Flow-induced vibration velocity effect similarity method based on equivalent mode

Abstract

The invention discloses a flow-induced vibration velocity effect similarity method based on an equivalent mode, and belongs to the field of aircraft structure dynamic strength optimization. According to the method, the scaling model is established, the flow velocity difference caused by different sound velocities of the scaling model and the full-size model is considered at the same time, a new thickness scaling factor is established in combination with the velocity ratio on the basis of a length scaling factor, and the structural vibration parameters of the full-size model are predicted through the scaling model. The influence caused by flow velocity difference can be made up, the characteristic frequency and the structural response of the full-size model can be accurately predicted through the scaling model, and the flow-induced vibration velocity effect similarity prediction precision based on the equivalent mode is improved. According to the method, a complex structure characteristic frequency is changed into a similar form only containing the combination of a thickness scaling factor and a length scaling factor through an equivalent modal method, and a curved plate flow-induced vibration structure response similar expression is deduced, so that the defects of a current flow-induced vibration similarity theory are overcome; and the prediction reliability of the aircraft structure dynamic response similarity method is improved.

Description

Technical Field

[0001] The present invention belongs to the field of dynamic strength optimization of aircraft structures, and relates to a similarity method for fluid-induced vibration velocity effect based on equivalent modes. Background Art

[0002] For an aircraft operating in a high-speed environment, the high-speed airflow will cause strong wall pulsating pressure loads on its surface. This strong pulsating pressure is coupled with the skin structure of the aircraft, generating intense structural buffeting, which undoubtedly poses challenges to the structural safety design of the aircraft. In addition, the pulsating pressure can also be transmitted from the skin structure into the instrument cabin through vibration, threatening the instrument equipment in the cabin and even causing damage. Therefore, conducting research on the wall pulsating pressure loads and fluid-induced vibrations of high-speed aircraft, as well as developing reliable ground test simulation technologies for wall pulsating pressure environments and experimental evaluation technologies for fluid-induced vibration responses, are crucial for the structural safety design and refined design of high-speed aircraft and can provide strong technical support.

[0003] Currently, noise experimental technology is an important means for fluid-induced vibration test evaluation. The noise experimental technology first obtains the equivalent sound pressure level of the pulsating pressure at typical positions on the aircraft surface through wind tunnel tests, and then in a traveling wave tube or reverberation chamber, uses an air flow loudspeaker to simulate the equivalent sound pressure level of the pulsating pressure obtained from the wind tunnel test to evaluate the structure. However, this fluid-induced vibration evaluation technology has significant defects. The defects are manifested in: being unable to simulate the spatial correlation of complex flows; being difficult to simulate the pulsating pressure power spectrum generated by real flows, and being unable to simulate the pulsating pressure loads in extreme environments. Given the deficiencies of traveling wave tubes and reverberation chambers in simulating fluid-induced dynamic loads, wind tunnel technology has become one of the alternative options for fluid-induced vibration assessment. However, due to the problem of excessive size of the original size model, it becomes difficult to select a test machine for testing according to the original scale model, and the full-scale model will increase the cost of wind tunnel tests. Therefore, the limited capabilities of existing equipment and economic reasons often prompt the use of a scaled model based on similarity theory. In this way, establishing a reliable similarity law for fluid-induced vibration based on the scaled model has become the key to realizing the ground test assessment of fluid-induced vibration.

[0004] Although the current research has preliminarily constructed a coupling similarity law between aerodynamic loads and structural responses based on the analytical method of fluid-induced vibration response, this similarity law mainly focuses on the similarity of flow Mach numbers, structural vibration modes, and characteristic frequencies, but ignores the change in flow velocity caused by different environmental sound speeds under ground test and flight conditions, which further affects the excitation frequency of the structure. Therefore, the matching characteristics between the aerodynamic loads of the scaled model and the structural characteristic frequencies of the full-scale model have changed, significantly reducing the prediction and evaluation accuracy of fluid-induced vibration. Summary of the Invention

[0005] To solve the problem that the current ground test fluid-induced vibration similarity law mainly focuses on Mach number and modal similarity, without in-depth research on flow velocity and even ignoring the influence of flow velocity changes, resulting in low evaluation accuracy, the purpose of the present invention is to provide a fluid-induced vibration velocity effect similarity method based on equivalent mode. Based on the geometric scale factor of the aircraft, a thickness scale factor is introduced, and the thickness factor is used to compensate for the problem that the aerodynamic load frequency and structural frequency are inconsistent due to the flow velocity difference between the test and the real situation; on this basis, combined with the equivalent mode method, a fluid-induced vibration velocity effect similarity method considering the flow velocity effect is derived, and a fluid-induced vibration velocity effect similarity method for curved plate structures is established, and the reliability of the prediction of the aircraft structure dynamic response similarity method is improved according to the fluid-induced vibration velocity effect similarity method for curved plate structures.

