An efficient path search method for dispersion curves

Abstract

The present invention provides an efficient path search method for a dispersion curve, comprising: performing a rough and fast pre-search with a large step size within a solution range of a dispersion equation to obtain a rough solution of each order of dispersion branches; judging the approximate distribution of each order of dispersion branches according to the rough solution, and determining a search direction of a fine search; scaling the range of the rough solution of the dispersion branch according to the determined search direction to obtain the upper and lower limits of a selected point of the dispersion branch; interpolating the upper and lower limits of each point to obtain a band search range containing the dispersion branch; the present invention determines the search upper and lower limits of each order of dispersion branches through a large range and large step size fast pre-search combined with frequency scaling, and obtains a fine band search range through interpolation, which greatly improves the calculation efficiency under the same frequency and wave number calculation range, while realizing dispersion branch separation, and performing separate calculations on specific branches of interest.

Description

Technical Field

[0001] The present invention relates to the field of ultrasonic guided wave technology, and in particular to a dispersion curve efficient path search method. Background Art

[0002] Guided wave dispersion curves are a key tool for understanding and utilizing wave propagation characteristics by studying the changes in wave number or propagation speed at different frequencies. Guided wave dispersion curves are widely used. In the field of non-destructive testing, dispersion curves are used to identify and locate defects inside materials. By observing the dispersion characteristics of ultrasonic waves, cracks, voids and other potential structural problems in materials can be detected. In piezoelectric acoustic devices, dispersion curves can be used to analyze the resonant frequency and modal distribution of the device. Then, the optimal operating mode at different frequencies can be determined, and appropriate materials and geometric parameters can be selected to achieve the desired acoustic characteristics.

[0003] As the complexity of materials increases, such as composite materials with dozens or even hundreds of layers, and piezoelectric acoustic devices involving complex electromechanical coupling effects, the calculation of dispersion curves becomes more time-consuming. As the material becomes more complex, the various branches of the dispersion curve also increase, and the dispersion modes that need to be processed become more diverse. In order to obtain satisfactory results, calculating dispersion curves usually requires a lot of time and computing resources. In addition, in practical applications, people are often only interested in a single dispersion branch or a few dispersion branches, and there is no need to calculate all dispersion branch results within the overall frequency and wavenumber range. Traditional search methods cannot calculate specific dispersion branches within a certain range, and can only calculate all results at the same time, which is also the reason for low computational efficiency. Summary of the invention

[0004] In order to solve the technical problems existing in the above-mentioned background technology, the present invention provides an efficient path search method for dispersion curves.

[0005] The present invention provides a dispersion curve efficient path search method, comprising the following steps:

[0006] Step S1, within the solution range, the dispersion equation performs a rough and fast pre-search with a large step length to obtain a rough solution of each order dispersion branch;

[0007] Step S2: judging the approximate distribution of each order dispersion branch according to the rough solution, and determining the search direction of the fine search;

[0008] Step S3, scaling the rough solution of the dispersion branch according to the determined search direction to obtain the upper limit and lower limit of the selected point of the dispersion branch;

[0009] Step S4, interpolating the upper and lower limits of each point to obtain a band search range including the dispersion branch;

[0010] Step S5: Perform fine search with small step length within each order of band search range to achieve independent calculation of a single dispersion branch and obtain the final dispersion curve.

[0011] Furthermore, in step S1, it specifically includes:

[0012] For the dispersion equation to be calculated, f(ω,k)=0; wherein ω represents the frequency and k represents the wave number;

[0013] In the solution range [ω a ,ω b ]×[k a ,k b ], a rough fast pre-search is performed with a large step size;

[0014] Among them, the large frequency step is one tenth of the entire frequency range, that is, (ω b -ω a ) / 10; the wave number step size is one tenth of the entire wave number range, that is, (k b -k a ) / 10;

[0015] A rough solution of the dispersion curve ω-k is obtained.

[0016] Furthermore, in step S2, the search direction is determined to be the frequency axis direction, and the frequency range of the rough solution of the dispersion branch is scaled to obtain the upper and lower limits of the frequency of the selected point of the dispersion branch; the upper and lower limits of the frequency of each point are interpolated to obtain a band search range including the dispersion branch.

