Waveform prediction method for Lamb wave response signal in variable-thickness plate

Abstract

The invention provides a waveform prediction method for a Lamb wave response signal in a variable-thickness plate. The method comprises the following steps: acquiring a frequency dispersion curve of a Lamb wave in an equal-thickness plate consistent with a target variable-thickness plate in material parameter; discretizing the Lamb wave propagation path to obtain the unit length of each discrete propagation path and the corresponding plate thickness; taking the frequency dispersion curve of the Lamb wave in the equal-thickness plate as a reference, and calculating to obtain a frequency-wave number curve of the Lamb wave under the plate thickness corresponding to the length of each discrete propagation path unit; calculating the equivalent frequency dispersion information of the Lamb wave according to the length of each discrete propagation path unit and the corresponding frequency-wave number curve; and according to the equivalent frequency dispersion information of the excitation signal and the Lamb wave, calculating to obtain a response prediction signal waveform. The method provided by the invention can predict the lamb wave response signal waveform of a specific mode in the variable thickness plate.

Description

Technical Field

[0001] This invention belongs to the field of acoustic detection, and specifically relates to a method for predicting the waveform of Lamb wave response signal in a plate with variable thickness. Background Technology

[0002] Lamb waves are a type of ultrasonic guided wave present in thin plates. A significant difference between them and ultrasonic body waves (i.e., transverse and longitudinal waves) is that ultrasonic guided waves exhibit dispersion characteristics; that is, the propagation characteristics of ultrasonic guided waves (such as phase velocity and group velocity) are related to the frequency-thickness product (the product of frequency and plate thickness). To date, researchers and related technical personnel both domestically and internationally have primarily focused on the propagation of Lamb waves in plates of uniform thickness, with relatively little research on the prediction of Lamb wave response signals in plates of variable thickness. However, variable thickness plates are widely used in practical engineering applications, such as in aero-engine and turbine blades, variable thickness shells in the shipbuilding industry, and variable thickness vertical tail structures in aircraft. Accurate and rapid prediction of the Lamb wave response signal waveform in variable thickness plates can lay the foundation for defect detection and evaluation in these plates based on Lamb waves.

[0003] Currently, research and applications of Lamb wave response signals in variable thickness plates primarily rely on finite element method (FEM) simulation. While FEM can predict Lamb wave response signals in variable thickness plates, it requires constructing a finite element model, resulting in complex modeling processes and high computational costs. Furthermore, FEM modeling necessitates geometric information of the entire variable thickness waveguide structure. These shortcomings significantly offset the advantage of Lamb waves over ultrasonic bulk waves in rapidly locating defects. Summary of the Invention

[0004] To address the aforementioned technical problems, the objective of this invention is to propose a method for predicting the waveform of the Lamb wave response signal in a plate with variable thickness, overcoming the shortcomings of existing technologies that require finite element modeling and involve large computational loads, and enabling the prediction of the Lamb wave response signal waveform in a plate with variable thickness.

[0005] To achieve the above objectives, the present invention adopts the following approach.

[0006] A method for predicting the Lamb wave response signal waveform in a plate with variable thickness, the method comprising the following steps:

[0007] Step 1 (S1): Obtain the dispersion curve of the Lamb wave in a plate of uniform thickness that has the same material parameters as the target variable thickness plate;

[0008] The second step (S2) is to discretize the Lamb wave propagation path and obtain the length of each discrete propagation path element and the corresponding plate thickness.

[0009] The third step (S3): Using the dispersion curve of the Lamb wave in a plate of uniform thickness as a reference, calculate the frequency-wavenumber curve of the Lamb wave under the plate thickness corresponding to the length of each discrete propagation path element.

[0010] Step 4 (S4): Calculate the equivalent dispersion information of the Lamb wave based on the length of each discrete propagation path unit and the corresponding frequency-wavenumber curve;

[0011] Step 5 (S5): Calculate the response prediction signal waveform based on the equivalent dispersion information of the excitation signal and the Lamb wave.

