Ultrasonic guided wave modal analysis method in fluid saturated porous medium

Abstract

The invention relates to an ultrasonic guided wave modal analysis method, device and equipment in a fluid saturated porous medium and a computer readable storage medium, and the method comprises the steps: determining a fluctuation control equation in a solid-fluid coupled porous medium domain; describing a conversion relation between the particle displacement of any position in the porous medium domain and the particle displacement of the corresponding section through a wave number and an angular frequency, and converting the fluctuation control equation in the solid-fluid coupled porous medium domain into a characteristic value solving form based on the conversion relation to obtain a characteristic equation; after specific boundary conditions are applied to the boundary of the porous medium, numerical solution is carried out on the characteristic equation; and according to a feature solving result, generating a modal analysis result of the ultrasonic guided wave. The technical scheme disclosed by the invention is particularly suitable for modal analysis of ultrasonic guided waves in a fluid saturated porous medium with an irregular section.

Description

Technical Field

[0001] The present disclosure relates to the technical field of ultrasonic guided wave modal analysis, and particularly to a method, device, equipment and computer-readable storage medium for ultrasonic guided wave modal analysis in a fluid-saturated porous medium. Background Art

[0002] A porous medium refers to a material with a large number of tiny pores, which are usually distributed inside or on the surface of the material. The existence of pores endows the porous medium with physical properties such as a high specific surface area, a lower density, and good fluid permeability. With the development of engineering technology, artificial porous media have been widely used. For example, the fluid-saturated porous medium in a battery is applied to the electrode material to increase the surface area of the electrode, thereby improving the capacity and charge-discharge speed of the battery. For example, the porous separator in a battery can be used to prevent short circuits between electrodes while allowing ions to pass through. The porous structure enables the separator to have a high ion conductivity and mechanical strength, effectively improving the safety and performance of the battery.

[0003] Porous media are widely used in engineering fields such as oil reservoirs, building earthquake resistance, and noise control. In-depth exploration of their wave propagation characteristics (such as attenuation laws and energy dissipation mechanisms) has important engineering significance. The wave propagation in a porous medium is affected by both the macroscopic medium structure and the microscopic pore properties (such as porosity, pore morphology, and fluid saturation), and the wave propagation characteristics are more complex. Studying the wave propagation law in a porous medium has important scientific significance.

[0004] As an elastic wave propagating in a bounded medium, ultrasonic guided waves are widely used in engineering testing due to their advantages such as long propagation distance and full coverage of the structural thickness. Due to the material heterogeneity of the fluid-saturated porous medium, modal analysis of ultrasonic guided waves in it has become the key to understanding the propagation law of ultrasonic guided waves in porous elastic materials and carrying out related applications.

[0005] In related technologies, there are the following several techniques for ultrasonic guided wave modal analysis in a fluid-saturated porous medium: The global matrix method integrates all the boundary conditions between the porous medium and the solid or fluid medium into a characteristic equation. This method requires constructing a global matrix describing the entire system. For cases with a large number of layers, the matrix to be processed is large, and the calculation amount and complexity are high; The transfer matrix method considers the internal interface boundary conditions step by step. This method has a matrix ill-conditioning phenomenon for cases with a large frequency-thickness product, affecting the stability of the calculation results; Due to the complex coupling relationship between the porous layer and the solid and fluid regions, the existing numerical methods have deficiencies in terms of accuracy, stability, and calculation efficiency. Summary of the Invention

[0006] To solve the above technical problems, the present disclosure provides a method, apparatus, device, and computer-readable storage medium for ultrasonic guided wave mode analysis in a fluid-saturated porous medium.

[0007] In a first aspect, an embodiment of the present disclosure provides a method for ultrasonic guided wave mode analysis in a fluid-saturated porous medium, including:

[0008] Determine the wave motion control equation in the solid-fluid coupled porous medium domain;

[0009] Describe the conversion relationship between the particle displacement at any position in the porous medium domain and the particle displacement at the corresponding cross-section through the wave number and angular frequency, and based on the conversion relationship, convert the wave motion control equation in the solid-fluid coupled porous medium domain into an eigenvalue solution form to obtain an eigenvalue equation;

[0010] After applying specific boundary conditions to the boundary of the porous medium domain, numerically solve the eigenvalue equation to obtain an eigenvalue solution result;

[0011] Generate a mode analysis result of the ultrasonic guided wave according to the eigenvalue solution result.

[0012] In a second aspect, an embodiment of the present disclosure provides an apparatus for ultrasonic guided wave mode analysis in a fluid-saturated porous medium, including:

[0013] A determination module for determining the wave motion control equation in the solid-fluid coupled porous medium domain;

[0014] A conversion module for describing the conversion relationship between the particle displacement at any position in the porous medium domain and the particle displacement at the corresponding cross-section through the wave number and angular frequency, and based on the conversion relationship, converting the wave motion control equation in the solid-fluid coupled porous medium domain into an eigenvalue solution form to obtain an eigenvalue equation;

[0015] A solution module for numerically solving the eigenvalue equation to obtain an eigenvalue solution result after applying specific boundary conditions to the porous medium boundary;

[0016] A generation module for generating a mode analysis result of the ultrasonic guided wave according to the eigenvalue solution result.

