CN116165270B - Method for calculating ultrasonic guided wave dispersion characteristics of pipeline structure - Google Patents
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
- G01N29/00—Investigating or analysing materials by the use of ultrasonic, sonic or infrasonic waves; Visualisation of the interior of objects by transmitting ultrasonic or sonic waves through the object
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- G—PHYSICS
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- G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
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- G—PHYSICS
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- G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
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Abstract
The invention discloses a method for calculating ultrasonic guided wave dispersion characteristics of a pipeline structure, which comprises the following steps: for particle vibration of guided waves in different directions in a circular tube, uniform displacement solutions are adopted to express wave propagation along the axial direction and the circumferential direction of a pipeline, and weak forms of wave control equations of the axial and the circumferential guided waves in an anisotropic tube under a cylindrical coordinate system are deduced; establishing a one-dimensional finite element model in the radial direction of the pipeline by utilizing the symmetry of the pipeline; the weak form expression of the wave equation of guided wave in the finite element software is defined, and the dispersion characteristics of guided wave propagating along different directions of the circular tube can be calculated respectively; the invention only needs to establish a one-dimensional finite element model of the pipeline, and can quickly solve the ultrasonic guided wave dispersion relation propagated in different directions in the pipeline through simple parameter setting without tedious programming.
Description
Technical Field
The invention relates to an ultrasonic guided wave detection technology, in particular to a method for calculating ultrasonic guided wave dispersion characteristics of a pipeline structure, and belongs to the technical field of nondestructive detection.
Background
Plumbing is an important vehicle that plays an important role in the transport of fluids and gases. Nowadays, as the use of oil and gas increases, the field of pipeline transportation has also been greatly developed. In the long-term service process, the pipeline may be damaged or cracked due to complex environmental factors, so that the risk of gas-liquid leakage is caused. The selection of an effective detection technique is critical to the safety detection of the pipeline. The ultrasonic guided wave detection which is one of the nondestructive detection technologies has the advantages of long-distance propagation, high propagation speed, wide propagation range and the like, and can be suitable for the safety detection of circular tube structures.
Ultrasonic guided waves in a pipe can be divided into two modes, axial guided waves and circumferential guided waves. The axial guided wave is mainly applied to long-distance detection of pipes, is mainly used for detecting defects and cracks distributed along the circumferential direction of the pipeline, and is insensitive to the defects distributed longitudinally in the pipeline. The circumferential guided wave is the guided wave which propagates along the circumferential direction of the circular tube, is sensitive to the longitudinal defects of the circular tube, and has a good effect when the circumferential guided wave is used for detecting the longitudinal defects in the circular tube. Under specific frequency, the ultrasonic guided wave can propagate along the length direction or the circumferential direction of the circular tube, the received signal is complete, and the ultrasonic guided wave can be reflected in the echo signal when encountering defects or discontinuous structures, so that the damage information of the structure can be effectively judged. And a proper excitation frequency is selected to carry out ultrasonic guided wave detection on the pipeline, so that the dispersion characteristic of the pipeline needs to be studied.
In a common pipeline ultrasonic guided wave dispersion characteristic research method, a traditional analysis method is suitable for solving an isotropic structure, and for a complex multilayer composite structure, the analysis method is difficult to obtain an analysis solution of the complex multilayer composite structure, and the problems of root loss and unstable calculation are faced. And the finite element rule needs to establish a three-dimensional model of the pipeline, so that the degree of freedom of solving is large and the calculation cost is high. The semi-analytic finite element method combines the advantages of the analytic method and the finite element method, is widely applied to research of guided wave dispersion characteristics, but most of the semi-analytic finite element methods solve a two-dimensional model of a pipeline, and although the degree of freedom of the solution is greatly reduced, a great amount of operation time is still needed when solving a dispersion curve of the pipeline under a high-frequency thick product. If the pipeline structure can be simplified into a one-dimensional model, the solving speed can be greatly improved.