[0012] Optionally, in the first step (S1), the dispersion curve of the Lamb wave in the plate of uniform thickness is: the frequency-thickness product-wavenumber curve of the Lamb wave in the plate of uniform thickness with the same density, elastic modulus, and Poisson's ratio parameters as the corresponding parameters in the target plate of variable thickness. The frequency-thickness product-wavenumber curve includes discrete points (fd, k0), where fd is the frequency-thickness product and k0 is the real part of the wavenumber.

[0013] Optionally, in the second step (S2), the length of the discrete propagation path unit is no greater than 1 / 20 of the target mode Lamb wave wavelength under the corresponding plate thickness.

[0014] Optionally, in the third step (S3), the formula for calculating the wavenumber is:

[0015] k j =interp1(fd, k0, f*d) j )

[0016] In the formula: interp1 represents the one-dimensional interpolation function, f is the frequency, and d j Let k represent the plate thickness corresponding to the j-th discrete propagation path element. j The wave number is obtained by interpolation using a one-dimensional interpolation function, and the asterisk (*) is the multiplication operator.

[0017] Optionally, the one-dimensional interpolation function includes a one-dimensional cubic spline interpolation function.

[0018] Optionally, in the fourth step (S4), the formula for calculating the equivalent dispersion information of the Lamb wave is as follows:

[0019]

[0020] In the formula: N is the number of discrete units when discretizing the Lamb wave propagation path in step (S2), Δx j Let be the length of the j-th discrete propagation path unit along the propagation path direction. For the equivalent dispersion information of the Lamb wave, d j This represents the plate thickness corresponding to the j-th discrete propagation path unit, and * is the multiplication operator.

[0021] Optionally, in step five (S5), the formula for calculating the response prediction signal waveform is:

[0022]

[0023] In the formula: IFFT is the inverse fast Fourier transform function, FFT is the fast Fourier transform function, s(t) is the time-domain excitation signal, e is the natural constant, i is the imaginary unit, y(t) is the time-domain Lamb wave response prediction signal, and t is time.

[0024] Compared with the prior art, the present invention has the following beneficial technical effects:

[0025] The present invention discloses a method for predicting the Lamb wave response signal waveform in a variable thickness plate, which can predict the Lamb wave response signal waveform in a variable thickness plate without the need for finite element modeling. Attached Figure Description

[0026] The accompanying drawings illustrate exemplary embodiments of the invention and, together with the description thereof, serve to explain the principles of the invention. These drawings are included to provide a further understanding of the invention and are incorporated in and constitute a part of this specification.

[0027] Figure 1 This is a schematic diagram of the cross-section of the target variable thickness aluminum plate in this embodiment;

[0028] Figure 2 The dispersion curve of the Lamb wave A0 mode in an aluminum plate with a thickness of 2 mm and the same material parameters as the target variable thickness plate in this embodiment;

[0029] Figure 3 A flowchart of a method for predicting the Lamb wave response signal waveform in a variable thickness plate provided in this embodiment of the invention;

[0030] Figure 4 In this embodiment, d is obtained by interpolation using a one-dimensional interpolation function. j wavenumber k at 5mm j Line graph;

[0031] Figure 5 This is the time-domain waveform of the sinusoidal pulse excitation signal with a center frequency of 100kHz and a cycle number of 5 using the Hanning window amplitude modulation in this embodiment.

[0032] Figure 6 This is a waveform diagram of the A0 mode Lamb wave prediction signal obtained by using the method of the present invention in an embodiment of the present invention. Detailed Implementation

[0033] The following is in conjunction with the appendix Figures 1 to 6The present invention will be further described in detail below with reference to the embodiments. It is to be understood that the specific embodiments described herein are for illustrative purposes only and are not intended to limit the scope of the invention. Furthermore, it should be noted that, for ease of description, only the parts relevant to the present invention are shown in the accompanying drawings.