[0017] In a third aspect, an embodiment of the present disclosure provides an electronic device, including: a processor; a memory for storing executable instructions of the processor; the processor for reading the executable instructions from the memory and executing the instructions to implement the method for ultrasonic guided wave mode analysis in a fluid-saturated porous medium described in the first aspect above.

[0018] Fourthly, an embodiment of the present disclosure provides a computer-readable storage medium storing a computer program, which when executed by a processor, implements the method for ultrasonic guided wave mode analysis in a fluid-saturated porous medium described in the first aspect above.

[0019] The technical solution provided by the embodiment of the present disclosure has the following advantages compared with the prior art: The conversion relationship between the particle displacement at any position in the porous medium domain and the particle displacement at the corresponding cross-section is described by the wave number and angular frequency. Based on the conversion relationship, the wave motion control equation in the solid-fluid coupled porous medium domain is converted into an eigenvalue solution form to obtain the characteristic equation. Furthermore, after applying specific boundary conditions to the porous medium boundary, the characteristic equation is numerically solved to obtain the characteristic solution result, and the mode analysis result of the ultrasonic guided wave is generated according to the characteristic solution result. Thus, a method for ultrasonic guided wave mode analysis in a fluid-saturated porous medium with high computational efficiency and accuracy is provided. For a layered structure with a regular cross-section, when the number of layers of the structure is large, compared with the global matrix method, the computational amount and computational complexity do not increase significantly. Compared with the transfer matrix method, for the case of a large frequency-thickness product, the calculation result has high stability. Moreover, the matrix method and the spectral element method can only solve uniform layered structures, and this method is also applicable to cross-section irregular structures that cannot be solved by methods such as the matrix method and the spectral element method. By accurately establishing the cross-section geometry, it is applicable to waveguides with any irregular shape. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] The accompanying drawings herein are incorporated into the specification and constitute a part of this specification, showing embodiments consistent with the present disclosure and used together with the specification to explain the principles of the present disclosure.

[0021] In order to more clearly illustrate the technical solutions in the embodiments of the present disclosure or the prior art, the following will briefly introduce the accompanying drawings required for describing the embodiments or the prior art. Obviously, for those of ordinary skill in the art, other drawings can also be obtained based on these drawings without creative efforts.

[0022] Figure 1 It is a schematic flowchart of a method for ultrasonic guided wave mode analysis in a fluid-saturated porous medium provided by an embodiment of the present disclosure;

[0023] Figure 2 It is a three-dimensional structure schematic diagram of a fluid-saturated porous medium provided by an embodiment of the present disclosure;

[0024] Figure 3 It is a schematic diagram of finite element mesh division provided by an embodiment of the present disclosure;

[0025] Figure 4 It is a schematic diagram of boundary conditions provided by an embodiment of the present disclosure;

[0026] Figure 5 Schematic diagram of the wave number - frequency dispersion curve of a porous graphite electrode material in air provided by an embodiment of the present disclosure;

[0027] Figure 6 Schematic diagram of the ultrasonic guided wave attenuation curve in a porous graphite electrode material in air provided by an embodiment of the present disclosure;

[0028] Figure 7 Schematic diagram of the structure of the S - mode thickness - direction displacement wave at a frequency of 1 MHz provided by an embodiment of the present disclosure;

[0029] Figure 8 Schematic diagram of the structure of the A - mode thickness - direction displacement wave at a frequency of 1 MHz provided by an embodiment of the present disclosure;

[0030] Figure 9 Schematic diagram of the structure of the SH - mode thickness - direction displacement wave at a frequency of 1 MHz provided by an embodiment of the present disclosure. Detailed implementation manners

[0031] In order to more clearly understand the above - mentioned objects, features and advantages of the present disclosure, the solutions of the present disclosure will be further described below. It should be noted that, without conflict, the embodiments of the present disclosure and the features in the embodiments may be combined with each other.

[0032] Many specific details are set forth in the following description in order to fully understand the present disclosure, but the present disclosure may also be implemented in other ways different from those described herein; obviously, the embodiments in the specification are only a part of the embodiments of the present disclosure, rather than all the embodiments.

[0033] Figure 1 Schematic flow chart of a method for ultrasonic guided wave mode analysis in a fluid - saturated porous medium provided by an embodiment of the present disclosure. The method provided by the embodiment of the present disclosure can be executed by an ultrasonic guided wave mode analysis device in a fluid - saturated porous medium. The device can be implemented by software and / or hardware and can be integrated on any electronic device with computing capabilities.

[0034] As Figure 1 shown, the method for ultrasonic guided wave mode analysis in a fluid - saturated porous medium provided by an embodiment of the present disclosure may include:

[0035] Step 101, determining the wave motion control equation in the porous medium domain of solid - fluid coupling.