Disclosure of Invention
In view of the above, the invention provides a method for calculating the dispersion characteristics of ultrasonic guided waves of a pipeline structure, which simplifies the pipeline into a radial one-dimensional model, and solves the dispersion characteristics of axial and circumferential guided waves of the pipeline in a weak form by using a uniformly derived fluctuation control equation.
A method for calculating ultrasonic guided wave dispersion characteristics of a pipeline structure comprises the following steps:
1. for particle vibration of sound waves in different directions in a circular tube, uniform displacement solutions are adopted to express wave propagation along the axial direction and the circumferential direction of a pipeline, and a uniform expression of a weak form of a fluctuation control equation of anisotropic pipeline axial direction and circumferential direction wave propagation under a cylindrical coordinate system is deduced:
1.1. the wave control equation in a typical anisotropic material is:
wherein sigma ij Is the stress tensor; ρ is the bulk density of the elastic solid; u (u) i Is a displacement vector.
1.2. Multiplying both sides of the wave equation of expression (1) by the test function v i And then integrating over the volume domain to obtain a weak form of the wave equation of the pipeline structure:
1.3. applying the divergence theorem to expression (2), the weak form of the equation can be defined as follows:
1.4. in expression (3), the integral over the boundary Γ tends to be 0, so the weak form of the equation can be expressed as:
1.5. stress-strain relationship in anisotropic elastic media
σ ij ＝C ijkl ε kl (5)
Wherein C is ijkl Fourth order stiffness tensor, which is elastic solid; epsilon kl As strain tensor
1.6. Strain expression expressed in terms of orthogonal components of displacement field in a cylindrical coordinate system:
1.7. particle vibration in different directions in a circular tube according to guided waves: particle motion of longitudinal wave is mainly in r sum (or)
A z-axis direction; the torsional wave particle motion is mainly in the theta axis direction; bending waves have particle vibrations in all three directions, circumferential, radial and axial; and the circumferential guided wave is a guided wave propagating along the circumference of the pipe. The uniform displacement solution is used for representing wave propagation along the axial direction and the circumferential direction of the pipeline:
in the above formula, m is Zhou Xiangjie times; k (K) z Coefficients that are wave vector components; ω is the angular frequency of the wave and k is the wave number.
1.8. Substituting the displacement expression of the particles into the weak form of the wave control equation, simplifying the solving problem of the three-dimensional domain into one-dimensional domain solving, and combining the expressions (5) and (6), wherein the weak form of the wave control equation of the anisotropic material is expanded as follows:
2. and constructing a one-dimensional finite element model in the radial direction of the pipeline by utilizing the symmetry of the pipeline.
3. And converting the integrated function in the expression (8) into a weak form integrated function expression which can be read by finite element software by using a weak form partial differential equation module.
4. Parameters in the weak form expression are defined in the parameter column: when solving the L (0, n) longitudinal mode and the T (0, n) torsional mode, let K Z =1, zhou Xiangjie times m=0; when solving F (m, n) bending mode, let K Z =1, zhou Xiangjie times m is a positive integer; when solving the circumferential guided wave, let K z =0, angular number m=kr; the dispersion characteristics of the guided wave propagating in different directions can be calculated separately. In addition, an anisotropic material stiffness matrix, radial dimensions of the tube, wave numbers and angular frequencies are defined.
5. After discretizing the model grid, adding parameterized scanning, scanning wave numbers or angular frequencies to search for characteristic values, and setting a scanning interval and the required characteristic value number.
6. Solving eigenvalue to obtain wave number and angular frequency according to phase velocity formula V p The phase velocity is calculated by =2pi f/k, and then calculated by formula V g Group velocity was calculated by =2pi Δf/Δk, and a dispersion curve was plotted.
Wherein Δf is the difference between adjacent frequency points in the same mode; Δk is the difference between adjacent wavenumbers.
