Nonlinear lamb wave excitation migration evaluation method and system under dispersion constraint

Abstract

The application discloses a nonlinear Lamb wave excitation deviation evaluation method and system under dispersion constraint, belongs to the technical field of ultrasonic nondestructive testing and structural health monitoring, and is based on a Rayleigh-Lamb frequency equation and a second-order perturbation theory to construct a second harmonic displacement field model, divides a phase velocity matching mode pair into an intersection type, a longitudinal wave type and a cutoff type; the contraction law of a propagation distance and a mode order on an excitation window is quantitatively analyzed, an excitation tolerance coefficient and a relative gain coefficient are introduced, a two-dimensional quantitative evaluation system of mode pairs is established, three typical mode pairs are divided and are adapted to different detection working conditions, and an aluminum alloy sheet experiment is completed to verify the application. The application adopts the above-mentioned nonlinear Lamb wave excitation deviation evaluation method under dispersion constraint, establishes a standardized mode evaluation system, and significantly improves detection sensitivity and engineering reliability.

Description

Technical Field

[0001] This invention belongs to the field of ultrasonic nondestructive testing and structural health monitoring technology, specifically relating to a method and system for evaluating nonlinear Lamb wave excitation migration under dispersion constraints. Background Technology

[0002] In the aerospace and rail transportation fields, thin metal sheet structures are widely used. These components, subjected to long-term alternating loads, are prone to early microscopic fatigue damage, including dislocation multiplication and microvoid initiation. Such early damage cannot be effectively identified by traditional linear ultrasonic testing methods. Nonlinear Lamb waves possess high detection sensitivity to the evolution of material microstructures, making them a core technology for nondestructive testing of early fatigue damage in thin sheets. However, the inherent dispersion characteristics of Lamb waves alter the phase velocity matching relationship between the fundamental and second harmonic waves, causing distortion in the excitation interval and a decrease in the accumulation efficiency of the second harmonic, severely limiting the reliability and stability of nonlinear Lamb wave detection.

[0003] However, existing nonlinear Lamb wave detection techniques rely solely on empirical selection of mode pairs using dispersion curves or on signal processing methods to compensate for waveform distortion caused by dispersion, resulting in numerous technical shortcomings: they fail to systematically reveal the shrinkage law of the excitation window with propagation distance under dispersion constraints, and cannot quantify the impact of propagation distance, mode type, and order on the size of the excitation window; they only focus on the harmonic response at the strictly phase velocity matching point, failing to discover the shift characteristics of the peak excitation efficiency, and the setting of excitation frequency parameters is entirely based on experience; they do not distinguish the differences in dispersion response between longitudinal wave and intersection mode pairs, and lack quantitative comparison of the excitation efficiency and frequency tolerance of the two types of modes; they lack a quantitative evaluation system that takes into account both excitation parameter tolerance and nonlinear signal gain, and there is no unified standard for mode pair selection, making it difficult to adapt to different detection distance and accuracy requirements.

[0004] Therefore, a new method is urgently needed. Summary of the Invention

[0005] The purpose of this invention is to provide a method and system for evaluating nonlinear Lamb wave excitation migration under dispersion constraints. This method establishes a standardized model evaluation system, which significantly improves detection sensitivity and engineering reliability.

[0006] To achieve the above objectives, this invention provides a method for evaluating nonlinear Lamb wave excitation migration under dispersion constraints, comprising the following steps: S1. Based on the Rayleigh-Lamb frequency equation and second-order perturbation theory, and combined with the boundary condition that the stress on the upper and lower surfaces of the thin plate is zero, a nonlinear Lamb wave second harmonic displacement field model for the thin plate is established. Define the minimum normalized accumulation distance of the second harmonic, clarify the relationship between the accumulation distance and the frequency-thickness product and the degree of dispersion, assign acoustic and mechanical parameters of the plate, and output displacement field model parameters and material acoustic parameters. S2 receives the material acoustic parameters output by S1, plots the Lamb wave phase velocity dispersion curve, and classifies the phase velocity matching mode pairs into three categories: intersection type, longitudinal wave type, and cutoff type according to the phase velocity matching criterion between the fundamental wave and the second harmonic Lamb wave. It then selects typical mode pairs that can be used in the project, solidifies the classification labels, and outputs the three types of mode pair datasets. S3 receives the minimum normalized accumulation distance parameter output by S1 and the three-mode pair dataset output by S2. With the effective accumulation of the second harmonic as a constraint, an efficiency amplitude threshold is set to define the high-efficiency excitation window. The width, height and overlap area of ​​the excitation window under different propagation distances and different mode orders are quantitatively calculated. The shrinkage law of the excitation window with the normalized accumulation distance is analyzed, and the window feature data is output. S4. Receive the second harmonic displacement field model parameters output by S1 and the three-mode pair dataset output by S2, solve the second harmonic surface displacement amplitude at each frequency point, and obtain the second harmonic excitation efficiency distribution characteristics. Define frequency offset, quantify the high-frequency offset characteristics of the peak excitation efficiency relative to the strictly phase velocity matching point, analyze the influence of mode order on frequency offset and extreme amplitude, and output peak amplitude, frequency offset and efficiency curve dataset. S5. Receive the window feature data output by S3, the efficiency curve and feature dataset output by S4, introduce the excitation tolerance coefficient and the relative gain coefficient, and construct a two-dimensional quantitative evaluation coordinate system with two coefficients. Based on the window overlap area, the excitation tolerance coefficient is defined, and based on the extreme value amplitude normalization, the relative gain coefficient is defined. Typical pattern pairs are clustered into three categories: broadband tolerance-dominated, high-sensitivity gain-dominated, and high-order restricted. The normalized evaluation coefficient and the pattern pair classification results are output. S6 receives the pattern pair clustering classification results output by S5, and selects the appropriate Lamb wave pattern pair and excitation parameters based on the actual detection distance and detection accuracy requirements; builds a nonlinear Lamb wave ultrasonic detection experimental platform, collects ultrasonic signals and calculates the relative nonlinear coefficients, and completes the verification and engineering detection parameter adaptation.

