A high-scale submodal test method for large flexible beam structures

Abstract

The present invention provides a high-scale submodal test method for a large flexible beam structure. First, a portion of the original beam structure length is taken to build a model. The prototype beam length is 4-8 times the length of the substructure beam. The cross-section of the prototype beam at each position is consistent with the cross-sectional shape of the substructure beam, and the material properties of the prototype beam are consistent with the material properties of the substructure beam. The substructure beam is then clamped with one end fixed and the other end free. The modal frequency of the substructure beam is then measured by tapping or sweeping. Finally, the structural mode of the large flexible beam is obtained based on a given modal frequency estimation formula, and the final result is obtained by averaging several groups of tests. The present invention can use a small-scale cantilever beam model to estimate the modal frequency of a large-scale beam in a "free-free" state.

Description

Technical Field

[0001] The present invention relates to the field of aerospace technology, and in particular to a high-proportion submodal test method for a large flexible beam structure. Background Art

[0002] Flexible beam structures are widely used in aerospace engineering, and their dynamic characteristics are directly related to the safety and performance optimization of the structure. In practical engineering, modal testing is required to analyze their modal parameters (including modal frequencies and vibration modes).

[0003] In the existing technology, traditional modal testing methods have the following main problems: 1. High testing costs: Modal testing usually needs to be performed on full-scale prototypes. Due to the large size of the prototype structure and the complexity of the operation, the testing cost is significantly increased. 2. Large measurement errors: Suspension testing is usually used for testing, but the suspension stiffness is close to the modal frequency of the beam structure, which can easily lead to distortion of the measurement results, especially in the low-frequency band. 3. Limited test conditions: Real prototype beam modal testing requires a large test space and high-performance experimental equipment, which is subject to many restrictions on site and conditions. Summary of the Invention

[0004] The present invention aims to provide a high-scale submodal testing method for large flexible beam structures. By utilizing a portion of the original beam model for testing and combining mathematical models with experimental formulas to infer the modal characteristics of the entire beam, this method significantly reduces experimental cost and complexity while improving the accuracy of test results. By testing a small substructure beam, combined with formula derivation and boundary condition correction, the modal parameters of the large flexible beam under "free-free" boundary conditions can be quickly and accurately predicted.

[0005] According to one object of the present invention, the present invention provides a high-scale submodal test method for a large flexible beam structure, comprising the following steps:

[0006] (1) Cut a portion of the prototype beam length as the substructure beam to ensure that the cross-sectional shape and material properties of the substructure beam are consistent with those of the prototype beam;

[0007] (2) Clamp the substructure beam with one end fixed and the other end free;

[0008] (3) Install sensors on the substructure beams and record sensor measurement data;

[0009] (4) Using fast Fourier transform (FFT) to process sensor measurement data and obtain the modal frequency of the substructure beam;

[0010] (5) Calculate the boundary correction coefficient a according to the formula:

[0011] a≈0.0022k 2-0.0340k+1.1521

[0012] Where a is defined as the boundary revision factor, and k is the ratio of the length of the prototype beam to the length of the substructure beam;

[0013] (6) Estimate the prototype beam modal frequency according to the formula:

[0014]

[0015] Among them, f 原型 is the first-order modal frequency of the prototype beam, f 子结构 is the modal frequency of the first-order beam of the substructure; a is defined as the boundary revision coefficient, and k is the ratio of the length of the prototype beam to the length of the substructure beam;

[0016] (7) Repeat the test on no less than three groups of substructure beams of different lengths and calculate the average value of the modal frequency as the final result.

[0017] Furthermore, the ratio of the prototype beam length to the substructure beam length is 4-8.

[0018] Furthermore, the difference in mass and stiffness distribution of the large flexible beam along the length direction does not exceed 20%.

[0019] Furthermore, the length of the prototype beam is not less than 20 meters and the first-order modal frequency is not higher than 1.5 Hz.

[0020] Furthermore, the stiffness of the fixed end of the substructure beam is not less than 20 times its first-order modal frequency.