7. In finite element software, a one-dimensional drawing is added to draw wave structure diagrams in different directions respectively.
The invention has the following advantages:
1) The method is based on the half-analytic finite element theory, only a one-dimensional finite element model of the pipeline is required to be established, the operand is very little, and the solving speed is high.
2) The method derives the weak form of the fluctuation control equation uniformly representing the axial and circumferential guided wave propagation of the pipeline, the frequency dispersion characteristics of different guided wave types in the pipeline can be solved respectively by simply setting the parameters in the weak form equation, and the calculated pipeline guided wave mode is complete and has no mode loss by utilizing finite element software.
Drawings
FIG. 1 is a block diagram of a step of calculating the axial ultrasonic guided wave dispersion relation of a pipeline based on weak form partial differential equation theory;
FIG. 2 is a schematic diagram of a three-dimensional model of the axial propagation of ultrasonic guided waves along a waveguide structure in an infinitely long hollow round tube;
FIG. 3 is a schematic view of a three-dimensional model of ultrasonic guided wave propagation along the circumferential direction of a pipe structure;
FIG. 4 is a schematic diagram of one-dimensional model selection of a pipeline in finite element software;
FIG. 5 is a schematic diagram showing the comparison of the phase velocity dispersion curve and the theoretical dispersion curve of the longitudinal mode and the torsional mode of the pipeline obtained by solving the method;
FIG. 6 is a graph showing the comparison of the group velocity dispersion curves of the longitudinal mode and the torsional mode of the pipeline obtained by solving the method with the theoretical dispersion curve;
FIG. 7 is a graph showing the comparison of a phase velocity dispersion curve and a theoretical dispersion curve of a bending mode of a pipeline obtained by solving the method;
FIG. 8 is a graph showing the comparison of a group velocity dispersion curve and a theoretical dispersion curve of a bending mode of a pipeline obtained by solving the method;
FIG. 9 is a schematic diagram showing the comparison of the phase velocity dispersion curve and the theoretical dispersion curve of each mode of the circumferential guided wave of the pipeline obtained by solving the method;
FIG. 10 is a graph showing the comparison of a group velocity dispersion curve and a theoretical dispersion curve of each mode of a circumferential guided wave of a pipeline obtained by solving the method;
FIG. 11 is a diagram of a radial displacement wave structure of the longitudinal mode L (0, 1) obtained by solving the method at the frequency of 0.492 MHz;
FIG. 12 is a diagram of the axial displacement wave structure of the longitudinal mode L (0, 1) at the frequency of 0.492MHz obtained by solving the method;
FIG. 13 is a diagram of a radial displacement wave structure of a Zhou Xianglei lamb wave CLT0 mode at a frequency of 0.514MHz, obtained by solving the method;
fig. 14 is a diagram of an axial displacement wave structure of a circumferential SH wave CSH0 mode obtained by solving by the method at a frequency of 0.710 MHz.
Detailed Description
Example 1
The following method examples for calculating the axial ultrasonic guided wave dispersion relation of the pipeline are provided by combining the content of the method, and the correctness of the method is verified by comparing the method with the theoretical calculation result, and the specific steps are shown in the figure 1:
1) And (3) carrying out uniform displacement solution on particle vibration of the guided wave in different directions in the circular tube to express wave propagation along the axial direction and the circumferential direction of the pipeline, and deducing to obtain a weak form expansion of a fluctuation control equation of the axial guided wave in the anisotropic tube under a cylindrical coordinate system:
2) The weak form partial differential equation module in commercial finite element software COMSOL Multiphysics 6.0.0 is used for analysis, and characteristic value research is selected. And constructing a one-dimensional model in the radial direction of the pipeline, wherein the inner radius of the pipeline model is 12mm, and the outer radius of the pipeline model is 15mm. The three-dimensional pipeline model and the wave propagation schematic diagram are shown in fig. 2, and the one-dimensional finite element model selection schematic diagram is shown in fig. 4.
