CN117113746A - Spiral guided wave dispersion curve solving method based on periodic boundary conditions - Google Patents
Spiral guided wave dispersion curve solving method based on periodic boundary conditions Download PDFInfo
- Publication number
- CN117113746A CN117113746A CN202310903662.9A CN202310903662A CN117113746A CN 117113746 A CN117113746 A CN 117113746A CN 202310903662 A CN202310903662 A CN 202310903662A CN 117113746 A CN117113746 A CN 117113746A
- Authority
- CN
- China
- Prior art keywords
- guided wave
- spiral
- dispersion curve
- periodic
- solving
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Pending
Links
- 239000006185 dispersion Substances 0.000 title claims abstract description 69
- 230000000737 periodic effect Effects 0.000 title claims abstract description 40
- 238000000034 method Methods 0.000 title claims abstract description 29
- 238000004364 calculation method Methods 0.000 claims abstract description 12
- 239000000463 material Substances 0.000 claims abstract description 6
- 239000002131 composite material Substances 0.000 claims abstract description 3
- 238000005452 bending Methods 0.000 claims description 27
- 238000006073 displacement reaction Methods 0.000 claims description 20
- 239000011159 matrix material Substances 0.000 claims description 8
- 229920001971 elastomer Polymers 0.000 claims description 4
- 239000000806 elastomer Substances 0.000 claims description 4
- 125000004122 cyclic group Chemical group 0.000 claims description 3
- 238000013016 damping Methods 0.000 claims description 2
- 238000009659 non-destructive testing Methods 0.000 abstract description 3
- 230000036541 health Effects 0.000 abstract description 2
- 238000012544 monitoring process Methods 0.000 abstract description 2
- 230000001737 promoting effect Effects 0.000 abstract description 2
- 230000007547 defect Effects 0.000 description 7
- 238000010586 diagram Methods 0.000 description 6
- 238000001514 detection method Methods 0.000 description 5
- 230000007246 mechanism Effects 0.000 description 4
- 239000002245 particle Substances 0.000 description 4
- 238000011160 research Methods 0.000 description 4
- 238000005516 engineering process Methods 0.000 description 3
- 230000008569 process Effects 0.000 description 3
- 230000008901 benefit Effects 0.000 description 2
- 230000005284 excitation Effects 0.000 description 2
- 241000276425 Xiphophorus maculatus Species 0.000 description 1
- 238000004458 analytical method Methods 0.000 description 1
- 238000013459 approach Methods 0.000 description 1
- 238000011161 development Methods 0.000 description 1
- 238000003384 imaging method Methods 0.000 description 1
- 230000035945 sensitivity Effects 0.000 description 1
- 239000007787 solid Substances 0.000 description 1
- 230000007480 spreading Effects 0.000 description 1
- -1 threaded pipes Substances 0.000 description 1
Classifications
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/20—Design optimisation, verification or simulation
- G06F30/23—Design optimisation, verification or simulation using finite element methods [FEM] or finite difference methods [FDM]
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F2113/00—Details relating to the application field
- G06F2113/14—Pipes
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F2113/00—Details relating to the application field
- G06F2113/26—Composites
Abstract
The invention discloses a method for solving a spiral guided wave dispersion curve based on periodic boundary conditions, which utilizes the periodic boundary conditions to solve the calculation of the spiral guided wave dispersion curve of any periodic variation circular tubular waveguide, such as circular pipes of various materials, such as a threaded pipe, a composite material pipe and the like. Firstly, calculating a dispersion curve of axial guided waves in a tubular structure under different frequencies by adopting a Floquet periodic boundary condition and a circularly symmetric boundary condition; then, a relational expression of the axial guided wave dispersion curve and the spiral guided wave dispersion curve is established, the group velocity of the spiral guided wave is solved, and the phase velocity of the spiral guided wave is solved by adopting a differential method according to the high-frequency convergence of the dispersion curve. The method solves the problem of solving the spiral guided wave dispersion curve of the tubular structure, and has important significance for promoting the further nondestructive testing and structural health monitoring of the spiral guided wave of the large-scale tubular structure.
Description
Technical Field
The invention aims to develop a method for solving a spiral guided wave dispersion curve based on periodic boundary conditions, solves the problem of solving the spiral guided wave dispersion curve in any material tubular structure, and has important significance for promoting the further nondestructive testing and structural health monitoring research of the spiral guided wave of a large tubular structure.
