CFRP plate elastic constant inversion method based on zero group velocity point wave number-frequency

Abstract

The invention provides a CFRP plate elastic constant inversion method based on zero group velocity point wave number-frequency, and belongs to the technical field of nondestructive testing of carbon fiber composite plates. In order to solve the problems that in the nondestructive testing process of the CFRP plate, a complete elastic constant matrix of the composite material cannot be obtained and the obtained elastic constant has obvious errors, the method comprises the following steps: calculating frequency dispersion curves in different directions according to the elastic constant of the carbon fiber composite material plate; obtaining theoretical wave number-frequency data based on the wave number-frequency data; carrying out full wave field scanning on the surface of the carbon fiber composite material plate, carrying out three-dimensional Fourier transform on time domain data obtained by the full wave field scanning, and extracting to obtain actually measured wave number-frequency data; and constructing an objective function of an error between the wave number-frequency data corresponding to the theoretical data and the actually measured data ZGV frequency point, and performing multi-parameter optimization on the objective function by using a particle swarm algorithm to obtain an inversion result of the elastic constant of the carbon fiber composite material plate.

Description

Technical Field

[0001] The invention relates to a CFRP plate elastic constant inversion method based on zero group velocity point wave number-frequency, and belongs to the technical field of non-destructive testing of carbon fiber composite material plates. Background Art

[0002] Carbon fiber-reinforced polymer (CFRP) is a growing alternative to traditional metal materials due to its high strength, corrosion resistance, and lightweight properties. It is widely used in a variety of industrial fields, including aerospace, wind power generation, and shipbuilding. To ensure the ideal strength of CFRP panels, accurately measuring their elastic constants is crucial. Traditional methods for measuring elastic constants typically involve cutting the sample at various angles, but this method is destructive and costly, making it unsuitable for on-site testing.

[0003] Therefore, it is very necessary to develop non-destructive testing methods for CFRP plates, and many non-destructive testing methods have emerged. Among them, ultrasonic testing is a widely used non-destructive testing method, which is widely used in the non-destructive testing of elastic constants of composite materials. Liu Yaolu et al. disclosed in the invention patent CN114428119A "A method for inverting the elastic constants of composite materials with anisotropic characteristics". This method solves the dispersion curve of the material through numerical calculation, and then compares the phase velocity curves of the A0 mode and the S0 mode in the ultrasonic guided wave with the theoretical calculation to invert the principal axis elastic modulus (E 11 ,E 22 ) and out-of-plane shear modulus (G 13 ,G 23 ). In this detection method, by comparing the relationship between different modal phase velocities and elastic constants, only the elastic modulus and shear modulus of the material can be obtained, and the complete elastic constant matrix of the composite material cannot be obtained.

[0004] In their invention patent CN115166051A, Guo Shifeng et al. disclosed "a method for measuring the elastic constants of fiber-reinforced resin-based composite materials". This method uses a probe to obtain echoes at different angles in a composite material plate, and calculates the propagation time of ultrasonic waves in a unidirectional composite material plate at different angles. The sum of the squares of the errors between the theoretical propagation time and the measured propagation time is selected as the objective function, and the objective function is optimized with multiple parameters using a particle swarm algorithm, ultimately obtaining the elastic constant matrix of the material. In the technical solution of Guo Shifeng et al., it is necessary to measure in two planes, one parallel and one orthogonal to the fiber direction of the CFRP plate. However, under actual conditions, the fiber direction is usually difficult to determine in advance, and it is impossible to accurately obtain data in the two parallel and orthogonal planes, which leads to errors in the elastic constants. Summary of the Invention

[0005] In order to solve the problem that a complete elastic constant matrix of the composite material cannot be obtained and the obtained elastic constants have obvious errors during the non-destructive testing of CFRP plates, the present invention proposes an inversion method for the elastic constants of CFRP plates based on the zero group velocity point wave number-frequency.

[0006] The technical solution adopted by the present invention to solve the above problems is: the present invention comprises the following steps:

[0007] Step 1: Calculate the dispersion curves in different directions based on the elastic constants of the carbon fiber composite plate;

[0008] Step 2: Extract the wavenumber-frequency data corresponding to the ZGV frequency point in the dispersion curve, and obtain the theoretical wavenumber-frequency data based on the wavenumber-frequency data

[0009] Step 3: Perform a full wave field scan on the surface of the carbon fiber composite material plate, perform a three-dimensional Fourier transform on the time domain data (x, y, t) obtained by the full wave field scan, and extract the measured wave number-frequency data

[0010] Step 4: Construct an objective function of the error between the wavenumber-frequency data corresponding to the ZGV frequency point of the theoretical data and the measured data, and use the particle swarm algorithm to perform multi-parameter optimization on the objective function to obtain the inversion results of the elastic constants of the carbon fiber composite plate.