[0034] It should be noted that, unless otherwise specified, the embodiments and features described in this invention can be combined with each other. The technical solution of this invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0035] Unless otherwise stated, the exemplary embodiments / exemplifications shown are to be understood as providing exemplary features of various details that provide ways in which the technical concept of the invention can be implemented in practice. Therefore, unless otherwise stated, the features of the various embodiments / exemplifications may be additionally combined, separated, interchanged and / or rearranged without departing from the technical concept of the invention.

[0036] The use of crosshairs and / or shading in the accompanying drawings is generally used to clarify the boundaries between adjacent components. Thus, unless otherwise stated, the presence or absence of crosshairs or shading does not convey or indicate any preference or requirement for the specific material, material properties, dimensions, proportions, commonalities between the illustrated components, or any other characteristics, properties, etc., of the components. Furthermore, in the accompanying drawings, the dimensions and relative dimensions of components may be exaggerated for clarity and / or descriptive purposes. When exemplary embodiments can be implemented differently, a specific process sequence may be performed in a different order than that described. For example, two consecutively described processes may be performed substantially simultaneously or in the reverse order of their description. Furthermore, the same reference numerals denote the same components.

[0037] When a component is referred to as being "on" or "above" another component, "connected to," or "joined to" another component, the component may be directly on, directly connected to, or directly joined to the other component, or there may be intermediate components. However, when a component is referred to as being "directly on" another component, "directly connected to," or "directly joined to" another component, there are no intermediate components. Therefore, the term "connection" can refer to a physical connection, an electrical connection, etc., and may or may not have intermediate components.

[0038] For descriptive purposes, the present invention may use spatial relative terms such as “below,” “under,” “below,” “down,” “above,” “above,” “higher,” and “side (e.g., in a “sidewall”)” to describe the relationship between one component and another component as shown in the accompanying drawings. In addition to the orientations depicted in the drawings, the spatial relative terms are also intended to encompass different orientations of the device during use, operation, and / or manufacture. For example, if the device in the drawings is flipped, a component described as “below” or “under” another component or feature would subsequently be positioned “above” said other component or feature. Thus, the exemplary term “below” can encompass both “above” and “below” orientations. Furthermore, the device may be otherwise positioned (e.g., rotated 90 degrees or in other orientations), thus interpreting the spatial relative descriptive terms used herein accordingly.

[0039] The terminology used herein is for the purpose of describing particular embodiments and is not intended to be limiting. As used herein, unless the context clearly indicates otherwise, the singular forms “a” and “the” are intended to include the plural forms as well. Furthermore, when the terms “comprising” and / or “including” and variations thereof are used in this specification, it indicates the presence of the stated features, integrals, steps, operations, parts, components, and / or groups thereof, but does not exclude the presence or addition of one or more other features, integrals, steps, operations, parts, components, and / or groups thereof. It should also be noted that, as used herein, the terms “substantially,” “about,” and other similar terms are used as approximate terms rather than as terms of degree, thus explaining the inherent biases in measurements, calculated values, and / or provided values ​​that would be recognized by one of ordinary skill in the art.

[0040] This invention provides a method for predicting the Lamb wave response signal waveform in a plate with variable thickness, the method comprising the following steps:

[0041] Step 1 (S1): Obtain the dispersion curve of the Lamb wave in a plate of uniform thickness that has the same material parameters as the target variable thickness plate;

[0042] The second step (S2) is to discretize the Lamb wave propagation path and obtain the length of each discrete propagation path element and the corresponding plate thickness.

[0043] The third step (S3): Using the dispersion curve of the Lamb wave in a plate of uniform thickness as a reference, calculate the frequency-wavenumber curve of the Lamb wave under the plate thickness corresponding to the length of each discrete propagation path element.

[0044] Step 4 (S4): Calculate the equivalent dispersion information of the Lamb wave based on the length of each discrete propagation path unit and the corresponding frequency-wavenumber curve;

[0045] Step 5 (S5): Calculate the response prediction signal waveform based on the equivalent dispersion information of the excitation signal and the Lamb wave.