Background
In recent years, research on ultrasonic guided waves in tubular structures has been focused mainly on two major categories of axial guided waves and circumferential guided waves, wherein the axial guided wave modes mainly include a torsional mode T (0, n), a longitudinal mode L (0, n) and a bending mode F (m, n), and the circumferential guided wave modes mainly include lamb-like waves (antisymmetric mode and symmetric mode) and horizontal shear waves. The axial guided wave is suitable for detecting circumferential distribution defects in the pipeline in a long distance, and the axial distribution defects are difficult to judge, so that the detection accuracy is low; the circumferential guide wave is suitable for detecting the axial distribution defects in the pipeline in a short distance, and has lower sensitivity for detecting the circumferential distribution defects; the spiral guided wave propagates along any spiral angle, so that the spiral guided wave can fully act on any type of defect, defect information is fully contained in the spiral guided wave, and high-precision detection of any defect is realized. Therefore, in order to solve the problem of low detection precision of long-distance and large-range ultrasonic guided waves in a tubular structure, researchers begin to research a spiral guided wave nondestructive detection technology capable of realizing high-precision detection. However, the solving method of the spiral guided wave dispersion curve in the tubular structure is not reported at home and abroad at present. Therefore, development of a method for solving the spiral guided wave dispersion curve in the tubular structure is highly needed. The method provides theoretical support for a spiral guided wave nondestructive testing technology in the tubular structure, and compensates for the application of a platy structure imaging technology in damage positioning in the tubular structure.
At present, the research of a spiral guided wave dispersion curve solving method based on a tubular structure is still in a preliminary stage, and a plurality of problems need to be solved, and the method mainly comprises the following steps: 1. how to solve the axial guided wave dispersion curve of the tubular structure by utilizing the periodic boundary conditions; 2. how to determine the relation expression of the axial group velocity and the spiral group velocity, and solving the group velocity of the spiral guided wave; 3. how to solve the phase velocity of the helical guided wave by using a differential method.
Disclosure of Invention
The invention aims to provide a method for solving a spiral guided wave dispersion curve based on periodic boundary conditions, which solves the problem of solving the spiral guided wave dispersion curve in a tubular structure.
By combining the problems, the method calculates the dispersion curves of the axial guided waves under different Zhou Xiangjie times in the tubular structure by adopting the Floquet periodic boundary conditions, then establishes a relational expression of the axial guided wave dispersion curves and the spiral guided wave dispersion curves, solves the group velocity of the spiral guided waves, and solves the phase velocity of the spiral guided waves by adopting a differential method according to the high-frequency convergence of the dispersion curves.
Based on the periodic boundary condition frequency dispersion curve solving principle, a finite element vibration equation of an elastomer is established through the Darby principle, and the motion equation is that
M is a mass coefficient matrix;
c, damping coefficient matrix;
k, a rigidity coefficient matrix;
f-load vector;
u-displacement vector;
-the first derivative of the displacement vector;
-the second derivative of the displacement vector.
When solving for the characteristic frequency, the finite element is in an undamped free vibration state, i.e., c=f=0. The displacement equation is
u＝Ue iωt (2)
U in the formula is a displacement vector matrix;
omega-angular frequency;
t-time.
Based on the above conditions, equation (1) can be simplified to
[K-ω 2 M]U＝0 (3)
The tubular structure (i.e., elastomer) is first discretized into periodic unit cells as shown in fig. 1. The periodic boundary condition of Floque is applied to the source surface and the target surface (the source surface and the target surface are parallel surfaces) of the unit cell, so that the periodic extension of the unit cell is realized, and the infinite tubular structure is simulated. The Floquet periodic boundary condition displacement field equation is
K-wave number in the formula;
u dst -a target surface displacement field;
u src -a source surface displacement field;
r—boundary space coordinates to which the boundary conditions apply.
The cyclic symmetry boundary condition is applied to the unit cell, so that the circumferential extension of the unit cell is realized, and the tubular structure is simulated. The displacement field equation of the circularly symmetric boundary condition is
Wherein R (θ) s ) -a loop boundary function;
m-Zhou Xiangjie times;
θ s -the corresponding fan angle of the unit cell.