[0007] Preferably, in S1, considering the zero boundary condition of the stress on the upper and lower surfaces of the thin plate, the nonlinear dynamic control equations are established: ; In the formula, For the density of the medium in the board, For the time of dissemination, Let be the displacement vector of the particle. These are the second-order elastic constants of the material. For the Laplacian gradient operator, It is a second-order driving force that penetrates the body. A nonlinear Lamb wave second harmonic displacement field model for a thin plate is established, specifically as follows: ; ; ; In the formula, This represents the actual second harmonic displacement field. It is a dispersion correction factor. For the second harmonic reference displacement solution under strict phase velocity matching, The phase mismatch factor, For the fundamental frequency Lamb wave number, For the distance the sound wave travels, This represents the difference in phase velocity between the fundamental wave and the second harmonic. For the base frequency Lower Lamb wave phase velocity, It is twice the harmonic frequency. Lower Lamb wave phase velocity; The minimum normalized accumulation distance of the second harmonic is expressed as: ; In the formula, To accumulate distance for minimum normalization, The thickness is half of the plate thickness.

[0008] Preferably, in S2, the phase velocity matching criterion satisfies: ; In the formula, The phase velocity of the fundamental frequency Lamb wave. The phase velocity of the Lamb wave is twice the harmonic frequency. Six typical engineering mode pairs were selected, including longitudinal wave types S1 / S2, S2 / S4, and S3 / S6, and intersection types A2 / S2, A2 / S4, and S3 / S6; the frequency-thickness scanning range was set to 0~10MHz·mm, the excitation frequency range was 2.25~4.25MHz and 6.75~7.75MHz, and the wedge excitation angle was fixed at 26°.

[0009] Preferably, in S3, 50% of the peak value of the second harmonic efficiency is used as the threshold to define the boundary of the high-efficiency window; the frequency window width calculation step is 0.01MHz, and the phase velocity calculation step is 0.01km / s.

[0010] Preferably, in S4, the frequency offset satisfies: ; In the formula, This is the frequency offset. The frequency corresponding to the peak efficiency. The theoretical frequency of the strictly phase velocity matching point; Set the frequency scan step size to 0.01MHz.

[0011] Preferably, in S5, the area of ​​the overlapping region between the excitation window and the 50% high-efficiency window is utilized. Define the excitation tolerance coefficient ; The normalized relative gain coefficient satisfies: ; In the formula, This is the normalized relative gain coefficient. For the extreme amplitude of the second harmonic efficiency in a single mode, The maximum extreme amplitude among all contrast mode pairs; The normalization interval of the evaluation coefficient is limited to [0,1], and the mean of the normalized cumulative distances of 50mm, 100mm, 150mm and 200mm is selected as the evaluation benchmark.

[0012] Preferably, in step S6, the ultrasound signal is acquired and the relative nonlinearity coefficient is calculated. The formula for calculating the relative nonlinearity coefficient is as follows: ; In the formula, These are the relative nonlinear coefficients. The amplitude of the second harmonic signal. The amplitude of the fundamental frequency Lamb wave signal; The testing platform is based on the Ritec-5000 instrument, with a system sampling frequency of 100MHz and 2048 Fourier transform sampling points. Each group of experiments is repeated 3 times and the average value is taken.