[0021] Furthermore, the installed sensor weighs no more than 5g.

[0022] Furthermore, the types of sensors include acceleration sensors or strain gauges. The acceleration sensor is installed at the free end of the substructure beam, and the strain gauge should be installed at the fixed end of the substructure beam.

[0023] Furthermore, no less than three groups of substructure beams of different lengths are selected for testing, and the error between the test results is no more than 10%.

[0024] Furthermore, the excitation methods include percussion excitation and sweep frequency excitation, and the excitation should ensure that the target frequency range is fully covered.

[0025] Furthermore, after the test is completed, the modal frequency is obtained through fast Fourier transform analysis, and the average value is calculated based on multiple groups of test results to improve the measurement accuracy.

[0026] The technical solution of this invention uses tests on small-scale substructure beams, combined with formula derivation and boundary condition correction, to quickly and accurately predict the modal parameters of large flexible beams under "free-free" boundary conditions. This small-scale substructure experiment avoids the high cost of large prototype beam testing; accuracy is improved, and the modified formula corrects for boundary condition differences, improving the accuracy of modal parameter predictions. This method is applicable to a variety of complex engineering models, including long-span beams and large flexible structures. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] In order to more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the specific embodiments or the description of the prior art. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0028] Figure 1 Schematic diagram of the principle of the conventional test method of the present invention;

[0029] Figure 2 This is a schematic diagram of the structure of the method according to an embodiment of the present invention;

[0030] Figure 3 Flow chart of the test method of the present invention;

[0031] In the picture:

[0032] 1. Suspension fixing surface; 2. Suspension cable; 3. Prototype beam; 4. Substructure beam; 5. Substructure beam fixing device. DETAILED DESCRIPTION

[0033] The following will clearly and completely describe the technical solutions of the present invention in conjunction with the embodiments. Obviously, the embodiments described are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0034] In the description of the present invention, it should be understood that the terms "center", "longitudinal", "lateral", "length", "width", "thickness", "up", "down", "front", "back", "left", "right", "vertical", "horizontal", "top", "bottom", "inside", "outside", "clockwise", "counterclockwise" and the like to indicate directions or positional relationships based on the directions or positional relationships shown in the accompanying drawings, and are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific direction, be constructed and operate in a specific direction, and therefore should not be understood as limiting the present invention.

[0035] In addition, the terms "first" and "second" are used for descriptive purposes only and should not be understood as indicating or implying relative importance or implicitly indicating the number of the indicated technical features. Therefore, the features defined as "first" and "second" may explicitly or implicitly include one or more of the said features. In the description of the present invention, "multiple" means two or more, unless otherwise clearly and specifically defined. In addition, the terms "installed", "connected", and "connected" should be understood in a broad sense. For example, it can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection or an electrical connection; it can be a direct connection, or it can be an indirect connection through an intermediate medium, or it can be a communication between the two elements. For those of ordinary skill in the art, the specific meanings of the above terms in the present invention can be understood according to the specific circumstances.

[0036] Example 1

[0037] like Figure 1-Figure 3 As shown,

[0038] A high-scale submodal test method for a large flexible beam structure comprises the following steps:

[0039] Substructure model construction:

[0040] The prototype beam is cut into parts according to the scale factor (4 to 8 times) as "sub-structure beams" to ensure the consistency of cross-sectional shape and material properties.

[0041] Boundary condition settings:

[0042] One end of the substructure beam is fixed and the other end is free, and the ends are fixed with a high-rigidity device to avoid the influence of boundary effects on the modal characteristic measurement.

[0043] Modal Excitation and Testing:

[0044] Apply knocking or sweeping excitation to the substructure beam, and collect dynamic response data through sensors (such as accelerometers and strain gauges) installed on the beam.

[0045] Fast Fourier transform analysis:

[0046] The modal frequencies and related modal parameters of the substructure beams are obtained by processing the data with fast Fourier transform (FFT).