Establishing an infinite pipe waveguide model, as shown in fig. 2, fig. 2 (a) is an infinite pipe waveguide diagram, fig. 2 (b) is an infinite pipe unit cell diagram, and the fan angle is theta s Here θ s The smaller and better the value of (2) is on the premise of meeting the calculation requirement, so as to prevent the occurrence of folding and pseudo modes, and the sector angle theta is usually s Less than or equal to 1 degree. The theory is applied to the tubular waveguide, as shown in fig. 3, the Floquet periodic boundary condition is added to the red parallel surface of the unit cell model, so that the unit cell model is periodically expanded in the axial direction to simulate an infinitely long tubular structure, and the circularly symmetric boundary condition is added to the red circumferential section of the unit cell model, so that the unit cell model is circularly and symmetrically expanded in the circumferential direction to simulate an infinitely large tubular waveguide, and calculation is greatly simplified.
Then defining the value range of wave number k and scanning by parameterizationThe characteristic frequency is obtained, and a characteristic frequency-wave number diagram is drawn to obtain dispersion curves of the periodic waveguide structure, as shown in fig. 4, the dispersion curves are generally periodic relative to wave numbers, and at low frequencies, the dispersion curves obtained by periodic boundary conditions are similar to those obtained by calculation by a semi-analytic finite element method, but at higher frequencies, additional curves appear. These additional curves are so-called fold phenomena, which are caused by the dispersion curves repeatedly folding over each other, as a direct result of the boundary conditions. When the curve reaches the wave numberThis occurs when s is the distance between two parallel planes and the selected unit cell is not the smallest repeatable unit cell. Therefore, it is possible to increase the wave number +.>To mitigate folding. For periodic waveguides, maximum wavenumber +.>Will be limited by the periodic characteristics but not by the uniform waveguide. That is, in the case of using a uniform waveguide, the unit cell can be reduced to such an extent that it is necessary to eliminate the band folding from the frequency wavenumber region of interest.
Next, the value of Zhou Xiangjie m is determined, the dispersion curve of the periodic waveguide structure under different Zhou Xiangjie times is calculated, and fig. 5 is the 0-10 order axial guided wave dispersion curve in the circular tube. The axial guided wave modes in the circular tube mainly comprise axisymmetric modes (torsion modes T (0, n), longitudinal modes L (0, n)) and non-axisymmetric modes (bending modes F (m, n)), and the spiral guided wave is firstly defined to be a set of different Zhou Xiangjie bending modes including the torsion modes T (0, n) and the longitudinal modes L (0, n), wherein the torsion modes T (0, n) and the longitudinal modes L (0, n) are bending modes with Zhou Xiangjie times being zero, and the characteristic frequency of the spiral guided wave is the dispersion characteristic of the bending modes under a spiral path.
Therefore, the dispersion characteristic of the bending mode under the spiral path is solved to be the dispersion curve of the spiral guided wave. The displacement field propagation term of the bending mode excited by the harmonic wave in the uniform isotropic circular tube structure based on the spiral propagation mechanism of the bending mode is
K in z -axial wave number;
omega-angular frequency;
m-Zhou Xiangjie times;
θ—circumferential angle.
The phase can be expressed as
φ＝ωt-k z z+mθ (7)
Phi-phase in middle
The axial phase velocity is
Lambda in z -axial wavelength;
t-wavelength period.
Assuming that the phase is 0 and the time is one wavelength period T, the equation (8) is substituted into the equation (7) to obtain the relational expression (9) of the axial distance z and the circumferential angle θ when the phase is 0, and the equation (10) is obtained when the circumferential angles are 0 and 2 pi, respectively.