[0046] Optionally, in the first step (S1), the dispersion curve of the Lamb wave in the plate of uniform thickness is: the frequency-thickness product-wavenumber curve of the Lamb wave in the plate of uniform thickness with the same density, elastic modulus, and Poisson's ratio parameters as the corresponding parameters in the target plate of variable thickness. The frequency-thickness product-wavenumber curve includes discrete points (fd, k0), where fd is the frequency-thickness product and k0 is the real part of the wavenumber.

[0047] Optionally, in the second step (S2), the length of the discrete propagation path unit is no greater than 1 / 20 of the target mode Lamb wave wavelength under the corresponding plate thickness.

[0048] Optionally, in the third step (S3), the formula for calculating the wavenumber is:

[0049] k j =interp1(fd, k0, f*d) j )

[0050] In the formula: interp1 represents the one-dimensional interpolation function, f is the frequency, and d j Let k represent the plate thickness corresponding to the j-th discrete propagation path element. j The wave number is obtained by interpolation using a one-dimensional interpolation function, and the asterisk (*) is the multiplication operator.

[0051] Optionally, the one-dimensional interpolation function includes a one-dimensional cubic spline interpolation function.

[0052] Optionally, in the fourth step (S4), the formula for calculating the equivalent dispersion information of the Lamb wave is as follows:

[0053]

[0054] In the formula: N is the number of discrete units when discretizing the Lamb wave propagation path in step (S2), Δx j Let be the length of the j-th discrete propagation path unit along the propagation path direction. For the equivalent dispersion information of the Lamb wave, d j This represents the plate thickness corresponding to the j-th discrete propagation path unit, and * is the multiplication operator.

[0055] Optionally, in step five (S5), the formula for calculating the response prediction signal waveform is:

[0056]

[0057] In the formula: IFFT is the inverse fast Fourier transform function, FFT is the fast Fourier transform function, s(t) is the time-domain excitation signal, e is the natural constant, i is the imaginary unit, y(t) is the time-domain Lamb wave response prediction signal, and t is time.

[0058] In one embodiment, reference is made to Figure 1 This is a schematic cross-sectional view of the target variable thickness aluminum plate according to an embodiment of the present invention. The material parameters of the target variable thickness aluminum plate are: density 2700 kg / m³. 3 The Young's modulus is 70 GPa and the Poisson's ratio is 0.33. In this embodiment, the target variable thickness aluminum plate has a linear thickness change from the leftmost end to the rightmost end and is symmetrical from top to bottom. The minimum thickness is 2 mm (left side thickness) and the maximum thickness is 8 mm (right side thickness). The length is 1500 mm and the width is 1000 mm.

[0059] In one embodiment, the Lamb wave response signal to be predicted is: the A0 mode Lamb wave signal received on the upper surface of the rightmost end of the variable thickness plate after the A0 mode Lamb wave is excited at the leftmost end of the variable thickness plate and propagates through the variable thickness plate.

[0060] Reference Figure 2 This figure shows the dispersion curve of the Lamb wave A0 mode in an aluminum plate with a thickness of 2 mm and the same material parameters as the target variable thickness plate, according to an embodiment of the present invention. The horizontal axis represents the frequency-thickness product fd (unit: MHz·mm), and the vertical axis represents the wavenumber k0 (unit: 1 / m). When obtaining this dispersion curve, the waveguide structure was a uniform thickness aluminum plate with the same material parameters as the corresponding material parameters of the target variable thickness plate, i.e., a density of 2700 kg / m³. 3 The Young's modulus is 70 GPa, Poisson's ratio is 0.33, and the thickness of the plate of uniform thickness is 2 mm. These values ​​were calculated using the free and open-source software DispersionCalculator.

[0061] Reference Figure 3 This is a flowchart illustrating a method for predicting the Lamb wave response signal waveform in a variable thickness plate, as exemplified by an embodiment of the present invention. The method includes the following steps:

[0062] In the first step, the dispersion curve of the Lamb wave in a plate of constant thickness that is consistent with the material parameters of the target variable thickness plate is obtained.