[0013] This invention also provides a nonlinear Lamb wave excitation migration evaluation system under dispersion constraints, comprising: The model building parameter assignment module is used to execute S1 to complete the modeling of the nonlinear Lamb wave second harmonic displacement field, the definition of the accumulated distance, and the assignment of mechanical and acoustic parameters of the plate. The pattern pair classification and calibration module is connected to the model construction parameter assignment module. It is used to execute S2, draw dispersion curves, classify three types of pattern pairs according to the phase velocity matching criterion, and select typical engineering pattern pairs. The excitation window pattern analysis module is connected to the mode pair classification and calibration module. It is used to execute S3, quantify the excitation window size under different propagation distances and mode orders, analyze the window contraction pattern, and output window feature data. The efficiency offset feature extraction module is connected to the excitation window regularity analysis module and is used to execute S4 to solve the second harmonic amplitude, calculate the frequency offset, and extract the excitation efficiency distribution and peak offset features. The two-dimensional quantitative evaluation clustering module is connected to the efficiency offset feature extraction module. It is used to execute S5, calculate the excitation tolerance coefficient and the relative gain coefficient, construct a two-dimensional evaluation system, and complete the pattern pair clustering. The parameter optimization experimental verification module is connected to the two-dimensional quantitative evaluation clustering module and is used to execute S6. Based on the clustering results, the mode pair and excitation parameters are optimized, and a detection platform is built to complete signal acquisition, nonlinear coefficient calculation and engineering verification.

[0014] Therefore, the present invention employs the above-mentioned nonlinear Lamb wave excitation migration evaluation method and system under dispersion constraints. Compared with the prior art, the technical solution of the present invention has the following beneficial effects: (1) By adopting the technical means of constructing a second harmonic displacement field model based on the Rayleigh-Lamb frequency equation and second-order perturbation theory and classifying the phase velocity matching mode pairs into three categories, the technical problems of existing technologies having no systematic mode classification and being unable to distinguish the differences in dispersion response are overcome, and the dispersion characteristics of different Lamb wave modes are accurately defined. (2) By adopting the technical means of quantitative analysis of the window contraction law, quantification of efficiency peak shift characteristics and introduction of dual coefficients to construct a two-dimensional quantitative evaluation system, the technical problems of traditional modality selection relying on experience and lacking unified quantitative evaluation standards are overcome, and a standardized model is established for the evaluation and clustering system. (3) By adopting the technical means of combining the optimal mode of propagation distance and accuracy requirements and experimental verification of aluminum alloy thin plates, the technical problems of Lamb wave dispersion causing excitation interval distortion, low second harmonic accumulation efficiency and poor detection reliability are overcome, and the sensitivity and engineering applicability of early fatigue damage detection of metal thin plates are significantly improved.

[0015] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0016] Figure 1 This is a schematic diagram of the nonlinear Lamb wave ultrasonic detection experimental system, representing an embodiment of the nonlinear Lamb wave excitation migration evaluation method under dispersion constraints of the present invention. Figure 2 This is a Lamb wave phase velocity dispersion curve diagram of an embodiment of the nonlinear Lamb wave excitation migration evaluation method under dispersion constraints of the present invention; Figure 3 This is a partially enlarged view of the Lamb wave phase velocity dispersion curve in an embodiment of the nonlinear Lamb wave excitation migration evaluation method under dispersion constraints of the present invention. Figure 4 This is a quantitative simulation analysis diagram showing the variation of the nonlinear Lamb wave excitation window characteristics with the minimum accumulation distance in an embodiment of the nonlinear Lamb wave excitation migration evaluation method under dispersion constraints of the present invention. Figure 4 (a) represents the change in excitation window width as a function of accumulation distance. Figure 4 (b) shows the change in excitation window height as a function of accumulation distance; Figure 5 This is a simulation comparison of the nonlinear Lamb wave second harmonic excitation efficiency versus excitation frequency in an embodiment of the nonlinear Lamb wave excitation migration evaluation method under dispersion constraints of the present invention. Figure 5 (a) represents the frequency response of the longitudinal wave mode. Figure 5 (b) represents the frequency response of the intersection mode; Figure 6 This is a comparison of the frequency response of different Lamb wave modes to the second harmonic excitation efficiency at different propagation distances, according to an embodiment of the nonlinear Lamb wave excitation migration evaluation method under dispersion constraints of the present invention. Figure 6 (a) indicates the P-wave mode for short propagation distance conditions. Figure 6 (b) indicates the same P-wave mode for long propagation distance conditions. Figure 6 (c) indicates that the intersection-type mode is suitable for short propagation distance conditions. Figure 6 (d) indicates that the same intersection-type mode is used for long propagation distance conditions; Figure 7 This is a scatter plot of two-dimensional quantitative evaluation of nonlinear Lamb wave modes in an embodiment of the nonlinear Lamb wave excitation migration evaluation method under dispersion constraints of the present invention. Figure 8 This is a comparison of the variation of the second harmonic amplitude of the nonlinear Lamb wave with propagation distance under different damage levels in an embodiment of the nonlinear Lamb wave excitation migration evaluation method under dispersion constraints of the present invention. Figure 9 This is a comparative schematic diagram showing the change of nonlinear Lamb wave second harmonic excitation efficiency with excitation frequency in an embodiment of the nonlinear Lamb wave excitation migration evaluation method under dispersion constraints of the present invention. Figure 10 This is a simulation comparison of the frequency response of the nonlinear Lamb wave second harmonic excitation efficiency in an embodiment of the nonlinear Lamb wave excitation migration evaluation method under dispersion constraints of the present invention. Figure 10 (a) represents the frequency response of different order mode pairs of the longitudinal wave type. Figure 10 (b) represents the frequency response of different order mode pairs in the intersection type. Figure 10 (c) represents the frequency response of the same P-wave mode at different propagation distances. Figure 10 (d) represents the frequency response of the same intersection-type mode to different propagation distances. Detailed Implementation