[0036] In this embodiment, the fluid-saturated porous medium (hereinafter referred to as the porous medium) includes a solid material and a fluid material. It is assumed that the solid material is a continuum, the pores are completely filled with fluid, and the ultrasonic guided wave is affected by the scattering attenuation of the solid phase and the viscous and inertial dissipation of the fluid phase during propagation. When performing ultrasonic guided wave mode analysis, the wave control equation is first determined. Optionally, the homogenization method is used to model the wave control equation in the porous medium domain. Among them, the porous medium domain is denoted as Ω, and the porous medium boundary is denoted as

[0037] Among them, the wave control equation in the coupled solid-fluid porous medium domain Ω is as follows:

[0038]

[0039] Among them, ρ 11 、ρ 12 、ρ 22 are the effective densities, u s is the average displacement field of the solid phase, u f is the average displacement field of the fluid phase, σ s is the solid-phase stress field, σ f is the fluid-phase stress field, b is the viscous damping factor, F is the viscous correction factor, t is the time, is the Hamiltonian operator;

[0040] ρ 12 =-(α ∞ -1)φρ f , ρ 11 =(1 - φ)ρ s -ρ 12 , ρ 22 =φρ f -ρ 12 , ρ s is the density of the solid, ρ f is the density of the fluid, φ is the porosity, α ∞ is the tortuosity;

[0041] b=ηφ 2 / k0

[0042]

[0043] Among them, I is the imaginary unit, M is the shape factor, f is the frequency, η is the dynamic viscosity of the fluid, and k0 is the low-frequency permeability of the solid material.

[0044] Among them, the stress-strain relationship in the solid phase and the fluid phase is:

[0045]

[0046] Among them, the strain εkk = ε 11 + ε 22 + ε 33 , where the subscripts i, j = 1, 2, 3 represent three orthogonal directions of the Cartesian coordinate system, and P, N, R, Q are Biot coefficients.

[0047]

[0048] N = G b

[0049]

[0050] Wherein, is the effective porosity of the fluid-saturated porous medium. K s is the bulk modulus of the solid material, K f is the bulk modulus of the fluid material, K b is the drained bulk modulus of the solid phase, G b is the drained shear modulus of the solid phase. δ ij is the Kronecker function. When i = j, δ ij = 1; when i ≠ j, δ ij = 0.

[0051] Thus, when the wavelength is greater than a specified multiple of the pore size, the wave control equation of the porous medium accurately describes the coupled dynamic behavior of the solid phase and the fluid phase, improving the calculation efficiency and accuracy compared with traditional numerical methods, and is applicable to the solution of the ultrasonic guided wave characteristics of fluid-saturated porous media with complex cross-sectional shapes of any kind.

[0052] In an embodiment of the present disclosure, both sides of the porous medium are fluid domains. Optionally, the fluids on both sides are simplified as ideal fluids for solution. Among them, the constitutive equation of the fluid domain is:

[0053]

[0054] Wherein, is the average displacement field, and p is the pressure in the fluid domain. The wave control equation in the fluid domain is

[0055]

[0056] Substituting the constitutive equation, the wave control equation in the fluid domain can be written as:

[0057]

[0058] Step 102: Describe the conversion relationship between the particle displacement at any position in the porous medium domain and the particle displacement of the corresponding cross-section through the wave number and angular frequency. Based on the conversion relationship, convert the wave motion control equation in the fluid-solid coupled porous medium domain into an eigenvalue solution form to obtain the characteristic equation. The characteristic equation is generally described by the simple harmonic wave hypothesis.

[0059] In the porous medium waveguide, the real coordinate space coincides with the complex coordinate space (i.e., ), and the coordinate stretching function is 1 (i.e., γ1 = γ2 = 1). Therefore, to simplify the derivation process, the equation of the porous medium waveguide is established in the real coordinate space.

[0060] In this embodiment, it is assumed that the ultrasonic guided wave propagates harmonically along the x3 direction. For any moment, the particle displacement at any position in the porous medium domain Ω can be described by the particle displacement at the corresponding position of the cross-section. Specifically, the conversion relationship between the particle displacement at any position in the porous medium domain Ω and the particle displacement of the corresponding cross-section is described through the wave number and angular frequency. The formula is as follows where, u i is the particle displacement at any position, U i is the particle displacement of the cross-section, k is the wave number, ω is the angular frequency, and t is the time.

[0061] The following is an explanation of the derivation process. Through the conversion relationship between the particle displacement at any position and the particle displacement of the corresponding cross-section, the displacement satisfies the following expression:

[0062]

[0063] Based on this, the component form of the wave motion control equation in the fluid-solid coupled porous medium domain Ω can be expressed as:

[0064]

[0065]

[0066] The above equations are all quadratic eigenvalue problems, where the eigenvalue is the wave number k and the eigenvector is the displacement wave structure. For linearization, a new variable V = kU is introduced. The wave motion control equation in the fluid-saturated porous medium domain Ω can be written as:

[0067]

[0068]

[0069] The above equation can be expressed as a linear eigenvalue solution problem. The general expression for linear eigenvalue solution is as follows:

[0070]

[0071] where λ is the eigenvalue, u is the eigenvector, and e a , d, c, α, r, β, a, f are coefficients, and the coefficients can be complex numbers, is the Hamiltonian operator.

[0072] Among them, for the porous medium, by comparing the wave control equation with the expression in the form of eigenvalue solution, the coefficients can be obtained: e a = r = f = 0,

[0073]

[0074]

[0075] where P, N, R, Q are Biot coefficients, I is the imaginary unit, ω is the angular frequency, and ρ 11 , ρ 12 , ρ 22 are the effective densities, b is the viscous damping factor, and F is the viscous correction factor.

