Structural dynamics scaled model test method for functionally graded plates

Abstract

The present invention discloses a structural dynamics scaled model test method for a functional gradient plate, comprising the following steps: S1, scaled model design: taking a large-sized functional gradient plate as a prototype, designing three scaled models of different sizes according to a consistent aspect ratio, wherein the thickness, material composition, material gradient distribution function, material preparation process and boundary conditions of the scaled models are completely consistent with those of the prototype; S2, modal testing: obtaining experimental results of the dynamic characteristics of the three scaled models through modal testing, the dynamic characteristics including structural natural frequency and modal vibration shape; S3, deriving a regular expression for how the natural frequency of the functional gradient plate changes with overall size; S4, similarity prediction: performing a similarity transformation on the regular expression for how the natural frequency changes with overall size to obtain an expression for a predicted value of the natural frequency of the prototype, and simultaneously taking the experimental result of the modal vibration shape of the first scaled model as a prediction result for the modal vibration shape of the prototype.

Description

Technical Field

[0001] The invention belongs to the technical field of mechanical models and tests, and in particular relates to a structural dynamics scaled model test method for functionally gradient plates. Background Art

[0002] Functionally graded materials are heterogeneous composite materials whose material composition and properties vary continuously and gradiently in space. They can alleviate the problem of thermal stress concentration in high-drop temperature environments in the aerospace field. At the same time, their thermal insulation / heat resistance, ablation resistance, specific strength and reusability are significantly better than traditional composite materials, and they are regarded as one of the most promising new composite materials. At present, the application of large-scale (referring to the maximum outline size of more than 5 meters) functionally graded plates in launch vehicles, reusable rockets, hypersonic aircraft, etc. is in the exploratory stage, and their actual load-bearing capacity, especially the dynamic characteristics, need to be verified and evaluated through experiments. Due to the limitations of the test platform size, development cycle, funding, etc., the dynamic test of large-scale structures usually adopts the means of scaled models. Therefore, the dynamic scaled model test of functionally graded plates is an essential technology for their application in engineering practice.

[0003] Because the material composition of functionally graded plates varies gradually across their thickness, existing fabrication processes cannot guarantee that the gradient of material properties remains similar even when the thickness is reduced. This means that the material's gradient characteristics cannot be scaled down. If such a scaled-down model with unscaled material gradient characteristics is used for testing, the experimental results will significantly deviate from the prediction of the prototype's dynamic characteristics.

[0004] In summary, the inability to scale down the gradient characteristics of materials seriously affects the effectiveness of the dynamic scaled model test of functionally graded plate structures. It is necessary to provide a feasible means to solve this problem. Summary of the Invention

[0005] The main purpose of the present invention is to provide a structural dynamics scaled model test method for functionally gradient plates, aiming to solve the problem of deviation in the similarity of structural dynamic characteristics of functionally gradient plates due to the inability to scale down the material gradient change characteristics in the scaled model test.

[0006] To achieve the above objectives, the present invention proposes a structural dynamics scaled model test method for functionally gradient plates (FGPs), which is used to predict the modal characteristics of FGPs whose maximum profile dimension exceeds a preset threshold, where the maximum profile dimension is the length or width of the FGPs. The method comprises the following steps:

[0007] S1, scaled model design:

[0008] Using a functionally gradient plate as a prototype, three scaled-down functionally gradient plates were designed as scaled models with consistent aspect ratios: a first scaled-down model, a second scaled-down model, and a third scaled-down model. The sizes of the three scaled-down models decreased sequentially, with the second scaled-down model being smaller than the first scaled-down model, and the third scaled-down model being smaller than the second scaled-down model.

[0009] S2, modal test:

[0010] Acquire experimental results of dynamic characteristics of the three scaled models through modal testing, wherein the dynamic characteristics include structural natural frequencies and modal vibration shapes;

[0011] S3, derive the regular expression of the natural frequency of the functionally graded plate changing with the overall size:

[0012] Assume that the regular expression of the natural frequency changing with the overall size is

[0013] y=a1x 2 +a2x,

[0014] Where a1 and a2 are two unknown parameters, x is the parameter describing the degree of overall size reduction, and y is the parameter describing the degree of change in the structural natural frequency.