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

[0007] A fluid-induced vibration velocity effect similarity method based on equivalent mode disclosed by the present invention includes the following steps:

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

[0009]

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

[0011] Step 2: Based on Step 1, consider the velocity effect and calculate the structural frequency of the real full-scale model.

[0012] Scale the structural dimensions to obtain the structural characteristic frequency of the scaled model:

[0013]

[0014] Among them, 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.

[0015] Flat plate frequency of the scaled model

[0016]

[0017] Curved plate frequency of the scaled model

[0018]

[0019] Obtain the structural characteristic frequency of the true full-scale model:

[0020]

[0021] E is the elastic modulus of the material of the full-scale model; ρ represents the density of the full-scale model; v represents the Poisson's ratio of the full-scale model; is the material scaling parameter; ω mn is the characteristic frequency of the full-scale model.

[0022] Step 3: Based on Step 1 and Step 2, calculate the structural response of the true full-scale model through the equivalent modal method.

[0023] Take the equivalent modal frequency as the characteristic frequency of the scaled model to replace the original characteristic frequency of the scaled model

[0024]

[0025] The similarity relationship between the full-scale model and the scaled model of the structural characteristic frequency becomes:

[0026]

[0027] Relationship between the power spectral density of the structural velocity response and the structural characteristic frequency:

[0028]

[0029] Among them, 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 )、ψ n (x A ,y A ) represents the vibration modes in the j and n directions; and Z n (ω) represents 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($\omega$) represents the acoustic-vibration excitation; represents a constant coefficient.

[0030] Based on Equations (6), (7), and (8), construct the scaling relationship of the velocity response power spectral density between the structural true full-scale model and the scaled model:

[0031]

[0032] wherein, $q$ represents the oncoming flow dynamic pressure of the full-scale model, represents the oncoming flow dynamic pressure of the scaled model; $\rho$ represents the density of the full-scale model, represents the density of the scaled model. $S$ v $(x$ A , $y$ A , $\omega$) represents the velocity response power spectral density of the true full-scale model; represents the velocity response power spectral density of the scaled model.

[0033] Step Four: Based on Step Three, apply the similarity method of the fluid-induced vibration velocity effect based on equivalent modes.

[0034] The scaled model uses the similarity method of the fluid-induced vibration velocity effect based on equivalent modes to predict and calculate the structural response of the true full-scale model. According to the similarity method in Step Three, the acoustic-vibration response of the true aircraft can be predicted through the scaled model in the wind tunnel test, and more reliable predicted responses can be obtained for different flow velocity ratios, improving the accuracy of the predicted results in the wind tunnel test engineering and solving the related engineering problems caused by different flow velocity ratios in the wind tunnel test.

[0035] Beneficial Effects:

[0036] 1. A similarity method of the fluid-induced vibration velocity effect based on equivalent modes disclosed by the present invention, by establishing a scaled model, simultaneously considering the flow velocity difference caused by different sound velocities between the scaled model and the full-scale model, constructing a new thickness scaling factor in combination with the velocity ratio on the basis of the length scaling factor, predicting the structural vibration parameters of the full-scale model through the scaled model, being able to make up for the influence brought by the flow velocity difference and accurately predicting the characteristic frequency and structural response of the full-scale model through the scaled model; further reducing the similarity theory prediction error caused by the flow velocity difference and improving the similarity prediction accuracy of the fluid-induced vibration velocity effect based on equivalent modes.

[0037] 2. Compared with the traditional scaled model similarity method, a flow-induced vibration velocity effect similarity method based on equivalent modes disclosed by the present invention transforms complex structural characteristic frequencies into a simple similarity form containing only the thickness scaling factor and the length scaling factor through the equivalent mode method, and derives a similarity expression for the structural response of the curved plate flow-induced vibration, making up for the deficiencies of the current flow-induced vibration similarity theory and further improving the reliability of the prediction of the dynamic response similarity method of the aircraft structure. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] Figure 1 is the frequency of the scaled model flat plate calculated under different modes

[0039] Figure 2 is a comparison diagram of the prediction results of the scaled model and the characteristic frequencies of the full-scale model.

