficiencies of the current flow-induced vibration similarity method, but also improves the reliability of the prediction of the structural dynamic response similarity method of the aircraft by constructing a flow-induced vibration similarity criterion considering the flow velocity effect.

[0084] The above specific description further details the purpose, technical solution, and beneficial effects of the invention. It should be understood that the above is only a specific embodiment of the present invention and is not used to limit the protection scope of the present invention. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A method for equivalent of fluid-induced vibration velocity effect in frequency bands, characterized in that: It includes the following steps: Step 1. Determine the model length scale factor σ and thickness scale factor σ according to the flow velocity ratio between the actual flight velocity V of the aircraft and the ground test flow velocity ; The thickness scale factor is obtained from the relationship between the length scale factor and the flow velocity difference: t ​ The geometric dimensions of the scaled model are equivalent to: length width thickness radius of curvature σR; to obtain the scaled model; where "ˉ" represents the parameters related to the scaled model; Step 2: Based on Step 1, perform modal identification on the scaled model, which is divided into three modes: partial flat plate, partial curved plate, and intermediate state. Calculate the scaled modes of the scaled model and the true modes of the flat plate with the same size, and compare the scaled modes with the true modes of the flat plate with the same size to preliminarily identify the partial flat plate mode and the non-flat plate mode. Define the structural frequency ratio Rate: Among them, the flat plate frequency of the scaled model The curved plate frequency of the scaled model is the elastic modulus of the material of the scaled model; represents the density of the scaled model; represents the Poisson's ratio of the scaled model; is the characteristic frequency of the scaled model; m is the modal number in the a direction; n is the modal number in the b direction; The magnitude of the Rate value divides the non-flat plate mode into two modes: partial curved plate and intermediate state. When 5 < Rate < 100, it is the intermediate mode, and when Rate ≤ 5, it is the partial curved plate mode. Step 3: Based on Step 2, use the sub-band method to predict the structural response of the full-scale model through the scaled model. The scaling relationship between the true full-scale model and the scaled model of the characteristic frequency of the partial flat plate mode: Among them, is the material scale parameter. Under the same material, ω mn is the characteristic frequency of the full-scale model; The relationship between the power spectral density of the structural velocity response and the structural characteristic frequency: Among them, S v (x A , y A , ω) represents the velocity response power spectral density; ω represents the angular frequency; ψ j (x A , y A ) and ψ n (x A , y A ) represent the vibration modes in the j and n directions; and Z n (ω) represents the impedance in the j and n directions; γ j and γ n represent the modal factors in the j and n directions; S pp (ω) represents the acoustic-vibration excitation; represents a constant coefficient. Construct the scaling relationship of the power spectral density of the velocity response between the true full-scale model and the scaled model of the partial flat plate structure according to Equations (3) and (4): where q represents the free-stream dynamic pressure of the full-scale model, represents the free-stream dynamic pressure of the scaled model; ρ represents the density of the full-scale model, represents the density of the scaled model; (x A , y A ) represents the arbitrary position coordinates of the relevant point; S v (x A , y A , ω) represents the velocity response power spectral density of the true full-scale model, represents the velocity response power spectral density of the scaled model; The scaling relationship between the true full-scale model and the scaled model of the characteristic frequency of the partial curved plate mode: Construct the scaling relationship of the power spectral density of the velocity response between the true full-scale model and the scaled model of the partial curved plate mode according to Equations (4) and (6): The scaling relationship between the true full-scale model and the scaled model of the characteristic frequency of the intermediate state mode: wherein, is an interpolation coefficient, which is given by the interpolation result; is the characteristic frequency of the scaled model; Construct the scaling relationship of the power spectral density of the velocity response between the true full-scale model and the scaled model of the intermediate state mode according to Equations (4) and (8): Based on the three modes of partial flat plate, partial curved plate, and intermediate state, use the sub-band method to obtain the scaling relationship of the velocity response. According to the scaling relationship, realize the sub-band equivalence of the fluid-induced vibration velocity effect.

2. The method according to claim 1, wherein: It also includes Step 4: Step 4: Based on Step 3, apply the sub-band equivalence method. The scaled model uses the sub-band equivalence method of the fluid-induced vibration velocity effect to predict and calculate the structural response of the full-scale model. According to the equivalence method in Step 3, the acoustic-vibration response of the real aircraft can be obtained by sub-band equivalence of the scaled model in the wind tunnel test, and more reliable acoustic-vibration responses can be obtained for different flow velocity ratios, improving the accuracy of the prediction results in the wind tunnel test engineering. Use the sub-band equivalence method to solve the related engineering problems caused by different flow velocity ratios in the wind tunnel test.

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