[0017] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. All other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention. Unless otherwise defined, the technical or scientific terms used in the present invention should have the ordinary meaning understood by those skilled in the art.

[0018] Example 1 like Figure 1 As shown, this embodiment provides a nonlinear Lamb wave excitation migration evaluation method system under dispersion constraints. It should be understood that the specific parameters, models and protocols mentioned in this embodiment are only examples to help those skilled in the art understand the present invention, and are not intended to limit the present invention.

[0019] The nonlinear Lamb wave excitation migration evaluation method system under dispersion constraints of the present invention includes the following steps: S1. Based on the Rayleigh-Lamb frequency equation and second-order perturbation theory, a displacement field model of the second harmonic of nonlinear Lamb wave in thin plate is established. The minimum normalized accumulation distance of the second harmonic is defined, and the correlation between the accumulation distance and the frequency-thickness product and the degree of dispersion is clarified. The displacement field model parameters and material acoustic parameters are output, providing basic model and material parameter support for downstream steps S2, S3 and S4.

[0020] In this step, based on the Rayleigh-Lamb frequency equation and second-order perturbation theory, the stress on the upper and lower surfaces of the thin plate is introduced as a zero boundary condition, and a nonlinear dynamic control equation is adopted, which is expressed as: ; In the formula, For the density of the medium in the board, For the time of dissemination, Let be the displacement vector of the particle. These are the second-order elastic constants of the material. For the Laplacian gradient operator, It is a second-order driving force.

[0021] Based on this, a second harmonic displacement field model is constructed to distinguish between two types of working conditions: strict phase velocity matching and approximate phase velocity matching. The model is expressed as follows: ; ; ; In the formula, This represents the actual second harmonic displacement field. It is a dispersion correction factor. For the second harmonic reference displacement solution under strict phase velocity matching, The phase mismatch factor, For the fundamental frequency Lamb wave number, For the distance the sound wave travels, This represents the difference in phase velocity between the fundamental wave and the second harmonic. For the base frequency Lower Lamb wave phase velocity, It is twice the harmonic frequency. Lower Lamb wave phase velocity.

[0022] At the same time, the minimum accumulation distance calculation formula is used, which is expressed as: ; In the formula, To accumulate distance for minimum normalization, The thickness is half of the plate thickness.

[0023] The acoustic and mechanical parameters of the 6061 aluminum alloy sheet have been assigned. The preset parameters in this embodiment are as follows: Longitudinal wave speed transverse wave speed of sound Second-order elastic constant , The board thickness is selected as 1mm or 2mm, and the normalized cumulative distance is calculated. The parameters are set to 50, 100, 150, 200, and 500. The simulation modeling is initialized only once, and the parameters are fixed throughout the process without being refreshed. This provides a unified theoretical basis and material parameter support for subsequent mode division, excitation window calculation, and excitation efficiency solution.

[0024] S2. Receive the material acoustic parameters output by S1, complete the identification of Lamb wave matching points and the classification and calibration of three types of mode pairs according to the phase velocity matching rules, divide the matching mode pairs on the dispersion curve into three types: intersection type, longitudinal wave type and cutoff type, output the three types of mode pair datasets, and synchronously transmit them to the downstream steps S3, S4 and S5.

[0025] In this step, the phase velocity dispersion curve of the aluminum plate is plotted, following the matching criterion between the fundamental and second harmonic phase velocities, as shown below: ; In the formula, The phase velocity of the fundamental frequency Lamb wave. It is the phase velocity of the Lamb wave at twice the harmonic frequency.