[0017] Furthermore, in step S2, the search direction is determined to be the wavenumber axis direction, and the wavenumber range of the rough solution of the dispersion branch is scaled to obtain the upper and lower limits of the wavenumbers of the selected points of the dispersion branch; the upper and lower limits of the frequency of each point are interpolated to obtain a band search range including the dispersion branch.

[0018] Furthermore, the large step length is 5% to 15% of the entire range, and the small step length is 0.5% to 15% of the entire range.

[0019] The beneficial effects of the present invention are:

[0020] The present invention provides an efficient path search method for dispersion curves. Through large-range and large-step fast pre-search, combined with frequency scaling, the upper and lower limits of each order dispersion branch search are determined, and a fine band search range is obtained by interpolation. Under the same frequency and wave number calculation range, the calculation efficiency is greatly improved, and the dispersion branch separation is realized at the same time, and specific branches of interest are calculated separately. BRIEF DESCRIPTION OF THE DRAWINGS

[0021] Figure 1 This is a rough dispersion curve diagram of an embodiment of the present invention;

[0022] Figure 2 Schematic diagram of searching for dispersion curves along the wave number direction;

[0023] Figure 3 A schematic diagram of searching for dispersion curves along the frequency direction;

[0024] Figure 4 This is a strip search range diagram according to an embodiment of the present invention;

[0025] Figure 5 This is a second-order dispersion branch diagram of an embodiment of the present invention;

[0026] Figure 6 This is a dispersion curve result diagram of an embodiment of the present invention. DETAILED DESCRIPTION

[0027] The following is a description of exemplary embodiments of the present disclosure in conjunction with the accompanying drawings, including various details of the embodiments of the present disclosure to facilitate understanding, which should be considered as merely exemplary. Therefore, it should be recognized by those of ordinary skill in the art that various changes and modifications may be made to the embodiments described herein without departing from the scope and spirit of the present disclosure. Similarly, for the sake of clarity and conciseness, descriptions of well-known functions and structures are omitted in the following description.

[0028] The present invention discloses a dispersion curve efficient path search method, comprising the following steps:

[0029] Step S1, within the solution range, the dispersion equation performs a rough and fast pre-search with a large step length to obtain a rough solution of each order dispersion branch;

[0030] Step S2: judging the approximate distribution of each order dispersion branch according to the rough solution, and determining the search direction of the fine search;

[0031] Step S3, scaling the rough solution of the dispersion branch according to the determined search direction to obtain the upper limit and lower limit of the selected point of the dispersion branch;

[0032] Step S4, interpolating the upper and lower limits of each point to obtain a band search range including the dispersion branch;

[0033] Step S5: Perform fine search with small step length within each order of band search range to achieve independent calculation of a single dispersion branch and obtain the final dispersion curve.

[0034] In step S1, it specifically includes:

[0035] For the dispersion equation to be calculated, f(ω,k)=0; wherein ω represents the frequency and k represents the wave number;

[0036] In the solution range [ω a ,ω b ]×[k a ,k b ], a rough fast pre-search is performed with a large step size;

[0037] Among them, the large frequency step is one tenth of the entire frequency range, that is, (ω b -ω a ) / 10; the wave number step size is one tenth of the entire wave number range, that is, (k b -k a ) / 10;

[0038] A rough solution of the dispersion curve ω-k is obtained.

[0039] In this embodiment, taking the longitudinal mode Lamb wave in an isotropic single-layer plate as an example, its dispersion equation is:

[0040]

[0041] Where ω is the dimensionless frequency and k is the dimensionless wave number.

[0042] The coefficient κ is defined as

[0043]

[0044] Wherein, v represents Poisson's ratio, and its value is v=0.25.

[0045] First, a large step size (here a wave number step size of 0.3) is used to quickly pre-search the dispersion curve in the wave number [0,5] and frequency [0,6] range. The results are as follows: Figure 1 shown.

[0046] In the subsequent refined search, you can follow the following Figure 2 The search can also be done along the wavenumber direction shown in Figure 3 Search in the frequency direction shown.