[0076] In an embodiment of the present disclosure, for the fluid domains on both sides of the porous medium, the fluid domain consists of a fluid region and an absorption region. Among them, the absorption region is implemented by, for example, a perfectly matched layer (PML, Perfectly Matched Layer). It should be noted that in this embodiment, the PML is taken as an example for illustration, but the absorption region can also be implemented by an absorbing layer (AbsorbingRegion) and other methods, and no specific limitation is made here. By determining the wave control equations in the fluid domains on both sides of the porous medium, the wave control equations in the fluid domains on both sides of the porous medium are converted into the form of eigenvalue solution to obtain the corresponding characteristic equations. Optionally, as shown in Figure 2 and Figure 3 , to simulate the infinite fluid domain in the x2 direction, the PML method is adopted, and the exponential decay of the wave field is realized in the complex coordinate space through the coordinate stretching technique. Among them, in the stretched coordinate system including the PML, assuming that the wave propagates harmonically along the direction, the sound pressure in the fluid can be described as The wave control equation in the fluid domain can also be expressed in the aforementioned form of eigenvalue solution, which is specifically expressed as follows:

[0077]

[0078] Among them, for the fluid domains on both sides of the porous medium, by comparing the wave control equation with the expression in the form of eigenvalue solution, the coefficients can be obtained: e a = K f ; a = -ρ f ω2 ; d = f = 0;

[0079]

[0080] where γ1 and γ2 are PML functions in the x1 and x2 directions respectively.

[0081] The general case of PML is described below: Using the PML method, the exponential decay of the wave field is realized in the complex coordinate space through the coordinate stretching technique. Among them, in the PML region, the stretched coordinates are:

[0082]

[0083] where γ1(x1) and γ2(x2) are non-zero complex-valued coordinate stretching continuous functions (also known as PML functions), which are used to control the attenuation of waves in the PML region and satisfy:

[0084] When , γ1(x1) = 1, when , Im{γ1} > 0; when , γ2(x2) = 1, when , Im{γ2} > 0. Therefore, this will make any function satisfy:

[0085]

[0086] Among them,

[0087] Step 103, after applying specific boundary conditions at the boundary of the porous medium, numerically solve the characteristic equation to obtain the characteristic solution result.

[0088] In this embodiment, the above two-dimensional frequency-domain eigenvalue solution problem is numerically solved, and all characteristic solution results that satisfy the boundary conditions and the wave control equation can be obtained. Among them, the characteristic solution results include eigenvalues and eigenvectors. The eigenvalues are complex numbers, the real part of the eigenvalue represents the wave number, the imaginary part represents the attenuation, and the eigenvector represents the displacement wave structure. Optionally, taking the porous medium and the two side regions as an example, the first characteristic equation is obtained according to the wave control equation of the solid-fluid coupling, and the second characteristic equation is obtained according to the wave control equation of the two side regions, and then the first characteristic equation and the second characteristic equation are numerically solved to obtain the characteristic solution result. Optionally, the numerical solution includes: discretizing the two-dimensional model into finite element meshes, and then numerically solving based on the discretized meshes. The discretization of the two-dimensional model can use second-order triangular Lagrangian elements, as Figure 3 shown.

[0089] Among them, the boundary conditions include interface boundary conditions, periodic boundary conditions, and stress-free boundary conditions, such as Figure 4As shown, the lateral boundary between the porous medium and the fluid region represents the interface boundary condition, the left and right sides represent the periodic boundary conditions, and the upper and lower sides represent the stress-free boundary conditions. Periodic boundary conditions are applied on both sides to simulate an infinitely large plate structure, and the periodic boundary conditions are regarded as a combination of Dirichlet boundary conditions and Neumann boundary conditions. The Neumann boundary condition and the Dirichlet boundary condition can be expressed as follows:

[0090]

[0091] u = m

[0092] The stress-free boundary condition is applied by imposing the Neumann boundary conditions q = 0, g = 0 at the free boundary; the interface boundary conditions include the displacement continuity boundary condition and the stress continuity boundary condition, which are set in the Figure 4 shown lateral boundary. In the waveguide structure of fluid-saturated porous media, the fluid not only completely fills the solid skeleton, but also forms displacement continuity boundary conditions and continuous stress boundary conditions with the solid-fluid two-phase medium at the porous medium boundary:

[0093] The displacement continuity boundary condition is

[0094] The stress continuity boundary condition is

[0095] where is the displacement of the fluid domain and p is the pressure of the fluid domain.

[0096] Writing the above equations as Neumann boundary conditions, at the porous medium boundary define the Neumann boundary condition at the interface as q = 0, g = [-φpn x -φpn y 0-(1-φ)pn x -(1-φ)pn y 0 0 0 0 0 0 0] T ; define the Neumann boundary condition at the interface in the adjacent fluid domain as where n is the unit normal vector of the interface pointing outside the domain, and n x and n y are the components of n.