[0047] Boundary correction formula:

[0048] The following boundary correction formula is used to correct the differences between different boundary conditions:

[0049] a≈0.0022k 2 -0.0340k+1.1521

[0050] Where a is defined as the boundary revision factor, and k is the ratio of the length of the prototype beam to the length of the substructure beam;

[0051] Modal frequency derivation:

[0052] Based on the modal frequencies of the substructure beams, the prototype beam modal frequencies are estimated using the following formula:

[0053]

[0054] Among them, f 原型 is the first-order modal frequency of the prototype beam, f 子结构 is the modal frequency of the first-order beam of the substructure; a is defined as the boundary revision coefficient, and k is the ratio of the length of the prototype beam to the length of the substructure beam;

[0055] Take the average value of multiple groups of experiments:

[0056] Repeat the test and select substructure beams of different lengths to obtain the average value of the modal frequency to improve the reliability of the results.

[0057] Example 2

[0058] like Figure 1 As shown, the traditional method is to perform a modal test on an aircraft prototype, fix the prototype beam 3 by suspension, fix the prototype beam 3 on the suspension fixing surface 1 by a suspension cable 2, and then perform a modal test by tapping or the like.

[0059] This embodiment provides a high-scale submodal test method for a large flexible beam structure, such as Figure 2 As shown, a portion of the prototype beam 3 is first taken as the substructure beam 4. Then, one end of the substructure beam is fixed using the substructure beam fixture 5, leaving the other end free. A modal test is then performed using sensors installed on the substructure beam 4. The calculated results are converted into vibration frequencies, and the modal frequencies of the prototype beam 3 are obtained using a conversion formula. This process is repeated 3 to 5 times with different substructure beam 4 lengths, and the average of the calculated results is used as the final modal frequency of the prototype beam 3.

[0060] The present invention provides a high-scale submodal testing method for a large flexible beam structure. First, a portion of the original beam structure length is taken to establish a model. The prototype beam length is 4, 5, 6, and 7 times the length of the substructure beam, respectively. The cross-section of the prototype beam at each position is consistent with the cross-sectional shape of the substructure beam, and the material properties of the prototype beam are consistent with the material properties of the substructure beam. The substructure beam is then clamped with one end fixed and the other end free. The modal frequency of the substructure beam is then measured by tapping or frequency sweeping. Finally, the structural mode of the large flexible beam is obtained based on a given modal frequency estimation formula, and the final result is obtained by averaging several groups of tests. The present invention can use a small-scale cantilever beam model to estimate the modal frequency of a large-scale beam in a "free-free" state.

[0061] like Figure 3 As shown, the embodiment of the present invention specifically includes the following steps:

[0062] Step 1: Take a portion of the length of the prototype beam as the "substructure beam" design model; and ensure that the cross-sectional shape and material properties of the "substructure beam" are consistent with those of the prototype beam.

[0063] Step 2: Fix one end of the "substructure beam" and release the other end to free its degree of freedom.

[0064] Step 3: Install or set sensors on the "substructure beam". The types of sensors include "accelerometer", "strain gauge", "laser vibrometer", etc.

[0065] Step 4: Record the sensor measurement data and use fast Fourier transform on the measurement data to find the modal frequency of the substructure model.

[0066] Step 5: Use the following formula to obtain the boundary revision coefficient between the "free-free beam" and the cantilever beam.

[0067] a≈0.0022k 2 -0.0340k+1.1521

[0068] Where: a is defined as the boundary revision coefficient, reflecting the error caused by changes in boundary conditions under different boundary conditions. k is defined as the cantilever measurement ratio, which represents the ratio of the prototype beam length L to the substructure beam length l.

[0069] Step 6: Estimate the modal frequency of the prototype beam using the following formula:

[0070]

[0071] f 原型 is the first-order modal frequency of the large flexible structure, f 子结构 is the first-order modal frequency of the cantilever substructure, k is the ratio of the length of the large flexible structure to the length of the cantilever substructure, and a is the boundary revision coefficient obtained in step 5.