3) Defining the elastic stiffness constant of the anisotropic material, the radial dimension of the pipeline, the wave number, the angular frequency and the coefficient K in a parameter column z And Zhou Xiangjie m times. The wave number and the angular frequency are set to 0, K Z =1, when solving the longitudinal mode L (0, n) and the torsional mode T (0, n), m=0 is set; when solving the bending mode F (1, n), m=1 is set. Wherein the material parameters of the pipe: young's modulus of 2.09GPa, poisson's ratio of 0.29 and density of 7824kg/m 3 The corresponding stiffness matrix is:
4) The derived weak expression is entered in one of the input fields of the weak form partial differential equation module, and the other two are set to 0. Defining the angular frequency as a eigenvalue, the integrated function in the wave control equation weak form is converted into a weak expression that COMSOL can read:
2*pi*r*((u3r+Kz*k*u1*i)*(C25*(conj(test(u1))/r-(m*conj(test(u2))*i)/r)-
C45*(Kz*conj(test(u2))*conj(k)*i+(m*conj(test(u3))*i)/r)-
C56*(conj(test(u2))/r-conj(test(u2r))+(m*conj(test(u1))*i)/r)+
C15*conj(test(u1r))+C55*(conj(test(u3r))-Kz*conj(test(u1))*conj(k)*i)-
C35*Kz*conj(test(u3))*conj(k)*i)+(u2r-u2/r+
(m*u1*i)/r)*(C26*(conj(test(u1))/r-(m*conj(test(u2))*i)/r)-
C46*(Kz*conj(test(u2))*conj(k)*i+(m*conj(test(u3))*i)/r)-
C66*(conj(test(u2))/r-conj(test(u2r))+(m*conj(test(u1))*i)/r)+
C16*conj(test(u1r))+C56*(conj(test(u3r))-Kz*conj(test(u1))*conj(k)*i)-
C36*Kz*conj(test(u3))*conj(k)*i)+u1r*(C12*(conj(test(u1))/r-
(m*conj(test(u2))*i)/r)-C14*(Kz*conj(test(u2))*conj(k)*i+
(m*conj(test(u3))*i)/r)-C16*(conj(test(u2))/r-conj(test(u2r))+
(m*conj(test(u1))*i)/r)+C11*conj(test(u1r))+C15*(conj(test(u3r))-
Kz*conj(test(u1))*conj(k)*i)-C13*Kz*conj(test(u3))*conj(k)*i)+
((m*u3*i)/r+Kz*k*u2*i)*(C24*(conj(test(u1))/r-(m*conj(test(u2))*i)/r)-
C44*(Kz*conj(test(u2))*conj(k)*i+(m*conj(test(u3))*i)/r)-
C46*(conj(test(u2))/r-conj(test(u2r))+(m*conj(test(u1))*i)/r)+
C14*conj(test(u1r))+C45*(conj(test(u3r))-Kz*conj(test(u1))*conj(k)*i)-
C34*Kz*conj(test(u3))*conj(k)*i)+(u1/r+
(m*u2*i)/r)*(C22*(conj(test(u1))/r-(m*conj(test(u2))*i)/r)-
C24*(Kz*conj(test(u2))*conj(k)*i+(m*conj(test(u3))*i)/r)-
C26*(conj(test(u2))/r-conj(test(u2r))+(m*conj(test(u1))*i)/r)+
C12*conj(test(u1r))+C25*(conj(test(u3r))-Kz*conj(test(u1))*conj(k)*i)-
C23*Kz*conj(test(u3))*conj(k)*i)-lambda^2*rho*conj(test(u1))*u1-
lambda^2*rho*conj(test(u2))*u2-lambda^2*rho*conj(test(u3))*u3+
Kz*k*u3*(C23*(conj(test(u1))/r-(m*conj(test(u2))*i)/r)-
C34*(Kz*conj(test(u2))*conj(k)*i+(m*conj(test(u3))*i)/r)-
C36*(conj(test(u2))/r-conj(test(u2r))+(m*conj(test(u1))*i)/r)+
C13*conj(test(u1r))+C35*(conj(test(u3r))-Kz*conj(test(u1))*conj(k)*i)-
C33*Kz*conj(test(u3))*conj(k)*i)*i)
wherein conj is a complex conjugate function; m is Zhou Xiangjie times; lambda is the characteristic value, namely the angular frequency, of the wave number during parameterized scanning; the test () function represents a test function.