[0097] In one embodiment of the present disclosure, a numerical solution of the characteristic equation is performed to obtain a characteristic solution result that satisfies the boundary conditions, including: for a set frequency scanning interval, calculating a plurality of candidate characteristic solution results that satisfy the boundary conditions at each frequency point; for each candidate characteristic solution result, calculating a first average energy flux density in the direction of wave propagation in the porous medium, a second average energy flux density in the direction of wave propagation in the fluid region, and a third average energy flux density in the direction of wave propagation in the absorption region; determining the candidate characteristic solution result that satisfies the preset condition as the characteristic solution result at the corresponding frequency point; wherein the preset condition includes: the first average energy flux density > the sum of the second average energy flux density and the third average energy flux density.

[0098] In this embodiment, the energy flux density of the sound wave in the waveguide is represented by the Poynting vector, and the Poynting vector in the wave propagation direction (x3) is where * represents the conjugate, and v * is the conjugate of the velocity vector, and σ is the stress matrix. The energy flux density in the direction of wave propagation in the fluid can be expressed as The energy flux density in the direction of wave propagation in the porous medium is The subscripts 1, 2, and 3 represent the three orthogonal directions of the Cartesian coordinate system. The average energy flux density is defined as where S is the area within the domain. The ultrasonic guided wave mode that can propagate in the porous medium satisfies

[0099] Step 104, generating a modal analysis result of the ultrasonic guided wave according to the characteristic solution result.

[0100] Among them, the modal analysis result of the ultrasonic guided wave includes modal characteristics such as the ultrasonic guided wave mode and dispersion characteristics, the phase velocity, group velocity, attenuation, energy flux density distribution, and wave structure corresponding to each mode.

[0101] As an example, generating a modal analysis result of the ultrasonic guided wave according to the characteristic solution result includes: determining the corresponding ultrasonic guided wave mode according to the eigenvector; for any ultrasonic guided wave mode, determining the dispersion curve of the ultrasonic guided wave mode according to the wave number at each frequency point. In this example, among all the ultrasonic guided wave modes that can propagate, the ultrasonic guided wave mode is determined as a symmetric mode, an antisymmetric mode, or a horizontal shear mode according to the dominant displacement direction of the ultrasonic guided wave mode in the thickness direction. For each ultrasonic guided wave mode, repeating the foregoing operation in all the solved frequency ranges can obtain the wave number-frequency dispersion curve of the ultrasonic guided wave mode.

[0102] According to the technical solution of the embodiment of the present disclosure, the conversion relationship between the particle displacement at any position in the porous medium domain Ω and the particle displacement of the corresponding cross-section is described by wave number and angular frequency. Based on the conversion relationship, the wave motion control equation in the fluid-saturated porous medium domain Ω is converted into an eigenvalue solution form to obtain the characteristic equation. Furthermore, after applying specific boundary conditions to the characteristic equation on the porous medium boundary After numerical solution of the characteristic equation, the characteristic solution result is obtained. According to the characteristic solution result, the modal analysis result of the ultrasonic guided wave is generated. Thus, a method for modal analysis of ultrasonic guided waves in fluid-saturated porous media with high computational efficiency and accuracy is provided. In this method, the wave propagation problem in the three-dimensional structure is reduced in dimension through the conversion relationship, and only the two-dimensional cross-section needs to be solved during modal analysis, thereby improving the computational efficiency. For a layered structure with regular cross-sections, when the number of layers of the structure is large, compared with the global matrix method, the computational amount and computational complexity do not increase significantly. Compared with the transfer matrix method, for a large frequency-thickness product, the computational result has high stability. Moreover, the matrix method and the spectral element method can only solve uniform layered structures, and this method is also applicable to cross-section irregular structures that cannot be solved by methods such as the matrix method and the spectral element method. By accurately establishing the cross-section geometry, it is applicable to waveguides with any irregular shape. In addition, commercial solution software can be directly applied, eliminating the process of writing code for iterative root finding to solve for dispersion. Further, the modal analysis result can provide important support for the performance characterization of porous materials (such as porosity, elastic modulus, etc.), the health state assessment of industrial batteries (such as the power and remaining life of lithium batteries, etc.), and the evaluation of biological structures (such as tissue elasticity, bone density, etc.), and is widely used in materials science, the energy field, and medical diagnosis, etc.

[0103] Taking a porous graphite electrode sheet in air as an example below, the implementation process of this method in commercial software is introduced. Porous graphite is one of the commonly used electrode materials in batteries such as lithium batteries due to its good electrical conductivity and stable chemical properties. The material parameters of other fluid-saturated porous media are different from this example, but the method proposed in the embodiment of the present disclosure can be used for solution.

[0104] Establish a geometric model. Based on obtaining the thickness information of the porous medium, a two-dimensional cross-section model is established. Among them, the PML length h on both sides of the fluid layer can be calculated by the formula h≥(6.9 / (k leak B)), where k leak is the longitudinal wave number leaking into the fluid, and B is the imaginary part of the PML function. In this model, the thickness of the porous medium is 0.05 mm, and the thickness of the air on both sides is 0.2 mm. The scanning frequency range is 200 kHz to 2 MHz, the frequency step is 200 kHz, and the minimum longitudinal wave number in the fluid is 3829.3 m -1 when the wave number is 200 kHz. Therefore, the PML length can be estimated as h≥150.16 μm, so the PML region length of 200 μm is selected.