[0011] Furthermore, step 1 specifically includes:

[0012] Step 1.1: Calculate the wave vector k of the wave propagating along the angle β in the carbon fiber composite plate and obtain the angular frequency ω, mass matrix M, and node displacement vector U of the wave propagating along the angle β;

[0013] Step 1.2: Obtain the displacement and strain matrix B and the transformation matrix T of the carbon fiber composite plate, and construct the stiffness matrix K based on the elastic constant matrix and the displacement and strain matrix of the carbon fiber composite plate mn ;

[0014] Step 1.3: Based on wave vector k and stiffness matrix K mn and the transformation matrix T to construct the matrix A, and construct the wave equation based on the matrix A, the angular frequency ω of the wave propagating along the angle β, the mass matrix M and the node displacement vector U;

[0015] Step 1.4: Solve the wave equation to obtain the frequency curve of the carbon fiber composite material plate. Use the coordinate transformation method to rotate the elastic constant matrix to obtain the dispersion curves of the carbon fiber composite material plate in different directions.

[0016] Furthermore, step 2 specifically includes:

[0017] Extract the wavenumber-frequency data corresponding to the ZGV frequency points in the dispersion curves in different directions, perform orthogonal decomposition on the wavenumber data of the ZGV frequency points, and obtain the theoretical wavenumber-frequency data by combining the frequencies of the ZGV frequency points. in, is the wave number of the theoretically calculated ZGV frequency point, f cal The frequency of the theoretically calculated ZGV frequency point.

[0018] Furthermore, the three-dimensional Fourier transform formula in step 3 is:

[0019]

[0020] In formula (1), F(k x ,k y ,f) is the wavenumber-frequency domain data of the ZGV frequency point after three-dimensional Fourier transform;

[0021] Near the ZGV frequency point, the frequency resonance slice with the largest amplitude energy is intercepted, and the distribution of the ZGV frequency point of the carbon fiber composite material plate in the wavenumber-frequency domain is extracted from it, and the measured wavenumber-frequency data of each ZGV frequency point is obtained.

[0022] Furthermore, the expression of the objective function constructed in step 4 is:

[0023]

[0024] In formula (2), is the wave number of the theoretically calculated ZGV frequency point, f cal The frequency of the theoretically calculated ZGV frequency point; is the wave number of the actual measured ZGV frequency point, f exp The frequency of the ZGV frequency point actually measured;

[0025] The theoretical wave number-frequency data and measured wavenumber-frequency data The initial error is substituted into the objective function to calculate the error, and the particle swarm optimization algorithm is used to perform multi-parameter optimization on the objective function, and the elastic constant value of the carbon fiber composite plate is obtained by inversion.

[0026] The beneficial effects of the present invention are:

[0027] 1. The present invention utilizes the high sensitivity of ZGV frequency point wavenumber-frequency information to the changes in the elastic constants of CFRP plates to perform CFRP plate parameter inversion, which can effectively improve the accuracy of CFRP plate parameter inversion. The present invention overcomes the problems of obvious errors in the elastic constants obtained in the prior art and incomplete elastic constant matrix.

[0028] 2. The present invention does not require water immersion, additional rotation devices, or prior knowledge of the fiber orientation of the material. It can achieve reference-free measurement on any plane, thereby improving the applicability of CFRP plate parameter inversion. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] Figure 1 A schematic flow chart of the inversion method for the elastic constants of CFRP plates based on the zero group velocity point wave number-frequency provided by the present invention;

[0030] Figure 2 Schematic diagram of the theoretical dispersion curve of the CFRP plate provided by the present invention;

[0031] Figure 3 A flow chart for obtaining theoretical wavenumber-frequency data provided by the present invention;

[0032] Figure 4 A flow chart for obtaining the measured wavenumber-frequency data provided by the present invention;

[0033] Figure 5 This is a schematic diagram comparing the ZGV frequency point wavenumber-frequency distribution diagram of the CFRP plate obtained by inversion with the increase of the number of iterations provided by the present invention and the actual distribution diagram. DETAILED DESCRIPTION

[0034] Combine Figure 1-5 This embodiment is described as follows. Figure 1 As shown, the steps of the CFRP plate elastic constant inversion method based on zero group velocity point wave number-frequency described in this embodiment include:

[0035] S1: Calculate the dispersion curves in different directions based on the elastic constant and density of the material, and extract the wavenumber-frequency data corresponding to the ZGV frequency point in each direction;

[0036] S101: For a wave propagating along an angle β, the wave vector k in the propagation direction is defined as:

[0037]

[0038] In formula (1), and is a unit vector;

[0039] S102: Constructing the wave equation;