[0026] Based on this formula, matching points are classified into intersection type, longitudinal wave type, and cutoff type, and six typical mode pairs suitable for engineering applications are selected: S1 / S2, S2 / S4, S3 / S6, A2 / S2, A2 / S4, and S3 / S6. Here, S represents a symmetrical Lamb wave mode, and A represents an antisymmetric Lamb wave mode. The naming rule for mode pairs is fundamental frequency mode / second harmonic mode. The six mode pairs are further classified according to dispersion characteristics: longitudinal wave type: S1 / S2, S2 / S4, S3 / S6; intersection type: A2 / S2, A2 / S4, S3 / S6. These six mode pairs exhibit high phase velocity matching accuracy, smooth dispersion curve changes, ease of ultrasonic transducer excitation, and significant second harmonic distance accumulation effect, making them suitable for engineering scenarios involving early fatigue damage detection of thin aluminum alloy plates.

[0027] The curing parameters for this step are set as follows: Frequency-thickness scanning range 0~10 The excitation frequency range is 2.25~4.25MHz and 6.75~7.75MHz, and the wedge excitation angle is fixed at 26°. The dispersion curve plotting and mode classification are performed only once, and the mode pair labels are permanently fixed, which can distinguish the dispersion characteristics of different mode pairs and establish a classification basis for subsequent differential analysis of excitation window and excitation efficiency.

[0028] S3 receives the minimum normalized accumulation distance parameter output by S1 and the three-mode pair dataset output by S2; with the effective accumulation of the second harmonic as a constraint, an efficiency amplitude threshold is set to define the high-efficiency excitation window, and the width, height and overlap area of ​​the excitation window under different propagation distances and different mode orders are quantitatively calculated. The shrinkage law of the excitation window with the normalized accumulation distance is analyzed, and the window feature data is output.

[0029] In this step, the effective accumulation of the second harmonic is used as a constraint. Following the S1 minimum accumulation distance formula, the effective range of frequency-phase velocity values ​​under different normalized accumulation distances is calculated. The high-efficiency window range is defined by using the efficiency peak value of 50% as a threshold, and the area of ​​the overlapping region between the excitation window and the high-efficiency window is solved.

[0030] The following operating parameters are used in this embodiment: The high-efficiency window uses 50% of the peak amplitude as the boundary threshold, with a frequency window width calculation step size of 0.01MHz and a phase velocity calculation step size of 0.01MHz. It automatically iterates and calculates the accumulated distance for each level, and updates the operating parameters synchronously. It can quantify the influence of propagation distance, mode order, and mode type on the excitation window, and provide the original basic data for subsequent excitation tolerance coefficient calculation.

[0031] S4 receives the second harmonic displacement field model parameters output by S1 and the three-mode pair dataset output by S2, calculates the second harmonic surface displacement amplitude, obtains the excitation efficiency distribution characteristics, quantifies the high-frequency offset characteristics of the peak excitation efficiency relative to the strictly matched point, analyzes the influence of mode order on offset and extreme amplitude, and outputs the peak amplitude, frequency offset and efficiency curve dataset to S5.

[0032] In this step, the second harmonic surface displacement amplitude is calculated point by point at each frequency. Following the S1 second harmonic displacement field calculation formula, the coordinates of the efficiency extremum points are extracted, and the frequency offset expression is defined: ; In the formula, This is the frequency offset. The frequency corresponding to the peak efficiency. The theoretical frequency of the strict phase velocity matching point.

[0033] The following calculation control parameters are preset in this embodiment: The frequency scanning step size is 0.01MHz, and the measured propagation distance is set to 100mm, 150mm, and 200mm. Continuous scanning is performed across the entire frequency range, and the amplitude characteristic data is refreshed in real time. This can clearly identify the rightward shift of the efficiency peak and the amplitude differences between different modes, providing core characteristic parameters for modeling the relative gain coefficient.

[0034] S5 receives the window feature data output by S3, the efficiency curve and feature dataset output by S4, introduces the excitation tolerance coefficient and relative gain coefficient, constructs a two-dimensional quantitative evaluation system for mode pairs, and classifies typical mode pairs into three categories: broadband tolerance-dominated, high-sensitivity gain-dominated, and high-order restricted.

[0035] In this step, a dual-coefficient evaluation model of excitation tolerance and relative gain is constructed based on window features and peak amplitude to complete pattern pair clustering classification. The normalized evaluation coefficients and pattern pair classification results output in this step are directly passed to S6.

[0036] The excitation tolerance coefficient is defined by the overlap area between the excitation window and the high-efficiency window. In the formula To determine the area of ​​overlap between the excitation window and the 50% high-efficiency window; based on the peak amplitude ratio of each mode, the normalized relative gain coefficient satisfies: ; In the formula, This is the normalized relative gain coefficient. For the extreme amplitude of the second harmonic efficiency in a single mode, This represents the maximum extreme amplitude among all contrast mode pairs.

[0037] By constructing a two-dimensional evaluation coordinate system with two coefficients, the six typical patterns are clustered into three categories: broadband tolerance-dominated, high-sensitivity gain-dominated, and high-order restricted.