[0105] Set material parameters. In this model, the density ρ of graphite material s = 2260 kg / m 3 , the bulk modulus K s = 28.8 GPa, the drained bulk modulus K b = 17.4 GPa, the drained shear modulus G b = 0.39 GPa, the porosity φ = 0.329, the tortuosity α ∞ = 2.03, the low-frequency permeability k0 = 0.04 darcy. The density ρ of air f = 1.2402 kg / m 3 , the bulk modulus K f = 1.4199×10 5 Pa, the viscosity η = 1.8×10 -5 Pas.

[0106] Set the governing equations in the domain. The problem in the domain is an eigenvalue solution problem, and the wave governing equation is expressed in the form of eigenvalue solution: where, in the porous medium, the independent variable to be solved is The independent variable to be solved in the adjacent fluid domain is u = p. The porous medium and the adjacent fluid are two separate eigenvalue solution problems, and the corresponding coefficients are set respectively.

[0107] Set the stress and displacement continuous boundary conditions at the interface, such as Figure 4 . Define the Neumann boundary condition at the interface in the porous medium as: q = 0, g = [0 - φpn y 0 0 -(1 - φ)pn y 0 0 0 0 0 0 0] T ; Define the Neumann boundary condition at the junction in the adjacent fluid domain as q = 0, where n y is the unit normal vector of the interface pointing outside the domain.

[0108] Apply periodic boundary conditions on both sides to simulate an infinite plate. The periodic boundary condition can be regarded as a combination of Dirichlet boundary condition and Neumann boundary condition. If one side is defined as source and the other side is defined as destiny, then there is Among them, Γ represents the independent variable in the physical field, which is displacement in the porous medium and sound pressure in the fluid. Optionally, for a heterogeneous fluid-saturated porous structure, based on the establishment of a two-dimensional model of the cross-sectional shape, the interface boundary conditions are set the same as in this example, but the periodic boundary conditions do not need to be set. For an annular periodic structure, one of the units can be selected to add annular periodic boundary conditions on both sides to simulate the annular periodic structure. The remaining boundaries are stress-free free conditions and do not require special settings.

[0109] Select the PML function. The absorption efficiency of the leaking ultrasonic guided wave in PML depends to a large extent on the selection of the PML function and the PML length. The PML function here is selected as: Among them Quantify the PML absorption, and select the common PML function here

[0110] Discretization. Discretize the two-dimensional cross-sectional model into a finite element mesh, and select second-order triangular Lagrangian elements to discretize the entire two-dimensional cross-sectional model.

[0111] Solve. Solve the eigenvalues at each frequency point through the set frequency scanning interval, and calculate all the eigenvalues at each frequency. The frequency range set here is 200 kHz to 2 MHz, the scanning step is 200 kHz, there are a total of 10 frequency points, and 100 complex eigenvalues are solved at each frequency point.

[0112] Result post-processing. The real part of the complex eigenvalue obtained by solving is the wave number k (unit 1 / m), and the imaginary part is the attenuation (unit Neper / m, 1 Neper = 8.686 dB). The eigenvalues with attenuation less than the threshold or no attenuation in this structure correspond to the propagable modes. The mode phase velocity can be calculated by V ph = 2πf / k. In the example of a porous graphite electrode in air, the attenuation caused by air is small. Among all the complex eigenvalues obtained by solving, the modes with smaller imaginary parts, or pure real numbers and the energy concentrated in the porous medium, can be selected as the propagable ultrasonic guided wave modes. Repeating this operation in all the solved frequency ranges can obtain the wave number-frequency dispersion curves of the symmetric mode (S mode), antisymmetric mode (A mode), and horizontal shear mode (SH mode), as Figure 5 shown, where the horizontal axis is the frequency (MHz), the vertical axis is the wave number (1 / m), the curve is the dispersion curve obtained by the stiffness matrix method (SMM), and the circular, square, and diamond marks are the dispersion curves obtained by this method. The attenuation obtained by this method is as Figure 6 shown, where the horizontal axis is the frequency (MHz), and the vertical axis is the attenuation (dB / m).

[0113] The eigenvector corresponding to each eigenvalue is the displacement wave structure. Among all the propagable modes, according to the dominant displacement direction of each mode along the thickness direction, the modes can be determined as the symmetric mode (the S mode with the dominant displacement in the x3 direction of and ), the anti-symmetric mode (the A mode with the dominant displacement in the x2 direction of and ), and the horizontal shear mode (the SH mode with the dominant displacement in the x1 direction of and ). As shown in Figures 7 - 9 , it shows the normalized displacement distribution along the thickness direction of the cross-section of the fluid-saturated porous medium. In Figures 7 - 9 , the horizontal axis is x2 (μm), and the vertical axis is the normalized displacement distribution.

[0114] It should be noted that the eigenvalue solving step in this method can be solved by commercial software or by using typical eigenvalue solving algorithms, such as programming and solving using the QR decomposition method, etc. Based on the obtained eigenvalues, the dispersion curves of each mode can be obtained by mode tracking using typical interpolation methods, or can be automatically tracked by comparing the differences between different eigenvectors. The partial differential control equations and boundary conditions describing this problem in the previous text are in the strong form, and the corresponding weak form can also be used, without specific restrictions here.

[0115] The embodiment of the present disclosure also proposes an ultrasonic guided wave mode analysis device in a fluid-saturated porous medium. The ultrasonic guided wave mode analysis device in a fluid-saturated porous medium includes: a determination module, a conversion module, a solving module, and a generation module.