[0040] Figure 3 is a comparison diagram of the structural velocity response power spectra of the scaled model and the full-scale model.

[0041] Figure 4 is a flow chart of a flow-induced vibration velocity effect similarity method based on equivalent modes of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0042] The following further describes the specific embodiments of the present invention in conjunction with the drawings and embodiments. The following embodiments are only used to more clearly illustrate the technical solutions of the present invention and cannot be used to limit the protection scope of the present invention.

[0043] In the following method, taking the curved plate structure of a certain aircraft as an example, a curved plate with the full-scale model a = 0.3m, b = 1.5m, curvature radius R = 1.5m, and thickness h = 0.01m and a scaled model with length-width scaling factor σ = 0.5, thickness scaling factor σ t = 0.454, and velocity ratio are taken. Taking the curved plate model as an example, this method develops a flow-induced vibration velocity effect similarity method based on equivalent modes. As Figure 4 shown, a flow-induced vibration velocity effect similarity method based on equivalent modes disclosed in this embodiment specifically includes the following implementation steps:

[0044] Step 1. Establishment of the scaled model. The dimensions of the aircraft curved plate structure are scaled to establish a scaled model.

[0045] Determine the model length scaling factor σ and thickness scaling factor σ according to the velocity ratio of the difference between the true flight flow velocity of the aircraft and the ground test flow velocity t . The thickness scaling factor is obtained from the relationship between the length scaling factor and the flow velocity ratio, as shown in formula (1):

[0046]

[0047] The structural dimensions consist of the length a, the width b, the thickness h, and the radius of curvature R. The following equivalent scale-down ratios are applied to the dimensions of the structure:

[0048]

[0049] Step 2: Calculation of the full-scale structural characteristic frequencies: Based on the scale-down relationship of the structural dimensions, see Equation (10)

[0050] The structural characteristic frequencies of the scaled-down model are obtained through finite element calculations, see Equation (2).

[0051] Characteristic frequencies

[0052]

[0053] The plate frequencies of the scaled-down model are calculated see Equation (3).

[0054] Plate frequencies

[0055]

[0056] The plate frequencies of the scaled-down model structure calculated by the analytical method are shown Figure 1 .

[0057] Based on the relationship between the curved plate frequencies, plate frequencies, and characteristic frequencies of the scaled-down model, the curved plate frequencies of the scaled-down model are obtained see Equation (4):

[0058]

[0059] Finally, based on the curved plate frequencies and plate frequencies of the scaled-down model, the full-scale model structural characteristic frequencies are obtained, see Equation (5):

[0060]

[0061] Step 3: Calculation of the full-scale structural response: Using the equivalent modal frequencies as the curved plate frequencies of the scaled-down model to replace the original scaled-down model characteristic frequencies

[0062] The form is shown in Equation (6):

[0063]

[0064] After replacement, the similarity relationship between the full-scale model and the scaled-down model of the structural characteristic frequencies becomes Equation (7)

[0065]

[0066] The comparison between the characteristic frequencies of the full-scale model obtained by calculating the frequencies of the scaled model through similarity methods and the characteristic frequencies of the full-scale model obtained by finite element calculation is shown in Figure 2 . Analysis Figure 2 The results show that the characteristic frequencies predicted and calculated by the similarity method of the fluid-induced vibration velocity effect based on equivalent modes are the same as those of the actual model.

[0067] Structural impedance Z j The scaling relationship is shown in Equation (11).

[0068]

[0069] where, 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.

[0070] The relationship between the power spectral density of the velocity response of the scaled model and the full-scale model is shown in Equation (9).

[0071] Velocity response:

[0072]

[0073] Step 4: Based on Step 3, apply the similarity method of the fluid-induced vibration velocity effect based on equivalent modes.