[0038] The simulation and experimental parameters are configured as follows in this embodiment: The normalization interval for the evaluation coefficients is limited to [0,1]. The average of four feature distances (50, 100, 150, and 200) is used as the evaluation benchmark. The average of multiple distances is calculated at once, and the classification result is output in a fixed manner. This establishes a quantitative evaluation standard that takes into account both parameter tolerance and signal gain, enabling precise optimization of Lamb wave mode pairs and excitation parameters under different detection conditions.

[0039] S6 receives the pattern pair clustering classification results output by S5, and based on the pattern pair clustering classification results, combined with the detection distance and accuracy requirements, selects the best matching Lamb wave pattern pair and excitation parameters for nonlinear ultrasonic detection of early fatigue damage in thin metal plates.

[0040] In this step, a nonlinear Lamb wave ultrasonic testing system is built, signals are collected, the relative nonlinear coefficient is calculated, and verification and engineering parameter adaptation and optimization are completed. The experimental nonlinear coefficient, optimal excitation frequency and detection distance output in this step can be directly used as engineering testing application parameters.

[0041] A detection platform was built using the Ritec-5000 instrument as the core, collecting time-domain signals of different propagation distances and mode pairs. Spectral analysis was performed using Fast Fourier Transform to extract the fundamental frequency and second harmonic amplitude. The formula for calculating the relative nonlinear coefficients is expressed as follows: ; In the formula, These are the relative nonlinear coefficients. The amplitude of the second harmonic signal. This represents the amplitude of the fundamental frequency Lamb wave signal.

[0042] The material damage state is quantitatively assessed based on this formula, and the theoretical law is verified by comparing the simulation results.

[0043] This embodiment sets the following baseline constraint parameters: The transducer wedge angle is fixed at 26°, the system sampling frequency is 100MHz, and the number of Fourier transform sampling points is 2048. Each group of experiments is repeated 3 times and the average value is taken to update the data. This can fully verify the correctness of the theory and simulation law, and output the excitation frequency, detection distance, and mode pair optimization scheme that can be directly implemented, supporting the engineering detection application of early fatigue damage of thin plates.

[0044] The selected mode pairs for the experiment included longitudinal wave types S1 / S2 and S2 / S4, and intersection types A2 / S4 and S2 / S4. The strict phase velocity matching points for each mode pair were as follows: S1 / S2 mode pair matching point 3.564 MHz·mm, phase velocity 6297 m / s; S2 / S4 mode pair matching point 7.117 MHz·mm, phase velocity 6302 m / s.

[0045] Unified curing experiment configuration parameters: the transducer wedge excitation angle was fixed at 26°, the system sampling frequency was 100MHz, and the number of fast Fourier transform sampling points was 2048; multiple sets of transducer propagation spacings were set at 100mm, 150mm, and 200mm to cover different detection distance conditions. Utilizing the frequency-thickness product multiple matching characteristic, the 1mm plate S1 / S2 mode pair and the 2mm plate S2 / S4 mode pair used the same excitation frequency of 3.56MHz, achieving single-set transducer compatibility for multi-mode pair testing. Aluminum plate parameters are shown in Table 1.

[0046] Table 1 Aluminum Plate Parameter Table

[0047] in, Let be the propagation velocity of the longitudinal wave in the material. Let be the propagation speed of the transverse wave in the material. The bulk modulus of the material. Let be the shear modulus of the material, and A, B, and C be the third-order elastic constants.

[0048] like Figures 2-10 As shown in the figure, the experiment shows that as the propagation distance increases from 50 mm to 200 mm, the excitation windows of both the longitudinal wave and intersection mode pairs shrink significantly. The average overlap window and average extreme amplitude at the four characteristic distances (50 mm, 100 mm, 150 mm, and 200 mm) are shown in Table 2. At a propagation distance of 200 mm, the window width of the intersection mode pair is only 0.0624 MHz, while that of the longitudinal wave is 0.1613 MHz. At a distance of 100 mm, the window width of the intersection mode is 0.1067 MHz, and that of the longitudinal wave is 0.2569 MHz. The experiment confirms that the excitation window shrinks significantly with the increase of propagation distance, and at the same distance, the excitation window of the longitudinal wave mode pair is always wider than that of the intersection mode, which is completely consistent with the calculation in this embodiment.

[0049] Table 2. Average Overlap Window and Average Extreme Amplitude

[0050] The extreme points of the nonlinear coefficients of all test mode pairs appeared on the high-frequency side of the theoretically strict phase velocity matching point, verifying the inherent characteristic that the peak excitation efficiency generally shifts to the right; and the frequency shift of the higher-order mode pairs is smaller than that of the lower-order mode pairs. Under the same order conditions, the peak value of the nonlinear coefficient of the intersection-type mode pair is significantly higher than that of the longitudinal wave type, but the high-efficiency frequency range is narrower and more sensitive to the excitation frequency deviation, which is consistent with the shift and amplitude change trend revealed in this embodiment.