[0116] The determination module is used to determine the wave motion control equation in the porous medium domain Ω of the solid-fluid coupling;

[0117] The conversion module is used to describe the conversion relationship between the particle displacement at any position in the porous medium domain Ω and the particle displacement of the corresponding cross-section through the wave number and angular frequency, and based on the conversion relationship, convert the wave motion control equation in the porous medium domain Ω of the solid-fluid coupling into an eigenvalue solving form to obtain an eigenvalue equation;

[0118] The solving module is used to numerically solve the eigenvalue equation after applying specific boundary conditions on the porous medium boundary to obtain an eigenvalue solving result;

[0119] The generation module is used to generate a mode analysis result of the ultrasonic guided wave according to the eigenvalue solving result.

[0120] The ultrasonic guided wave mode analysis device in a fluid-saturated porous medium provided by the embodiments of the present disclosure can execute any ultrasonic guided wave mode analysis method provided by the embodiments of the present disclosure, and has functional modules and beneficial effects corresponding to the execution of the method. The content not described in detail in the device embodiments of the present disclosure can be referred to the description in any method embodiment of the present disclosure.

[0121] The embodiments of the present disclosure also provide an electronic device, which includes one or more processors and a memory. The processor can be a central processing unit (CPU) or other forms of processing units with data processing capabilities and / or instruction execution capabilities, and can control other components in the electronic device to execute desired functions. The memory can include one or more computer program products, and the computer program products can include various forms of computer-readable storage media, such as volatile memory and / or non-volatile memory. Volatile memory can include, for example, random access memory (RAM) and / or cache memory, etc. Non-volatile memory can include, for example, read-only memory (ROM), hard disk, flash memory, etc. One or more computer program instructions can be stored on the computer-readable storage media, and the processor can run the program instructions to implement the methods of the embodiments of the present disclosure above and / or other desired functions. Various contents such as input signals, signal components, noise components, etc. can also be stored in the computer-readable storage media.

[0122] In one example, the electronic device may further include: an input device and an output device, and these components are interconnected through a bus system and / or other forms of connection mechanisms. In addition, the input device may include, for example, a keyboard, a mouse, etc. The output device can output various information to the outside, including the determined distance information, direction information, etc. The output device can include, for example, a display, a speaker, a printer, and a communication network and its connected remote output devices, etc. In addition, according to specific application scenarios, the electronic device may further include any other appropriate components such as a bus, an input / output interface, etc.

[0123] In addition to the above methods and devices, the embodiments of the present disclosure may also be a computer program product, which includes computer program instructions that cause the processor to execute any method provided by the embodiments of the present disclosure when the processor runs.

[0124] A computer program product may be written in any combination of one or more programming languages for programming code to perform the operations of the embodiments of the present disclosure. The programming languages include object-oriented programming languages such as Java, C++, etc., and also include conventional procedural programming languages such as the "C" language or similar programming languages. The programming code may be executed entirely on the user computing device, partially on the user device, executed as a stand-alone software package, partially on the user computing device and partially on a remote computing device, or entirely on a remote computing device or server.

[0125] In addition, an embodiment of the present disclosure may also be a computer-readable storage medium having computer program instructions stored thereon, and the computer program instructions, when run by a processor, cause the processor to execute any method provided by the embodiments of the present disclosure.

[0126] The computer-readable storage medium may employ any combination of one or more readable media. The readable media may be a readable signal medium or a readable storage medium. The readable storage medium may, for example, include but is not limited to an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any combination of the above. More specific examples (non-exhaustive list) of the readable storage medium include: an electrical connection having one or more wires, a portable disk, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), an optical fiber, a portable compact disc read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the above.

[0127] It should be noted that in this document, relational terms such as "first" and "second" are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any actual relationship or order between these entities or operations. Moreover, the term "comprising", "including" or any other variant thereof is intended to cover a non-exclusive inclusion, such that a process, method, article or device comprising a series of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such process, method, article or device. Without further limitation, an element defined by the statement "comprising an..." does not exclude the presence of additional identical elements in the process, method, article or device comprising the element.

[0128] The above are only specific embodiments of the present disclosure, enabling those skilled in the art to understand or implement the present disclosure. Various modifications to these embodiments will be obvious to those skilled in the art, and the general principles defined herein can be implemented in other embodiments without departing from the spirit or scope of the present disclosure. Therefore, the present disclosure will not be limited to the embodiments described herein, but rather will be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for ultrasonic guided wave mode analysis in a fluid-saturated porous medium, characterized in that, The method includes: Determining the wave control equation in the poroelastic medium domain with solid-fluid coupling; Describing the conversion relationship between the particle displacement at any position in the poroelastic medium domain and the particle displacement at the corresponding cross-section through the wave number and angular frequency, and converting the wave control equation in the poroelastic medium domain with solid-fluid coupling into an eigenvalue solution form based on the conversion relationship to obtain the characteristic equation; After applying specific boundary conditions on the poroelastic medium boundary, numerically solving the characteristic equation to obtain the characteristic solution result; Generating the modal analysis result of the ultrasonic guided wave according to the characteristic solution result.