[0063] Among them, the Lamb wave dispersion curve in the uniform thickness plate is the frequency-thickness product-wavenumber curve of the Lamb wave in the uniform thickness plate with the same density, elastic modulus, and Poisson's ratio parameters as the corresponding parameters in the target variable thickness plate, i.e., a series of discrete points (fd, k0); where fd is the frequency-thickness product and k0 is the real part of the wavenumber; after this step, the obtained dispersion curve is as follows: Figure 2 As shown.

[0064] The second step is to discretize the Lamb wave propagation path and obtain the length of each discrete propagation path element and the corresponding plate thickness.

[0065] The third step: Using the Lamb wave dispersion curve in a plate of uniform thickness as a reference, interpolation is used to calculate the frequency-wavenumber curve of the Lamb wave under the plate thickness corresponding to the length of each discrete propagation path element.

[0066] Reference Figure 4 d is the plate thickness d corresponding to the j-th discrete propagation path unit obtained by interpolation using a one-dimensional interpolation function in this embodiment of the invention. j wavenumber k at 5mm j curve, i.e. Figure 4 For what is obtained in the third step, when d j wavenumber k at 5mm j curve.

[0067] Step 4: Based on the length of each discrete propagation path element and the corresponding frequency-wavenumber curve, calculate the equivalent dispersion information of the Lamb wave. The calculation method is as follows:

[0068]

[0069] In the formula: N is the number of discrete units when discretizing the Lamb wave propagation path in the second step, and Δx j Let be the length of the j-th discrete propagation path unit along the propagation path direction. For the equivalent dispersion information of the Lamb wave, d j This represents the plate thickness corresponding to the j-th discrete propagation path unit.

[0070] Step 5: Based on the equivalent dispersion information of the excitation signal and the Lamb wave, calculate the response prediction signal waveform. The calculation method is as follows:

[0071]

[0072] In the formula: IFFT is the inverse fast Fourier transform function, FFT is the fast Fourier transform function, s(t) is the time-domain excitation signal, e is the natural constant, and i is the imaginary unit. The equivalent dispersion information calculated in step (S4) is y(t), which is the time-domain Lamb wave response prediction signal, where t is time, and * is the multiplication operator.

[0073] The response prediction signal can lay the foundation for damage detection in variable thickness plates based on Lamb waves.

[0074] Reference Figure 5The figure shows the time-domain waveform of the excitation signal in an embodiment of the present invention. In this embodiment, the excitation signal s(t) is a sinusoidal pulse signal with a center frequency of 100kHz and a cycle number of 5, modulated by a Hanning window. The wavelength of the Lamb wave in the A0 mode corresponding to this excitation signal is 13mm.

[0075] Reference Figure 6 The figure shows a Lamb wave prediction signal waveform in A0 mode provided by an embodiment of the present invention. The predicted signal waveform obtained in the figure has undergone amplitude normalization processing. The propagation distance corresponding to the predicted signal is 1500 mm, and the corresponding Lamb wave mode is A0 mode. The excitation source is at the leftmost end of the variable thickness plate, and the response receiving point of the predicted response signal is at the upper surface of the rightmost end of the variable thickness plate. As can be seen from the figure, the wave packet dispersion phenomenon caused by the dispersion effect after the Lamb wave propagates can be observed in this signal. Comparing this predicted signal with the response signal obtained by traditional finite element simulation, the Pearson correlation coefficient between the two is 99.98%, proving that the signal predicted by the present invention has a strong correlation with the response signal obtained by traditional finite element simulation, thus proving the correctness of the predicted signal of the present invention.