[0051] Under the same propagation distance of 150mm, the peak amplitude of the higher-order mode pair is higher than that of the lower-order mode pair, but its excitation window is narrower and its excitation parameter tolerance is lower. The experimental response characteristics of the broadband tolerance type and the high-sensitivity gain type mode pair match the dual-coefficient evaluation classification results established in this technical solution, proving that the constructed evaluation system of excitation tolerance coefficient and relative gain coefficient and the three-type mode pair classification method have engineering applicability.

[0052] The experiment, from multiple dimensions such as excitation window contraction characteristics, efficiency peak shift characteristics, mode pair type and order differences, and quantitative evaluation classification, is highly consistent with the numerical calculation results of this embodiment. This verifies the correctness and engineering practical value of the model, calculation, and mode pair optimization evaluation method of this embodiment. It can provide a reliable experimental basis for mode selection, excitation frequency setting, and detection distance configuration for early fatigue damage detection of nonlinear Lamb wave thin plates.

[0053] Therefore, the present invention adopts the above-mentioned nonlinear Lamb wave excitation migration evaluation method system under dispersion constraint. This method establishes a standardized model evaluation system, which significantly improves detection sensitivity and engineering reliability.

[0054] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0055] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A method for evaluating nonlinear Lamb wave excitation migration under dispersion constraints, characterized in that, Includes the following steps: S1. Based on the Rayleigh-Lamb frequency equation and second-order perturbation theory, and combined with the boundary condition that the stress on the upper and lower surfaces of the thin plate is zero, a nonlinear Lamb wave second harmonic displacement field model for the thin plate is established. Define the minimum normalized accumulation distance of the second harmonic, clarify the relationship between the accumulation distance and the frequency-thickness product and the degree of dispersion, assign acoustic and mechanical parameters of the plate, and output displacement field model parameters and material acoustic parameters. S2 receives the material acoustic parameters output by S1, plots the Lamb wave phase velocity dispersion curve, and classifies the phase velocity matching mode pairs into three categories: intersection type, longitudinal wave type, and cutoff type according to the phase velocity matching criterion between the fundamental wave and the second harmonic Lamb wave. It then selects typical mode pairs that can be used in the project, solidifies the classification labels, and outputs the three types of mode pair datasets. S3 receives the minimum normalized accumulation distance parameter output by S1 and the three-mode pair dataset output by S2. With the effective accumulation of the second harmonic as a constraint, an efficiency amplitude threshold is set to define the high-efficiency excitation window. The width, height and overlap area of ​​the excitation window under different propagation distances and different mode orders are quantitatively calculated. The shrinkage law of the excitation window with the normalized accumulation distance is analyzed, and the window feature data is output. S4. Receive the second harmonic displacement field model parameters output by S1 and the three-mode pair dataset output by S2, solve the second harmonic surface displacement amplitude at each frequency point, and obtain the second harmonic excitation efficiency distribution characteristics. Define frequency offset, quantify the high-frequency offset characteristics of the peak excitation efficiency relative to the strictly phase velocity matching point, analyze the influence of mode order on frequency offset and extreme amplitude, and output peak amplitude, frequency offset and efficiency curve dataset. S5. Receive the window feature data output by S3, the efficiency curve and feature dataset output by S4, introduce the excitation tolerance coefficient and the relative gain coefficient, and construct a two-dimensional quantitative evaluation coordinate system with two coefficients. Based on the window overlap area, the excitation tolerance coefficient is defined, and based on the extreme value amplitude normalization, the relative gain coefficient is defined. Typical pattern pairs are clustered into three categories: broadband tolerance-dominated, high-sensitivity gain-dominated, and high-order restricted. Output normalized evaluation coefficients and pattern pair classification results; S6 receives the pattern pair clustering classification results output by S5, and selects the appropriate Lamb wave pattern pair and excitation parameters based on the actual detection distance and detection accuracy requirements; builds a nonlinear Lamb wave ultrasonic detection experimental platform, collects ultrasonic signals and calculates the relative nonlinear coefficients, and completes the verification and engineering detection parameter adaptation.