[0015] The experimental results of the structural natural frequencies of the three scaled models obtained in step S2 and Construct three sets of two-dimensional data coordinates, namely (1,1), and Then, the specific values of the unknown parameters a1 and a2 are obtained by fitting using the least squares method; where L and f represent the overall size and structural natural frequency of the functionally graded plate, respectively, and the subscripts m1, m2, and m3 represent the first, second, and third scaled models, respectively. are the overall sizes of the first, second and third scale models respectively, are the experimental values of the structural natural frequencies of the first, second and third scaled models obtained in step S2, respectively;

[0016] S4, Similarity Prediction:

[0017] The regular expression of the variation of the natural frequency with the overall size derived in step S3 is subjected to a similarity transformation to obtain the expression of the predicted value of the natural frequency of the prototype; at the same time, the experimental results of the modal vibration shape of the first scaled model are taken as the predicted results of the modal vibration shape of the prototype.

[0018] Furthermore, the thickness, material composition and material gradient distribution function of the three scaled models are the same as those of the prototype, and the material preparation process used is also completely consistent with the material preparation process used in the prototype.

[0019] Furthermore, the boundary conditions of the three scaled models are consistent with those of the prototype.

[0020] Furthermore, the boundary conditions of the three scaled models and the boundary conditions of the prototype are all four-side clamped conditions.

[0021] The expression for the predicted value of the natural frequency of the prototype in step S4 is:

[0022]

[0023] Where, f pre represents the predicted value of the prototype's natural frequency, the subscript pro represents the prototype, a1 and a2 are the parameters obtained by fitting in step S3, L pro and L m1 Represent the overall size of the prototype and the first scale model, f m1 It represents the experimental value of the structural natural frequency of the first scale model.

[0024] Furthermore, the preset threshold is 5 meters.

[0025] Compared with the existing technologies and methods, the present invention has the following beneficial effects:

[0026] 1) The present invention can achieve similarity prediction of the dynamic characteristics of large-scale functionally gradient plates without changing the functionally gradient material preparation process, greatly facilitating the manufacture of scaled model test pieces, thereby reducing the cost of scaled model testing and shortening the testing cycle;

[0027] 2) The present invention can ensure that both the natural frequency and the modal vibration shape achieve a high similarity prediction accuracy;

[0028] 3) The present invention is applicable to the currently immature functional gradient material preparation process, and can include factors that are difficult to consider in the design, such as defects, pores, discontinuous gradient changes of actual materials, and low precision. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the results shown in these drawings without paying any creative work.

[0030] Figure 1 is a flow chart of the present invention;

[0031] Figure 2 It is a schematic diagram of the structural dimensions of the prototype object and the scaled model in the specific English embodiment of the present invention. DETAILED DESCRIPTION

[0032] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention without making any creative efforts shall fall within the scope of protection of the present invention.

[0033] The dynamic scale model test process of a functional gradient plate is used as a specific embodiment, and according to Figure 1 The method flow of the present invention is implemented as shown.

[0034] Rather than using a single scaled model, this invention employs three scaled models of varying sizes to achieve similar dynamic characteristics for predicting the dynamic characteristics of large-scale functionally gradient plates. The term "large" refers to a maximum profile dimension (specifically, the length or width) exceeding 5 meters, exceeding the test object size permitted by conventional testing platforms.

[0035] Reference Figure 1 , the present invention includes the following four steps:

[0036] S1, scaled model design:

[0037] Using a large-scale (overall outline size greater than 5 meters) functionally gradient plate as the prototype, three reduced-size functionally gradient plates were designed as scaled models according to a consistent aspect ratio: the first, second, and third scaled models. The sizes of the three scaled models decrease in sequence, i.e., the size of the first scaled model > the size of the second scaled model > the size of the third scaled model. At the same time, the thickness, material composition, and material gradient distribution function of the three scaled models are the same as those of the prototype, and the material preparation process used is also completely consistent with the material preparation process used in the prototype. In addition, the boundary conditions of the three scaled models are consistent with those of the prototype, all of which are four-sided clamped conditions.

[0038] S2, modal test:

[0039] The experimental results of the dynamic characteristics of the three scaled models are obtained through modal testing, and the dynamic characteristics include the natural frequency and modal vibration shape of the structure.