5) And (3) meshing the finite element model, and selecting a finer size. And adding parametric scanning to scan the wave number k, wherein the scanning range is [0,5 pi/a ], and a is the thickness of the pipeline. In eigenvalue solution, the number of needed eigenvalues is set to 20.
6) In the "result" of the COMSOL software, the wavenumber and angular frequency are obtained, where angular frequency ω=2pi/f, using phase velocity calculation formula V p =2pi f/k and group velocity calculation formula V g The dispersion relation of the waveguide structure is calculated =2pi Δf/Δk. The dispersion curves are shown in fig. 5, 6, 7 and 8.
7) And respectively drawing wave structure diagrams in different directions by one-dimensional drawing groups added into finite element software. The normalized wave structure diagram is shown in fig. 11 and 12.
Example 2
The following examples of calculation methods of circumferential guide frequency dispersion relation of a pipeline structure are provided by combining the content of the method, and the correctness of the method is verified by comparing the results of theoretical calculation, and the specific steps are shown in figure 1: 1) And (3) for particle vibration of sound waves in different directions in the circular tube, uniform displacement solutions are adopted to express wave propagation along the axial direction and the circumferential direction of the pipeline, and weak form expansion of a wave control equation of circumferential guided waves in the anisotropic tube under a cylindrical coordinate system is obtained by deduction:
2) And selecting a weak form partial differential equation module in finite element analysis software COMSOL Multiphysics 6.0.0 for analysis, and selecting a characteristic value research. And constructing a one-dimensional model in the radial direction of the pipeline, wherein the inner radius of the pipeline model is 12mm, and the outer radius of the pipeline model is 15mm. The three-dimensional pipeline model and the wave propagation schematic diagram are shown in fig. 3, and the one-dimensional finite element model selection schematic diagram is shown in fig. 4.
3) Defining the elastic stiffness constant of the anisotropic material, the radial dimension of the pipeline, the wave number, the angular frequency and the coefficient K in a parameter column z The number of angles m. The wave number and the angular frequency are set to 0, K z The angle wave number m=kr1, and r1=13.5mm is the intermediate value of the inner radius and the outer radius of the circular tube; wherein the material parameters of the pipeline:
young's modulus of 2.09GPa, poisson's ratio of 0.29 and density of 7824kg/m 3 . Corresponding stiffness moment
The array is as follows:
4) The derived weak expression is entered in one of the input fields of the weak form partial differential equation module, and the other two are set to 0. Defining angular frequency as characteristic value, and forming weak shape of pipeline wave control equation