2. The nonlinear Lamb wave excitation migration evaluation method under dispersion constraints according to claim 1, characterized in that, In S1, taking into account the zero boundary condition of the stress on the upper and lower surfaces of the thin plate, the nonlinear dynamic control equations are established: ； In the formula, For the density of the medium in the board, For the time of dissemination, Let be the displacement vector of the particle. Let be the second elastic constant of the material. For the Laplacian gradient operator, It is a second-order driving force that penetrates the body. A nonlinear Lamb wave second harmonic displacement field model for a thin plate is established, specifically as follows: ； ； ； In the formula, This represents the actual second harmonic displacement field. It is a dispersion correction factor. For the second harmonic reference displacement solution under strict phase velocity matching, The phase mismatch factor, For the fundamental frequency Lamb wave number, For the distance the sound wave travels, This represents the difference in phase velocity between the fundamental wave and the second harmonic. For the base frequency Lower Lamb wave phase velocity, It is twice the harmonic frequency. Lower Lamb wave phase velocity; The minimum normalized accumulation distance of the second harmonic is expressed as: ； In the formula, To accumulate distance for minimum normalization, The thickness is half of the plate thickness.

3. The nonlinear Lamb wave excitation migration evaluation method under dispersion constraints according to claim 2, characterized in that, In S2, the phase velocity matching criterion satisfies: ； In the formula, The phase velocity of the fundamental frequency Lamb wave. The phase velocity of the Lamb wave is twice the harmonic frequency. Six typical engineering mode pairs were selected, including longitudinal wave types S1 / S2, S2 / S4, and S3 / S6, and intersection types A2 / S2, A2 / S4, and S3 / S6; the frequency-thickness scanning range was set to 0~10MHz·mm, the excitation frequency range was 2.25~4.25MHz and 6.75~7.75MHz, and the wedge excitation angle was fixed at 26°.

4. The nonlinear Lamb wave excitation migration evaluation method under dispersion constraints according to claim 3, characterized in that, In S3, 50% of the peak value of the second harmonic efficiency is used as the threshold to define the boundary of the high-efficiency window; the frequency window width is calculated in step 0.01MHz, and the phase velocity is calculated in step 0.01km / s.

5. The nonlinear Lamb wave excitation migration evaluation method under dispersion constraints according to claim 4, characterized in that, In S4, the frequency offset satisfies: ； In the formula, This is the frequency offset. The frequency corresponding to the peak efficiency. The theoretical frequency of the strictly phase velocity matching point; Set the frequency scan step size to 0.01MHz.

6. The nonlinear Lamb wave excitation migration evaluation method under dispersion constraints according to claim 5, characterized in that, In S5, the overlapping area of ​​the excitation window and the 50% high-efficiency window is utilized. Define the excitation tolerance coefficient ; The normalized relative gain coefficient satisfies: ； In the formula, This is the normalized relative gain coefficient. For the extreme amplitude of the second harmonic efficiency in a single mode, The maximum extreme amplitude among all contrast mode pairs; The normalization interval of the evaluation coefficient is limited to [0,1], and the average of the normalized cumulative distances of 50mm, 100mm, 150mm and 200mm is selected as the evaluation benchmark.

7. The nonlinear Lamb wave excitation migration evaluation method under dispersion constraints according to claim 6, characterized in that, In S6, the ultrasound signal is acquired and the relative nonlinearity coefficient is calculated. The formula for calculating the relative nonlinearity coefficient is as follows: ； In the formula, These are the relative nonlinear coefficients. The amplitude of the second harmonic signal. The amplitude of the fundamental frequency Lamb wave signal; The testing platform is based on the Ritec-5000 instrument, with a system sampling frequency of 100MHz and 2048 Fourier transform sampling points. Each group of experiments is repeated 3 times and the average value is taken.

8. A nonlinear Lamb wave excitation migration evaluation system under dispersion constraints, applied to the nonlinear Lamb wave excitation migration evaluation method under dispersion constraints as described in any one of claims 1-7, characterized in that, include: The model building parameter assignment module is used to execute S1 to complete the modeling of the nonlinear Lamb wave second harmonic displacement field, the definition of the accumulated distance, and the assignment of mechanical and acoustic parameters of the plate. The pattern pair classification and calibration module is connected to the model construction parameter assignment module. It is used to execute S2, draw dispersion curves, classify three types of pattern pairs according to the phase velocity matching criterion, and select typical engineering pattern pairs. The excitation window pattern analysis module is connected to the mode pair classification and calibration module. It is used to execute S3, quantify the excitation window size under different propagation distances and mode orders, analyze the window contraction pattern, and output window feature data. The efficiency offset feature extraction module is connected to the excitation window regularity analysis module and is used to execute S4 to solve the second harmonic amplitude, calculate the frequency offset, and extract the excitation efficiency distribution and peak offset features. The two-dimensional quantitative evaluation clustering module is connected to the efficiency offset feature extraction module. It is used to execute S5, calculate the excitation tolerance coefficient and the relative gain coefficient, construct a two-dimensional evaluation system, and complete the pattern pair clustering. The parameter optimization experimental verification module is connected to the two-dimensional quantitative evaluation clustering module and is used to execute S6. Based on the clustering results, the mode pair and excitation parameters are optimized, and a detection platform is built to complete signal acquisition, nonlinear coefficient calculation and engineering verification.

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