[0040] S3, derive the regular expression of the natural frequency of the functionally graded plate changing with the overall size:

[0041] The regular expression of the variation of the natural frequency with the overall size containing two undetermined parameters is adopted, and the natural frequency experimental results of the three scaled models obtained in step S2 are used as three two-dimensional data coordinates. The specific values of the undetermined parameters are obtained by data fitting.

[0042] S4, Similarity Prediction:

[0043] The regular expression of the change of natural frequency with overall size is transformed similarly to obtain the expression of the predicted value of the natural frequency of the prototype; at the same time, the experimental results of the modal vibration shape of the first scaled model are taken as the predicted results of the modal vibration shape of the prototype.

[0044] The test method of the present invention can solve the problem of deviation in the similarity of structural dynamic characteristics of functionally gradient plates in scaled model tests due to the inability to scale down the material gradient change characteristics, while ensuring that both the natural frequency and the modal vibration shape achieve a high similarity accuracy.

[0045] The following is a detailed description using a functional gradient plate as an example.

[0046] First, design a scaled model:

[0047] like Figure 2 As shown, a functional gradient plate is used as the prototype object, denoted as pro, with a length and width of 5m and a thickness of 0.02m. The material components are aluminum alloy and ceramics, and the material gradient distribution function is

[0048]

[0049] Where P represents the material properties (including elastic modulus, density, and Poisson's ratio), subscripts 1 and 2 represent aluminum alloy and ceramic, respectively, h is the thickness, and z is the thickness direction coordinate.

[0050] The physical properties of the material components are shown in Table 1.

[0051] Table 1 Material properties of the examples

[0052]

[0053] like Figure 2 As shown, three scaled models of different sizes were designed: the first scaled model m1, the second scaled model m2, and the third scaled model m3. The scale ratios of the first scaled model were set to 2 / 25, the second scaled model m2 to 1 / 20, and the third scaled model m3 to 1 / 25. The lengths (and widths) of the first scaled model m1, the second scaled model m2, and the third scaled model m3 were 0.4m, 0.25m, and 0.2m, respectively. The material preparation processes (including thickness, material composition, and gradient distribution function) for the three scaled models were identical to those of the prototype. The boundary conditions of the three scaled models were consistent with those of the prototype, with all four sides clamped.

[0054] Then, perform the modal test:

[0055] According to the design parameters of the scaled model in step S1, a model test piece is manufactured, and the natural frequency experimental values of the three scaled model test pieces are obtained through modal testing. and The specific results are shown in Table 2.

[0056] Table 2 Experimental values of natural frequencies of three scaled models in the embodiment

[0057]

[0058] Secondly, the regular expression of the change of natural frequency with overall size is derived:

[0059] The expression y=a1x is used to express the regularity of the natural frequency with the overall size, which contains two undetermined parameters. 2 +a2x. In the formula, a1 and a2 are two unknown parameters, and x and y constitute the two-dimensional data coordinates (x, y).

[0060] According to the result table 2 obtained in step S2, the three data coordinates corresponding to each scaled model are established, which are (1,1), and As shown in Table 3, L and f represent the length (width) of the plate and the natural frequency of the structure, respectively, and the subscripts m1, m2, and m3 represent the first, second, and third scaled models, respectively.

[0061] Table 3 Two-dimensional data coordinates in the embodiment

[0062]

[0063] The results in Table 3 are used as the regular expression of the change of natural frequency with overall size: y = a1x 2 The coordinate points of +a2x are fitted, and the undetermined parameter values corresponding to each mode are shown in Table 4.

[0064] Table 4 Undetermined parameter values in the embodiments

[0065]

[0066] Finally, make similarity predictions:

[0067] Perform similarity transformation on the regular expression of the change of natural frequency with overall size, and obtain the expression of the prototype's natural frequency prediction value:

[0068]

[0069] Where, f pre represents the predicted value of the natural frequency of the prototype, the subscript pro represents the prototype, and a1 and a2 are the parameters obtained by fitting in step S3.

[0070] In this embodiment, Lpro =5, At the same time, a1 and a2 are given in Table 4, and then substituted into the above expression to calculate the predicted value of the prototype natural frequency f pre As shown in Table 5. At the same time, the experimental results of the modal vibration shape of the first scaled model are taken as the prediction results of the prototype modal vibration shape.