The wave source is used to transmit vibration to the medium to form wave front, and each wave front has the same vibration phase and each particle can be used as the wave source for the next particle. As can be seen from the formula (9), the axial distance and the circumferential angle are in a linear relationship, when the phase is0, the wave front in the circular tube is a spiral line, namely a straight line with an inclined angle in the expansion plate, and the inclined angle is the spiral angle beta in the circular tube, as shown in fig. 6, and the wave front in the circular tube and the wave front in the expansion plate corresponding to the inclined angle beta. Based on the wavefront principle, each particle on the wavefront of the bending mode can be used as a source of the next particle propagation, so that the bending mode can be obtained by loading the helical line in the circular tube with load. FIG. 7 is a graph showing a helical propagation mechanism of bending mode, in which a blue inclined line shows a helical load wave source exciting bending mode, the inclined angle is a helix angle, axial intervals between two ends of the wave source are mλ, and the circumferential expansion distance is 2πR m Wherein R is m Is the average value of the inner diameter and the outer diameter of the circular tube; the solid purple line shows a bending mode propagation path, and it is known from the wavefront theory that the wave propagation direction is perpendicular to the wave source, and the bending mode propagates in a direction having a helix angle with the axial direction. From the geometric relationship in fig. 7, bending mode excitation and wave propagation helix angle can be expressed by equation (11). The helix angle expression will be used in the bending mode spiral solution process.
And finally, solving the spiral path bending mode dispersion characteristic, namely the spiral guided wave dispersion characteristic. In a uniformly isotropic circular tube, the bending mode displacement field propagation term under harmonic excitation represented by a helical path can be expressed as
K in s -helical wave number;
s-distance travelled under the spiral path.
Spiral phase velocity C ps And spiral group velocity C gs The expression is equation (13), and the relationship between the screw group velocity and the screw phase velocity satisfies equation (14).
The helical group velocity and the axial group velocity satisfy the same Time-of-Flight (Time-of-Flight) during wave propagation to obtain equation (15).
S is the propagation distance of a spiral path;
z—axial propagation distance.
Based on the spiral propagation mechanism diagram of the bending mode of FIG. 7, the expression of the spiral group velocity and the axial group velocity is obtained by taking the formula (11) into the formula (15)
The helical guided wave group velocity can be calculated from equation (16) as shown in fig. 8. The spiral phase velocity may then be iteratively derived from the spiral group velocity according to equation (14) in relation to the spiral phase velocity. The derivative of the formula (14) about the spiral phase velocity can be approximated by a difference, and then the spiral phase velocity dispersion curve can be obtained by determining only one initial spiral phase velocity triggering iteration process. Since the bending mode phase velocities of the circumferential orders are approximately equal at high frequencies, independent of Zhou Xiangjie times, i.e., independent of the helix angle, the helical phase velocity at high frequencies can be approximated by the axial phase velocity. Therefore, the forward difference is adopted in the formula (14), the axial phase velocity with high approximation accuracy is used as an initial value to trigger a reverse iteration process, a spiral phase velocity dispersion curve is obtained, the spiral phase velocity iteration formula is shown as the formula (17), and the spiral guided wave phase velocity is calculated and obtained as shown in fig. 9.
The invention has the following advantages: a major advantage of this approach is that it has a relatively fast calculation speed and is very simple to implement. Any commercial finite element software that supports Floquet periodic boundary conditions and/or circularly symmetric boundary conditions can perform these calculations. Thus, the method does not require a complete understanding of the finite element theory of the semi-analytical finite element method, but provides an accurate dispersion curve that is critical to helical guided wave studies. In addition, the method can be applied to spiral guided wave calculation of many other periodically changing waveguides, such as round pipes of various materials, such as threaded pipes, composite pipes and the like.
Drawings
FIG. 1 is a periodic unit cell of an elastomer that is discretizable.
Fig. 2 is an infinite tube waveguide model. (a) an infinite tube waveguide schematic; (b) infinite cell schematic diagram.
Fig. 3 is a schematic diagram of the application of periodic boundary conditions to a tubular waveguide. (a) a periodic unit cell; (b) a Floquet period boundary condition; (c) a circularly symmetric boundary condition.
Fig. 4 is a dispersion curve of a periodic waveguide structure. (a) a frequency wavenumber curve; (b) a phase velocity dispersion curve.
Fig. 5 is a graph of the dispersion of periodic waveguide structures at different Zhou Xiangjie times. (a) a frequency wavenumber curve; (b) a phase velocity dispersion curve.
Fig. 6 shows the wavefront in the tube and the wavefront in the expansion plate corresponding thereto. (a) wavefront (helix) in the tube; (b) spreading the wavefront (tilting line) in the plate.
Fig. 7 is a graph of the spiral propagation mechanism of bending modes.
Fig. 8 is a graph of helical guided wave group velocity.
Fig. 9 is a graph of helical guided wave phase velocity.