The multiplicative function in the equation is converted into a weak expression that can be read by COMSOL:
2*pi*r*((u3r+Kz*k*u1*i)*(C25*(conj(test(u1))/r-(m*conj(test(u2))*i)/r)-
C45*(Kz*conj(test(u2))*conj(k)*i+(m*conj(test(u3))*i)/r)-
C56*(conj(test(u2))/r-conj(test(u2r))+(m*conj(test(u1))*i)/r)+
C15*conj(test(u1r))+C55*(conj(test(u3r))-Kz*conj(test(u1))*conj(k)*i)-
C35*Kz*conj(test(u3))*conj(k)*i)+(u2r-u2/r+
(m*u1*i)/r)*(C26*(conj(test(u1))/r-(m*conj(test(u2))*i)/r)-
C46*(Kz*conj(test(u2))*conj(k)*i+(m*conj(test(u3))*i)/r)-
C66*(conj(test(u2))/r-conj(test(u2r))+(m*conj(test(u1))*i)/r)+
C16*conj(test(u1r))+C56*(conj(test(u3r))-Kz*conj(test(u1))*conj(k)*i)-
C36*Kz*conj(test(u3))*conj(k)*i)+u1r*(C12*(conj(test(u1))/r-
(m*conj(test(u2))*i)/r)-C14*(Kz*conj(test(u2))*conj(k)*i+
(m*conj(test(u3))*i)/r)-C16*(conj(test(u2))/r-conj(test(u2r))+
(m*conj(test(u1))*i)/r)+C11*conj(test(u1r))+C15*(conj(test(u3r))-
Kz*conj(test(u1))*conj(k)*i)-C13*Kz*conj(test(u3))*conj(k)*i)+
((m*u3*i)/r+Kz*k*u2*i)*(C24*(conj(test(u1))/r-(m*conj(test(u2))*i)/r)-
C44*(Kz*conj(test(u2))*conj(k)*i+(m*conj(test(u3))*i)/r)-
C46*(conj(test(u2))/r-conj(test(u2r))+(m*conj(test(u1))*i)/r)+
C14*conj(test(u1r))+C45*(conj(test(u3r))-Kz*conj(test(u1))*conj(k)*i)-
C34*Kz*conj(test(u3))*conj(k)*i)+(u1/r+
(m*u2*i)/r)*(C22*(conj(test(u1))/r-(m*conj(test(u2))*i)/r)-
C24*(Kz*conj(test(u2))*conj(k)*i+(m*conj(test(u3))*i)/r)-
C26*(conj(test(u2))/r-conj(test(u2r))+(m*conj(test(u1))*i)/r)+
C12*conj(test(u1r))+C25*(conj(test(u3r))-Kz*conj(test(u1))*conj(k)*i)-
C23*Kz*conj(test(u3))*conj(k)*i)-lambda^2*rho*conj(test(u1))*u1-
lambda^2*rho*conj(test(u2))*u2-lambda^2*rho*conj(test(u3))*u3+
Kz*k*u3*(C23*(conj(test(u1))/r-(m*conj(test(u2))*i)/r)-
C34*(Kz*conj(test(u2))*conj(k)*i+(m*conj(test(u3))*i)/r)-
C36*(conj(test(u2))/r-conj(test(u2r))+(m*conj(test(u1))*i)/r)+
C13*conj(test(u1r))+C35*(conj(test(u3r))-Kz*conj(test(u1))*conj(k)*i)-
C33*Kz*conj(test(u3))*conj(k)*i)*i)
wherein conj is a complex conjugate function; lambda is the characteristic value, namely the angular frequency, of the wave number during parameterized scanning; m is the angular number, m=kr1; k is the circumferential wave number; the test () function represents a test function.
5) And (3) meshing the finite element model, and selecting a finer size. And adding parametric scanning to scan the wave number k, wherein the scanning range is [0,5 pi/a ], and a is the thickness of the pipeline. In eigenvalue solution, the number of needed eigenvalues is set to 20.
6) Adding global calculation to the "result" of the COMSOL software to obtain wave number and angular frequency, wherein ω=2pi/f, and calculating a formula V by using the phase velocity p =2pi f/k and group velocity calculation formula V g The dispersion relation of the waveguide structure is calculated =2pi Δf/Δk. The dispersion curves are shown in fig. 9 and 10.
7) And respectively drawing wave structure diagrams in different directions by one-dimensional drawing groups added into finite element software. The normalized wave structure diagram is shown in fig. 13 and 14.