[0071] Table 4 Predicted values of prototype natural frequency in the embodiment

[0072]

[0073] The beneficial effects achieved by the present invention are as follows:

[0074] 1) Through the implementation steps of the present invention, it is possible to achieve similarity prediction of the dynamic characteristics of large-scale functionally gradient plates without changing the functionally gradient material preparation process, greatly facilitating the manufacture of scaled model test pieces, thereby reducing the cost of scaled model testing and shortening the testing cycle;

[0075] 2) The present invention can ensure that both the natural frequency and the modal vibration shape achieve a high similarity prediction accuracy;

[0076] 3) The present invention is applicable to the currently immature functional gradient material preparation process, and can include factors that are difficult to consider in the design, such as defects, pores, discontinuous gradient changes of actual materials, and low precision.

[0077] The above description is only a preferred embodiment of the present invention and does not limit the patent scope of the present invention. All equivalent structural transformations made by using the contents of the present invention description and drawings under the inventive concept of the present invention, or direct / indirect application in other related technical fields are included in the patent protection scope of the present invention.

Claims

1. A structural dynamics scaled model test method for functionally graded plates, used to predict the modal characteristics of functionally graded plates with a maximum profile dimension exceeding a preset threshold, characterized by: The following steps are involved: S1, scaled model design: Using the functionally gradient plate as a prototype, three functionally gradient plates of reduced sizes are designed as scaled models according to a consistent aspect ratio: a first scaled model, a second scaled model, and a third scaled model; the sizes of the three scaled models decrease in sequence, i.e., the size of the second scaled model is smaller than the size of the first scaled model, and the size of the third scaled model is smaller than the size of the second scaled model; S2, modal test: Obtaining experimental results of dynamic characteristics of the three scaled models through modal testing, wherein the dynamic characteristics include structural natural frequencies and modal vibration shapes; S3, construct the regular expression of the natural frequency of the functionally graded plate changing with the overall size: y=a1x 2 +a2x, Where a1 and a2 are two unknown parameters, x is the parameter describing the degree of overall size reduction, and y is the parameter describing the degree of change in the structural natural frequency. The experimental results of the structural natural frequencies of the three scaled models obtained in step S2 and Construct three sets of two-dimensional data coordinates, namely (1,1), and The specific values of the undetermined parameters a1 and a2 are obtained by fitting the regular expression of the natural frequency changing with the overall size; wherein L and f represent the overall size and structural natural frequency of the functionally gradient plate, respectively, and the subscripts m1, m2, and m3 represent the first, second, and third scaled models, respectively. are the overall sizes of the first, second and third scale models respectively, are the experimental values of the structural natural frequencies of the first, second, and third scaled models obtained in step S2, respectively; S4, Similarity Prediction: The regular expression of the variation of the natural frequency with the overall size obtained in step S3 is subjected to similarity transformation to obtain the expression of the predicted value of the natural frequency of the prototype; at the same time, the experimental results of the modal vibration shape of the first scaled model are taken as the predicted results of the modal vibration shape of the prototype.

2. The structural dynamics scaled model test method for functionally graded plates according to claim 1, characterized in that: The thickness, material composition and material gradient distribution function of the three scaled models are the same as those of the prototype, and the material preparation process used is also consistent with the material preparation process used in the prototype.

3. The structural dynamics scaled model test method for functionally graded plates according to claim 1, characterized in that: The boundary conditions of the three scaled models are consistent with those of the prototype.

4. The structural dynamics scaled model test method for functionally graded plates according to claim 3, characterized in that: The boundary conditions of the three scaled models and the prototype are all four-side clamped conditions.

5. The structural dynamics scaled model test method for functionally graded plates according to any one of claims 1 to 4, characterized in that: In step S3, specific values of the undetermined parameters a1 and a2 are obtained by least square fitting.

6. The structural dynamics scaled model test method for functionally graded plates according to any one of claims 1 to 4, characterized in that: The expression for the predicted value of the natural frequency of the prototype in step S4 is: Where, f pre represents the predicted value of the prototype's natural frequency, the subscript pro represents the prototype, a1 and a2 are the parameters obtained by fitting in step S3, L pro and L m1 Represent the overall size of the prototype and the first scale model, f m1 It represents the experimental value of the structural natural frequency of the first scale model.

7. The structural dynamics scaled model test method for functionally graded plates according to any one of claims 1 to 4, characterized in that: The preset threshold is 5 meters.

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