[0047] pass Figure 1 The preliminary search results show that the curve is widely distributed in the wave number range, so we use Figure 3 The search is performed along the frequency direction as shown.

[0048] Taking the second-order branch as an example, select the points of the second-order branch obtained by the fast pre-search, scale the frequencies of these points by adding or subtracting 0.15, and obtain the upper and lower limits of the scaled frequency respectively. Connect these upper and lower limits by linear interpolation to obtain the band search range that includes the second-order branch, such as Figure 4 As shown, the upper curve represents the upper limit of the second-order branch, and the lower curve represents the lower limit of the second-order branch.

[0049] A small step size fine search (wave number step size 0.02) is carried out within the obtained band search range. Since the upper and lower frequency limits within the band search range are very narrow and only the curve of the second-order branch is included, the second-order dispersion branch can be quickly calculated separately, such as Figure 5 shown.

[0050] Repeating this process for other branches, we can quickly obtain the overall dispersion curves of each order branch separation in the wave number [0,5] and frequency [0,6] range, such as Figure 6 shown.

[0051] Compared with the large region with a wave number and frequency range of [0,5]×[0,6], the area of ​​the strip region is very small, so the calculation efficiency is greatly increased, and the strip region contains only one branch, so the dispersion curve of a single branch can be calculated.

[0052] The present invention determines the upper and lower limits of each order of dispersion branch search through large-range and large-step fast pre-search combined with frequency scaling, obtains a fine band search range through interpolation, and greatly improves the calculation efficiency within the same frequency and wavenumber calculation range. At the same time, it realizes dispersion branch separation and performs separate calculations on specific branches of interest.

[0053] The above specific implementations do not constitute a limitation on the protection scope of the present disclosure. It should be understood by those skilled in the art that various modifications, combinations, sub-combinations and substitutions can be made according to design requirements and other factors. Any modification, equivalent substitution and improvement made within the spirit and principle of the present disclosure shall be included in the protection scope of the present disclosure.

Claims

1. A dispersion curve efficient path search method, characterized in that: The following steps are involved: Step S1, within the solution range, the dispersion equation performs a rough and fast pre-search with a large step length to obtain a rough solution of each order dispersion branch; Step S2: judging the approximate distribution of each order dispersion branch according to the rough solution, and determining the search direction of the fine search; Step S3, scaling the rough solution of the dispersion branch according to the determined search direction to obtain the upper limit and lower limit of the selected point of the dispersion branch; Step S4, interpolating the upper and lower limits of each point to obtain a band search range including the dispersion branch; Step S5: Perform fine search with small step length within each order of band search range to achieve independent calculation of a single dispersion branch and obtain the final dispersion curve.

2. The method for searching a dispersion curve efficient path according to claim 1, characterized in that: In step S1, it specifically includes: For the dispersion equation to be calculated, f(ω,k)=0; wherein ω represents the frequency and k represents the wave number; In the solution range [ω a ,ω b ]×[k a ,k b ], a rough fast pre-search is performed with a large step size; Among them, the large frequency step is one tenth of the entire frequency range, that is, (ω b -ω a ) / 10; the wave number step size is one tenth of the entire wave number range, that is, (k b -k a ) / 10; A rough solution of the dispersion curve ω-k is obtained.

3. The method for searching a dispersion curve efficient path according to claim 1, characterized in that: In step S2, the search direction is determined to be the frequency axis direction, and the frequency range of the rough solution of the dispersion branch is scaled to obtain the upper and lower limits of the frequency of the selected point of the dispersion branch; the upper and lower limits of the frequency of each point are interpolated to obtain a band search range including the dispersion branch.

4. The method for searching a dispersion curve efficient path according to claim 1, characterized in that: In step S2, the search direction is determined to be the wavenumber axis direction, and the wavenumber range of the rough solution of the dispersion branch is scaled to obtain the upper and lower limits of the wavenumbers of the selected points of the dispersion branch; the upper and lower limits of the frequency of each point are interpolated to obtain a band search range including the dispersion branch.

5. The method for searching a dispersion curve efficient path according to claim 1, characterized in that: The large step size is 5% to 15% of the entire range, and the small step size is 0.5% to 15% of the entire range.

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