2. The method according to claim 1, characterized in that The characteristic equation includes a first characteristic equation and a second characteristic equation. The first characteristic equation is obtained from the wave control equation in the poroelastic medium domain with solid-fluid coupling, and the second characteristic equation is obtained from the wave control equation in the fluid domains on both sides of the poroelastic medium.

3. The method according to claim 2, wherein The boundary conditions include interface boundary conditions, periodic boundary conditions, and stress-free boundary conditions.

4. The method according to claim 2, wherein The fluid domains on both sides of the poroelastic medium are composed of a fluid region and an absorption region. The numerically solving the characteristic equation to obtain the characteristic solution result includes: For a set frequency scanning interval, calculating multiple candidate characteristic solution results that satisfy the boundary conditions at each frequency point; For each of the candidate characteristic solution results, calculating the first average energy flux density in the direction of wave propagation in the poroelastic medium, the second average energy flux density in the direction of wave propagation in the fluid region, and the third average energy flux density in the direction of wave propagation in the absorption region; Determining the candidate characteristic solution result that satisfies the preset conditions as the characteristic solution result at the corresponding frequency point; wherein, the preset conditions include: the first average energy flux density > the sum of the second average energy flux density and the third average energy flux density.

5. The method according to claim 1 or 2, characterized in that, The determining the wave control equation in the poroelastic medium domain with solid-fluid coupling includes: Using the homogenization method to model the wave control equation in the poroelastic medium domain with solid-fluid coupling; Wherein, the wave control equation in the poroelastic medium domain with solid-fluid coupling is as follows: where ρ 11 , ρ 12 , ρ 22 are effective densities, u s is the solid-phase average displacement field, u f is the fluid-phase average displacement field, σ s is the solid-phase stress field, σ f is the fluid-phase stress field, b is the viscous damping factor, F is the viscous correction factor, t is time, is the Hamiltonian operator; ρ 12 = -(α ∞ - 1)φρ f ,ρ 11 = (1 - φ)ρ s - ρ 12 ,ρ 22 = φρ f - ρ 12 ,ρ s is the density of the solid, ρ f is the density of the fluid, φ is the porosity, α ∞ is the tortuosity; b = ηφ 2 / k0 Wherein, \(I\) is the imaginary unit, \(M\) is the shape factor, \(f\) is the frequency, \(\eta\) is the dynamic viscosity of the fluid, and \(k_0\) is the low-frequency permeability.

6. The method according to claim 5, wherein The expression of the eigenvalue solution form is as follows: where λ is the eigenvalue, u is the eigenvector, and e a , d, c, α, r, β, a, f are coefficients; For the porous medium, e a = r = f = 0, Wherein, P, N, R, Q are Biot coefficients, related to the moduli of the solid phase and the fluid phase, I is the imaginary unit, ω is the angular frequency, ρ 11 , ρ 12 , ρ 22 are effective densities, b is the viscous damping factor, F is the viscous correction factor, is the Hamiltonian operator.

7. The method according to claim 3, characterized in that, The interface boundary conditions include displacement continuity boundary conditions and stress continuity boundary conditions. The method further includes: Converting the displacement continuity boundary conditions and stress continuity boundary conditions into the form of Neumann boundary conditions: Wherein, at the poroelastic medium boundary, the Neumann boundary condition at the junction is defined as \(q = 0\), g = [-φpn x -φpn y 0 - (1 - φ)pn x -(1 - φ)pn y 0 0 0 0 0 0 0] T ; In the fluid domain, the Neumann boundary condition at the junction is defined as where p is the pressure in the fluid domain, n x and n y are the components of n, and n is the unit normal vector of the interface pointing outside the domain.

8. The method according to claim 1, wherein The characteristic solution result includes an eigenvalue and an eigenvector. The eigenvalue is a complex eigenvalue. The real part of the eigenvalue represents the wave number, and the imaginary part represents the attenuation. The eigenvector represents the displacement wave structure. The generating the modal analysis result of the ultrasonic guided wave according to the characteristic solution result includes: Determining the corresponding ultrasonic guided wave mode according to the eigenvector; For any one of the ultrasonic guided wave modes, determining the dispersion curve of the ultrasonic guided wave mode according to the wave number at each frequency point.

9. An ultrasonic guided wave mode analysis device in a fluid-saturated porous medium, characterized in that Includes: A determination module, configured to determine the wave motion control equation in the porous medium domain with solid-fluid coupling; A conversion module, configured to describe the conversion relationship between the particle displacement at any position in the porous medium domain and the particle displacement at the corresponding cross section through the wave number and angular frequency, and convert the wave motion control equation in the porous medium domain with solid-fluid coupling into an eigenvalue solution form based on the conversion relationship to obtain an eigenvalue equation; A solution module, configured to numerically solve the eigenvalue equation after applying specific boundary conditions to the porous medium boundary to obtain an eigenvalue solution result; A generation module, configured to generate a modal analysis result of the ultrasonic guided wave according to the eigenvalue solution result.

10. An electronic device, characterized in that, Comprising: A processor; A memory for storing executable instructions of the processor; The processor is configured to read the executable instructions from the memory and execute the instructions to implement the ultrasonic guided wave modal analysis method in any one of the above claims 1-8 for the fluid-saturated porous medium.

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