[0076] In one embodiment of the method, in the second step, the length of the discrete propagation path unit is no greater than 1 / 20 of the target mode Lamb wave wavelength under the corresponding point plate thickness, to ensure sufficient prediction accuracy. The smaller the discrete propagation path unit length, the higher the accuracy, but the computational load will also increase accordingly. To balance prediction accuracy and computational load, Δx is taken in this embodiment. j =0.5mm. Because the Lamb wave propagation path length set in this embodiment is 1500mm, and the propagation path length is equal to NΔx j At this point, in the corresponding fourth step, the number of discrete units N = 3000.

[0077] In one embodiment of the method, the specific calculation method for the interpolation calculation in the third step is as follows:

[0078] k j =interp1(fd, k0, f*d) j ),

[0079] In the formula: interp1 represents the one-dimensional interpolation function, fd and k0 are a series of discrete points on the frequency-thickness product-wavenumber curve described in step (S1), f is the frequency, and d j Let k represent the plate thickness corresponding to the j-th discrete propagation path element. j The wavenumber is obtained by interpolation using a one-dimensional interpolation function.

[0080] In one embodiment of the method, the one-dimensional interpolation function is a one-dimensional cubic spline interpolation function.

[0081] In the description of this specification, the references to terms such as "one embodiment / mode," "some embodiments / modes," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment / mode or example is included in at least one embodiment / mode or example of this application. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment / mode or example. Moreover, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments / modes or examples. Furthermore, without contradiction, those skilled in the art can combine and integrate the different embodiments / modes or examples described in this specification, as well as the features of different embodiments / modes or examples.

[0082] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one of that feature. In the description of this application, "multiple" means at least two, such as two, three, etc., unless otherwise explicitly specified.

[0083] Those skilled in the art should understand that the above embodiments are merely for illustrating the present invention and are not intended to limit the scope of the invention. Those skilled in the art can make other changes or modifications based on the above disclosure, and these changes or modifications still fall within the scope of the present invention.

Claims

1. A method for predicting the Lamb wave response signal waveform in a plate with variable thickness, characterized in that, The method includes the following steps: Step 1 (S1): Obtain the dispersion curve of the Lamb wave in a plate of uniform thickness that has the same material parameters as the target variable thickness plate; The second step (S2) is to discretize the Lamb wave propagation path and obtain the length of each discrete propagation path element and the corresponding plate thickness. The third step (S3): Using the dispersion curve of the Lamb wave in a plate of uniform thickness as a reference, calculate the frequency-wavenumber curve of the Lamb wave under the plate thickness corresponding to the length of each discrete propagation path element. Step 4 (S4): Calculate the equivalent dispersion information of the Lamb wave based on the length of each discrete propagation path unit and the corresponding frequency-wavenumber curve; Step 5 (S5): Calculate the response prediction signal waveform based on the equivalent dispersion information of the excitation signal and the Lamb wave.

2. The method according to claim 1, characterized in that, Preferably, in the first step (S1), the dispersion curve of the Lamb wave in the plate of uniform thickness is: the frequency-thickness product-wavenumber curve of the Lamb wave in the plate of uniform thickness with the same density, elastic modulus, and Poisson's ratio parameters as the corresponding parameters in the target plate of variable thickness. The frequency-thickness product-wavenumber curve includes discrete points (fd, k0), where fd is the frequency-thickness product and k0 is the real part of the wavenumber.

3. The method according to claim 1, characterized in that, In the second step (S2), the length of the discrete propagation path unit is no greater than 1 / 20 of the target mode Lamb wave wavelength under the corresponding plate thickness.

4. The method according to claim 2, characterized in that, In the third step (S3), the formula for calculating the wave number is: k j =interp1(fd, k0, f*d) j ).

5. The method according to claim 4, characterized in that, The one-dimensional interpolation function includes a one-dimensional cubic spline interpolation function.

6. The method according to claim 1, characterized in that, In the fourth step (S4), the formula for calculating the equivalent dispersion information of the Lamb wave is as follows:

7. The method for predicting the Lamb wave response signal waveform in a variable thickness plate according to claim 6, characterized in that, In step five (S5), the formula for calculating the response prediction signal waveform is:

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