Detailed Description
In the embodiment, the spiral guided wave dispersion curve based on the periodic boundary condition is solved by adopting the com software and the matlab software.
Taking the calculation of a spiral guided wave dispersion curve in a circular tube as an example, the specific operation steps are as follows:
step 1: geometric modeling is performed based on modeling software and material properties are added. Calculating the dispersion curve of the periodic waveguide structure requires establishing a minimum waveguide unit, i.e. a unit cell structure, and a circular tube structure preferably establishes a fan-shaped angle theta s The unit cell structure with the angle less than or equal to 1 degree can prevent the folding phenomenon of a dispersion curve by minimizing the sector angle, and can also avoid the occurrence of a pseudo mode, and the maximum sector angle theta at present s The calculated result is better at less than or equal to 1 degree. The inner diameter of the model constructed in this embodiment is R inner =186 mm, outer diameter R outer 186mm, thickness s=1mm, fan angle is angle θ s =1°, as shown in fig. 2. The material has Young modulus 206GPa, poisson's ratio 0.28 and density 7800kg/m 3 。
Step 2: and setting boundary conditions and meshing the cell structure. And setting boundary conditions of the cell structure, and adding Floque period boundary conditions and circularly symmetric boundary conditions on corresponding surfaces respectively, as shown in figure 3. Setting Zhou Xiangjie m values in the cyclic symmetry boundary condition, and modifying m values can calculate the dispersion curves of the periodic waveguide structures under different Zhou Xiangjie times. And (3) carrying out grid division on the unit cell structure, wherein the size of the grid has small influence on the solution of the characteristic frequency, so that a conventional grid is selected.
Step 3: and carrying out characteristic frequency solving on the cell model with the boundary setting and grid division completed. According toAnd (3) carrying out characteristic frequency solving on the unit cell structure according to formulas 1-5 in the value range of the artificial wave number k, and solving the characteristic frequency through parameterized scanning. The parameter scanning is to set a parameter each time, the model is operated again, the operation between different parameters is independent, and the value range of the parameter k is +.>The number of required characteristic frequencies is arbitrarily set to a required value, and the characteristic frequency search reference value is 0Hz. The default solver is a PARDISO, i.e., a direct linear solver. Global counting after calculationAnd calculating to obtain the characteristic frequency-wave number result of the unit cell. FIG. 4 is a graph of 0 th order axial guided wave dispersion in a circular tube, and FIG. 5 is a graph of 0-10 th order axial guided wave dispersion in a circular tube. The mid-frequency dispersion curve is generally periodic with respect to wavenumber, and at low frequencies, the dispersion curve obtained by the periodic boundary conditions will be similar to the dispersion curve calculated by the semi-analytical finite element method, but at higher frequencies, additional curves will occur. These additional curves are the so-called fold phenomenon, which is caused by the dispersion curves repeatedly folding over each other, which is a direct result of the boundary conditions. When the curve reaches wavenumber->This occurs when s is the distance between two parallel planes and the selected unit cell is not the smallest repeatable unit cell. Therefore, it is possible to increase the wave number +.>To mitigate folding.
Step 4: and solving a spiral guided wave dispersion curve according to the characteristic frequency-wave number result. And carrying out formula deduction on the spiral guided wave according to the theory. First, defining a spiral guided wave as a set of bending modes under different Zhou Xiangjie times including a torsional mode T (0, n) and a longitudinal mode L (0, n), wherein the torsional mode T (0, n) and the longitudinal mode L (0, n) are bending modes with zero Zhou Xiangjie times, and the characteristic frequency of the spiral guided wave is the dispersion characteristic of the bending modes under a spiral path. And establishing a relational expression (16) of the axial guided wave dispersion curve and the spiral guided wave dispersion curve, solving the group velocity of the spiral guided wave, and solving the phase velocity of the spiral guided wave by adopting a differential method, namely a formula (17), according to the high-frequency convergence of the dispersion curve. In order to avoid the folding phenomenon of the dispersion curve, the data of 0-1000kHz in fig. 5, namely the dispersion curve without folding phenomenon, is extracted and the group velocity and phase velocity analysis are performed based on the formula (13), then the spiral guided wave group velocity is calculated according to the formula (16) as shown in fig. 8, and the spiral guided wave phase velocity is calculated according to the formula (17) as shown in fig. 9. The solution of the spiral guided wave dispersion curve can be completed.