[0072] Step 7: Select "substructure beams" of different lengths and repeat steps 1 to 6 to obtain multiple sets of measurement results.

[0073] In step eight, the different measurement results obtained in step seven are averaged, and the obtained result is used as the modal frequency of the prototype beam.

[0074] In this embodiment, the difference in mass and stiffness distribution along the length of the large flexible beam should be less than 20%.

[0075] In this embodiment, the length of the beam structure is not less than 20 m, and the first-order modal frequency is not higher than 1.5 Hz.

[0076] In this embodiment, the ratio of the length of the prototype beam to the length of the "substructure beam" is preferably 4 to 8.

[0077] In this embodiment, the modal frequency of the end fixing structure is not less than 20 times the first-order modal frequency of the "substructure beam".

[0078] In this embodiment, the weight of the installed acceleration sensor should not exceed 5g.

[0079] In this embodiment, the weight for mounting the acceleration sensor should be mounted at the free end of the structure.

[0080] In this embodiment, the weight of the “strain gauge” should be installed at the fixed end of the structure.

[0081] In this embodiment, within the scope of claim 3, no less than three groups of "substructure beams" of different lengths should be selected, and the difference between different measurement results should not be higher than 10% of the measurement average.

[0082] The present invention can conduct tests on a local model, reducing the requirements for test space and test equipment. The end-fixed method is used to conduct the test, thus avoiding interference with the test results due to the stiffness of the suspension rope.

[0083] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the above embodiments, or replace some or all of the technical features therein with equivalents. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A high-scale submodal test method for a large flexible beam structure, characterized in that: The following steps are involved: (1) Cut a portion of the prototype beam length as the substructure beam to ensure that the cross-sectional shape and material properties of the substructure beam are consistent with those of the prototype beam; (2) Clamp the substructure beam with one end fixed and the other end free; (3) Install sensors on the substructure beams and record sensor measurement data; (4) Using fast Fourier transform (FFT) to process sensor measurement data and obtain the modal frequency of the substructure beam; (5) Calculate the boundary correction coefficient a according to the formula: a≈0.0022k 2 -0.0340k+1.1521 Where a is defined as the boundary revision factor, and k is the ratio of the length of the prototype beam to the length of the substructure beam; (6) Estimate the prototype beam modal frequency according to the formula: Among them, f 原型 is the first-order modal frequency of the prototype beam, f 子结构 is the modal frequency of the first-order beam of the substructure; a is defined as the boundary revision coefficient, and k is the ratio of the length of the prototype beam to the length of the substructure beam; (7) Repeat the test on no less than three groups of substructure beams of different lengths and calculate the average value of the modal frequency as the final result.

2. The method according to claim 1, characterized in that The ratio of the prototype beam length to the substructure beam length is 4 to 8.

3. The method according to claim 1, characterized in that The mass and stiffness distribution of the large flexible beam along the length direction does not differ by more than 20%.

4. The method according to claim 1, wherein The length of the prototype beam is not less than 20 meters and the first-order modal frequency is not higher than 1.5 Hz.

5. The method according to claim 1, characterized in that The stiffness of the fixed end of the substructure beam is not less than 20 times its first-order modal frequency.

6. The method according to claim 1, characterized in that The weight of the installed sensor does not exceed 5g.

7. The method according to claim 1, characterized in that The types of sensors include acceleration sensors or strain gauges. The acceleration sensors are installed at the free ends of the substructure beams, and the strain gauges should be installed at the fixed ends of the substructure beams.

8. The method according to claim 1, characterized in that No less than three groups of substructure beams of different lengths are selected for testing, and the error between the measured results is no more than 10%.

9. The method according to claim 1, characterized in that There are two types of excitation: percussion excitation and sweep frequency excitation. The excitation should ensure that the target frequency range is fully covered.

10. The method according to claim 1, characterized in that After the test is completed, the modal frequency is obtained through fast Fourier transform analysis, and the average value is calculated based on multiple groups of test results to improve measurement accuracy.

Images