[0040] In this embodiment, the constructed wave equation has the following eigenvalue form:

[0041] [A-ω 2 M]U=0 (2);

[0042] In formula (2), ω is the angular frequency, M is the mass matrix, U is the node displacement vector, and A is the matrix. The matrix A can be defined as:

[0043] A=k 2 (s 2 K 22 +c 2 K 33 -csK 23 -csK 32 )+ikT T (-cK 13 -sK 21 +sK 12 +cK 31 )T+K 11 (3);

[0044] In formula (3), s = sin(β), c = cos(β), T is the transformation matrix, and the stiffness matrix K in equation (3) is mn It depends on the elastic constant matrix of the composite plate and the relationship between displacement and strain, which is defined as:

[0045]

[0046] In formula (4), B is the matrix related to displacement and strain, and C is the elastic tensor. For a transversely isotropic plate, C is defined as:

[0047]

[0048] In formula (5), the transversely isotropic plate satisfies C 23 =C 22 -2C 44 ;

[0049] S103: Solve formula (2) to obtain the dispersion curve of the CFRP plate. To obtain the dispersion curves of the CFRP plate in different directions, this embodiment uses a coordinate transformation method to perform a rotation transformation on the elastic constant matrix:

[0050]

[0051] In formula (6), l is the rotation tensor, and its expression is:

[0052]

[0053] S104: On the obtained dispersion curve, there is a point where the group velocity is 0 but the phase velocity is finite, which is called the zero group velocity frequency point, such as Figure 3As shown, this embodiment extracts the ZGV frequency points in the dispersion curves in different directions, and performs orthogonal decomposition on the corresponding wavenumbers. The wavenumber-frequency information of the theoretically calculated ZGV frequency points is obtained by combining the frequencies of the ZGV frequency points. The expression of the orthogonal decomposition is:

[0054]

[0055] The theoretical dispersion curve of the CFRP plate obtained in this embodiment is as follows: Figure 2 As shown in the figure, the point (k0, f0) is the ZGV frequency point. The wavenumber-frequency information of the ZGV frequency point is highly sensitive to the change of the elastic constant of the CFRP plate. The wavenumber-frequency information of this point is selected as the input of the objective function.

[0056] S2: Scan the full wavefield of the CFRP plate, perform 3D Fourier transform on the acquired time domain data, and intercept the resonance slice with the maximum amplitude energy near the ZGV frequency point to obtain the measured wavenumber-frequency data;

[0057] S201: Scan the center area of ​​the CFRP plate, such as Figure 4 As shown in Figure 2, the three-dimensional Fourier transform is used to process the surface scan data. The three-dimensional Fourier transform can convert the time domain (x, y, t) data into the wave number-frequency domain (k x ,k y ,f) data, the three-dimensional Fourier transform formula is as follows:

[0058]

[0059] In formula (9), F(k x ,k y ,f) is the wavenumber-frequency domain data of the ZGV frequency point after three-dimensional Fourier transform;

[0060] S202: Near the ZGV frequency point, intercept each frequency resonance slice with the largest amplitude energy, extract the distribution of the ZGV frequency point of the CFRP plate in the wavenumber-frequency domain, and obtain the (k x ,k y ,f)information.

[0061] S3: Construct an objective function for the error between the theoretical calculation and the actual measured ZGV frequency point corresponding wave number-frequency data;

[0062] In this embodiment, the theoretical wave number-frequency data and measured wavenumber-frequency data Substitute the initial error into the objective function and the expression of the constructed objective function is:

[0063]

[0064] In formula (10), is the wave number of the theoretically calculated ZGV frequency point, f cal The frequency of the theoretically calculated ZGV frequency point; is the wave number of the actual measured ZGV frequency point, f exp is the frequency of the actual measured ZGV frequency point.

[0065] S4: Use particle swarm optimization to optimize the multi-parameters of the objective function and invert the elastic constant matrix of the material with high precision.

[0066] When the theoretical wave number and frequency are close to the actual wave number and frequency, the value of the objective function (10) tends to be minimum. The particle swarm algorithm is used to optimize the multi-parameters of the objective function. When the objective function reaches the convergence condition, the values ​​of the five elastic constants can be determined.

[0067] like Figure 5 As shown, when the maximum number of iterations is reached, the CFRP plate obtained by inversion is

[0068] The difference between the ZGV frequency wavenumber-frequency distribution and the actual distribution is small, indicating that the inversion results are highly accurate. To further verify this accuracy, the relative deviation between the actual and theoretical elastic constants was calculated. The results, shown in Table 1, show that the inversion accuracy is within the error range. This verification shows that the present invention utilizes ZGV frequency wavenumber-frequency information to demonstrate high sensitivity to changes in the elastic constants of CFRP plates, effectively improving the accuracy of CFRP plate parameter inversion. Furthermore, the present invention eliminates the need for water immersion, additional rotational devices, or prior knowledge of the material's fiber orientation during the CFRP plate parameter inversion process, enabling reference-free measurement on any plane and broadening its applicability.