[0074] The scaled model uses the similarity method of the fluid-induced vibration velocity effect based on equivalent modes to predict and calculate the structural response of the real full-scale model. The curve of the power spectral density function of the structural velocity response is shown in Figure 3 . Comparative analysis Figure 3 The result analysis shows that the similarity method of the fluid-induced vibration velocity effect based on equivalent modes uses a simple scaling method and can successfully predict the structural response results of the full-scale model considering the velocity difference phenomenon. According to the similarity method in Step 3, the acoustic-vibration response of the real aircraft can be predicted through the scaled model of the wind tunnel test, and more reliable predicted responses can be obtained for different flow velocity ratios, improving the accuracy of the predicted results in wind tunnel test engineering and solving the related engineering problems caused by different flow velocity ratios in wind tunnel tests.

[0075] When conducting ground wind tunnel tests on aircraft, when using the similarity method of flow-induced vibration velocity effect based on equivalent modes of the present invention to predict the structural response, in order to ensure a reduction in the deviation of the final structural response results, the same support method should be selected as much as possible for the scaled model and the full-scale model. If models with different support methods are to be used, it is necessary to prove that different support methods will not affect the final results of the test. At the same time, while ensuring the scaling of material dimensions, the similarity of material properties should also be ensured to maximize the compliance of the wind tunnel ground test with the actual situation.

[0076] Currently, in most aircraft ground wind tunnel tests, the flow velocities of the scaled model and the full-scale model are different. Conventional scaled equivalent methods mostly solve aircraft ground wind tunnel tests based on structural dimensions. The change in flow velocity caused by the different ambient sound speeds under ground test and flight conditions is ignored, further affecting the excitation frequency of the structure. Aiming at this deficiency of the current flow-induced vibration similarity theory, the similarity method of flow-induced vibration velocity effect based on equivalent modes proposed by the present invention not only solves the prediction similarity problem in terms of flow velocity difference, but also proposes a method of using equivalent modes for complex aircraft structure frequencies to simplify similarity, greatly reducing the equivalent theory prediction error caused by velocity difference. It can not only reduce the difficulty of aircraft structure similarity, but also improve the reliability of the prediction of the dynamic response similarity method of aircraft structures.

[0077] 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 similarity method for the velocity effect of fluid-induced vibration based on equivalent modes, 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 of the actual flight velocity V of the aircraft to the ground test flow velocity ; The thickness scale factor is obtained from the relationship between the length scale factor and the flow velocity ratio: t ​ The geometric dimensions of the scaled model are equivalent to: length width thickness radius of curvature to obtain the scaled model; where "ˉ" represents the parameters related to the scaled model; Step 2: Based on Step 1, calculate the structural frequency of the true full-scale model considering the velocity effect; Scale down the structural dimensions to obtain the structural characteristic frequencies of the scaled model: Among them, is the elastic modulus of the scaled model material; 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; Flat frequency of the scaled model Curved Plate Frequency of the Scale Model Obtain the structural characteristic frequencies of the true full-scale model: $E$ is the elastic modulus of the full-scale model material; $\rho$ represents the density of the full-scale model; $v$ represents the Poisson's ratio of the full-scale model; is the material scale parameter; $\omega$ mn is the characteristic frequency of the full-scale model; Step 3: Based on Step 1 and Step 2, calculate the structural response of the true full-scale model by the equivalent modal method; Take the equivalent modal frequency as the characteristic frequency of the scaled model to replace the original characteristic frequency of the scaled model The similarity relationship between the full-scale model and the scaled model of the structural characteristic frequencies becomes: The relationship between the structural velocity response power spectral density and the structural characteristic frequencies: 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 scaled relationship of the structural velocity response power spectral density between the true full-scale model and the scaled model of the structure according to Eqs. (6), (7), and (8): where q represents the incoming flow dynamic pressure of the original scale model, represents the incoming flow dynamic pressure of the scaled model; ρ represents the density of the full-scale model, represents the density of the scaled model; 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.

2. The method according to claim 1, wherein: It also includes Step 4: Step 4: Based on Step 3, apply the similarity method of fluid-induced vibration velocity effect based on equivalent modes; The scaled model uses the similarity method of fluid-induced vibration velocity effect based on equivalent modes to predict and calculate the structural response of the true full-scale model; according to the similarity method in Step 3, the acoustic-vibration response of the true aircraft can be predicted by the scaled model in the wind tunnel test, and more reliable predicted responses can be obtained for different flow velocity ratios, improving the accuracy of the predicted results in the wind tunnel test engineering and solving the related engineering problems caused by different flow velocity ratios in the wind tunnel test.

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