The invention discloses a method for calculating ultrasonic guided wave dispersion characteristics of a pipeline structure, which comprises the following steps: for particle vibration of guided waves in different directions in a circular tube, uniform displacement solutions are adopted to express wave propagation along the axial direction and the circumferential direction of a pipeline, and weak forms of wave control equations of the axial and the circumferential guided waves in an anisotropic tube under a cylindrical coordinate system are deduced; establishing a one-dimensional finite element model in the radial direction of the pipeline by utilizing the symmetry of the pipeline; defining a wave-guiding wave equation weak form expression in finite element software, and respectively calculating wave-guiding dispersion characteristics propagated along different directions of a circular tube by setting parameters in the weak form expression; the invention only needs to establish a one-dimensional finite element model of the pipeline, and can quickly solve the ultrasonic guided wave dispersion relation propagated in different directions in the pipeline through simple parameter setting without tedious programming.
Finally, it should be noted that: the invention is not limited to the specific embodiments described above, but various obvious changes, readjustments and substitutions can be made by a person skilled in the art without departing from the scope of the invention. Therefore, while the present invention has been described in detail with reference to the above-identified embodiments, it is not limited to the above-identified embodiments, but may include many other equivalent embodiments without departing from the spirit of the invention, the scope of which is defined by the appended claims.
Claims (4)
1. The method for calculating the ultrasonic guided wave dispersion characteristic of the pipeline structure is characterized by comprising the following steps of:
(1) for particle vibration of sound waves in different directions in a circular tube, uniform displacement solutions are adopted to express wave propagation along the axial direction and the circumferential direction of a pipeline, and weak forms of wave control equations of axial and circumferential guided waves in an anisotropic tube under a cylindrical coordinate system are deduced;
(2) utilizing the symmetry of the pipeline structure to establish a one-dimensional finite element model of the pipeline, wherein the model size is the thickness size along the radial direction of the pipeline;
(3) defining a weak form expression of a fluctuation control equation for uniformly expressing the axial and circumferential guided waves of the pipeline in finite element software;
(4) setting parameters m and K in the weak expression according to the types of the solved axial guided wave and the circumferential guided wave Z Wherein m is Zhou Xiangjie times, K Z Is the coefficient of the wave vector. Defining material parameters of the pipeline, radial dimension parameters of the pipeline and parameters of parameterized scanning;
(5) adding parameterized scanning, and setting a eigenvalue solution;
(6) passing the obtained result through a phase velocity formula V p =2pi f/k and group velocity formula V g =2pi Δf/Δk, phase velocity and group velocity of each mode are calculated and dispersion curves are drawn,
wherein Δf is the difference between adjacent frequency points in the same mode, and Δk is the difference between adjacent wave numbers;
(7) in finite element software, a one-dimensional drawing is added to draw wave structure diagrams in different directions respectively.
2. The method for calculating the dispersion characteristics of ultrasonic guided waves of a pipeline structure according to claim 1, wherein the waveguide structure is a hollow circular tube, and the solved ultrasonic guided waves are axial guided waves and circumferential guided waves.
3. The method for calculating the ultrasonic guided wave dispersion characteristics of a pipeline structure according to claim 1, wherein the displacement solutions of the axial and circumferential guided wave propagation of the pipeline are represented in a unified manner, and the displacement solutions are represented by the following formula:
in the above formula, m is Zhou Xiangjie times; k (K) Z Is a coefficient of the wave vector component.
4. The method for calculating the ultrasonic guided wave dispersion characteristics of a pipeline structure according to claim 1, wherein parameters m and K in the weak expression are set according to the types of the solved axial guided wave and the circumferential guided wave, respectively Z The method specifically comprises the following steps: when solving the L (0, n) longitudinal mode and the T (0, n) torsional mode, let K Z =1, zhou Xiangjie times m=0; when solving F (m, n) bending mode, let K Z =1, zhou Xiangjie times m is a positive integer; when solving the circumferential guided wave, let K Z =0, and the number of angles m=kr.
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