[0069] Table 1

[0070]

[0071] The above description is merely a preferred embodiment of the present invention and does not constitute any form of limitation to the present invention. Although the present invention has been disclosed as a preferred embodiment as above, it is not intended to limit the present invention. Any technician familiar with the present profession can make some changes or modifications to equivalent embodiments of equivalent changes using the technical content disclosed above without departing from the scope of the technical solution of the present invention. However, any simple modification, equivalent replacement and improvement of the above embodiments made according to the technical essence of the present invention, within the spirit and principles of the present invention, without departing from the content of the technical solution of the present invention, shall still fall within the scope of protection of the technical solution of the present invention.

Claims

1. The inversion method of elastic constants of CFRP plates based on zero group velocity point wave number-frequency is characterized by: include: Step 1: Calculate the dispersion curves in different directions based on the elastic constants of the carbon fiber composite plate; Step 2: Extract the wavenumber-frequency data corresponding to the ZGV frequency point in the dispersion curve, and obtain the theoretical wavenumber-frequency data based on the wavenumber-frequency data Step 3: Perform a full wave field scan on the surface of the carbon fiber composite material plate, perform a three-dimensional Fourier transform on the time domain data (x, y, t) obtained by the full wave field scan, and extract the measured wave number-frequency data Step 4: Construct an objective function of the error between the wavenumber-frequency data corresponding to the ZGV frequency point of the theoretical data and the measured data, and use the particle swarm algorithm to perform multi-parameter optimization on the objective function to obtain the inversion results of the elastic constants of the carbon fiber composite plate.

2. The CFRP plate elastic constant inversion method based on zero group velocity point wave number-frequency according to claim 1, characterized in that: Step 1 specifically includes: Step 1.1: Calculate the wave vector k of the wave propagating along the angle β in the carbon fiber composite plate and obtain the angular frequency ω, mass matrix M, and node displacement vector U of the wave propagating along the angle β; Step 1.2: Obtain the displacement and strain matrix B and the transformation matrix T of the carbon fiber composite plate, and construct the stiffness matrix K based on the elastic constant matrix and the displacement and strain matrix of the carbon fiber composite plate mn ; Step 1.3: Based on wave vector k and stiffness matrix K mn and the transformation matrix T to construct the matrix A, and construct the wave equation based on the matrix A, the angular frequency ω of the wave propagating along the angle β, the mass matrix M and the node displacement vector U; Step 1.4: Solve the wave equation to obtain the frequency curve of the carbon fiber composite material plate. Use the coordinate transformation method to rotate the elastic constant matrix to obtain the dispersion curves of the carbon fiber composite material plate in different directions.

3. The CFRP plate elastic constant inversion method based on zero group velocity point wave number-frequency according to claim 1, characterized in that: Step 2 specifically includes: Extract the wavenumber-frequency data corresponding to the ZGV frequency points in the dispersion curves in different directions, perform orthogonal decomposition on the wavenumber data of the ZGV frequency points, and obtain the theoretical wavenumber-frequency data by combining the frequencies of the ZGV frequency points. in, is the wave number of the theoretically calculated ZGV frequency point, f cal The frequency of the theoretically calculated ZGV frequency point.

4. The CFRP plate elastic constant inversion method based on zero group velocity point wave number-frequency according to claim 1, characterized in that: The three-dimensional Fourier transform formula in step 3 is: In formula (1), F(k x ,k y ,f) is the wavenumber-frequency domain data of the ZGV frequency point after three-dimensional Fourier transform; Near the ZGV frequency point, the frequency resonance slice with the largest amplitude energy is intercepted, and the distribution of the ZGV frequency point of the carbon fiber composite material plate in the wavenumber-frequency domain is extracted from it, and the measured wavenumber-frequency data of each ZGV frequency point is obtained.

5. The CFRP plate elastic constant inversion method based on zero group velocity point wave number-frequency according to claim 1, characterized in that: The expression of the objective function constructed in step 4 is: In formula (2), is the wave number of the theoretically calculated ZGV frequency point, f cal The frequency of the theoretically calculated ZGV frequency point; is the wave number of the actual measured ZGV frequency point, f exp The frequency of the actual measured ZGV frequency point; The theoretical wave number-frequency data and measured wavenumber-frequency data The initial error is substituted into the objective function to calculate the error, and the particle swarm optimization algorithm is used to perform multi-parameter optimization on the objective function, and the elastic constant value of the carbon fiber composite plate is obtained by inversion.

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