Claims (1)
1. A method for solving a spiral guided wave dispersion curve based on a periodic boundary condition is characterized by comprising the following steps of: the method is applied to spiral guided wave calculation of any periodic variation circular tubular waveguide, wherein the any periodic variation circular tubular waveguide comprises a threaded circular pipe and a composite circular pipe; the method comprises the following steps:
step 1: establishing a geometric model of the periodically-changing circular tube based on modeling software, and adding material properties; calculating the dispersion curve of the periodically-changing circular tube waveguide structure requires establishing a minimum circular tube waveguide unit, namely a unit cell structure, wherein the fan-shaped angle of the unit cell structure is less than 0 DEG and less than theta s ≤1°；
Step 2: setting boundary conditions and grid division of a unit cell structure; adding boundary conditions to the cell structure, and respectively adding Floque period boundary conditions and circularly symmetric boundary conditions to corresponding surfaces; setting a Zhou Xiangjie m value in a cyclic symmetry boundary condition, wherein the m value corresponds to a dispersion curve of the periodic waveguide structure under m Zhou Xiangjie times; the cell structure is subjected to grid division, and the size of the grid has small influence on the solution of the characteristic frequency, so that a conventional grid is selected;
step 3: carrying out characteristic frequency solving on a unit cell model with boundary setting and grid division completed; according toDefining a wave number k value range, carrying out characteristic frequency solving on a unit cell structure according to formulas 1-5, and solving the characteristic frequency through parameterized scanning; the parameter scanning is to set a parameter each time, the model is operated again, the operation between different parameters is independent, and the value range of the parameter k is +.>The number of the required characteristic frequencies is arbitrarily set as a required value, and the characteristic frequency searching reference value is 0Hz; the default solver is a PARDISO, namely a direct linear solver; performing global calculation after calculation to obtain a unit cell model characteristic frequency-wave number result; characteristic frequency-wavenumber plot versus waveThe number is periodic, the dispersion curve obtained by the periodic boundary condition is similar to the dispersion curve obtained by the semi-analytic finite element method calculation at low frequency of 0-1000kHz, but an additional curve can appear at high frequency of more than 1500kHz, and the wave number is increased>To mitigate folding;
establishing a finite element vibration equation of the elastomer according to the Darby principle, wherein the motion equation is as follows
M is a mass coefficient matrix;
c, damping coefficient matrix;
k, a rigidity coefficient matrix;
f-load vector;
u-displacement vector;
-the first derivative of the displacement vector;
-the second derivative of the displacement vector;
when the characteristic frequency is solved, the finite element is in an undamped free vibration state, namely C=f=0; the displacement equation is
u＝Ue iωt (2)
U in the formula is a displacement vector matrix;
omega-angular frequency;
t-time;
based on the above conditions, equation (1) is reduced to
[K-ω 2 M]U＝0 (3)
The Floquet periodic boundary condition displacement field equation is
K-wave number in the formula;
u dst -a target surface displacement field;
u src -a source surface displacement field;
r—boundary space coordinates applying boundary conditions;
the displacement field equation of the circularly symmetric boundary condition is
Wherein R (θ) s ) -a loop boundary function;
m-Zhou Xiangjie times;
θ s -sector angle corresponding to the unit cell;
step 4: solving a spiral guided wave dispersion curve according to the characteristic frequency-wave number result; firstly, defining a spiral guided wave as a set of bending modes under different Zhou Xiangjie times including a torsion mode T (0, n) and a longitudinal mode L (0, n), wherein the torsion mode T (0, n) and the longitudinal mode L (0, n) are bending modes with zero Zhou Xiangjie times, and the characteristic frequency of the spiral guided wave is the dispersion characteristic of the bending modes under a spiral path; establishing a relational expression (6) of an axial guided wave dispersion curve and a spiral guided wave dispersion curve, solving the group velocity of the spiral guided wave, and solving the phase velocity of the spiral guided wave by adopting a differential method, namely a formula (7), according to the high-frequency convergence of the dispersion curve;
c in the formula ps -helical phase velocity;
C gs -spiral group velocity;
C pz -axial phase velocity;
C gz -axial group velocity;
m-Zhou Xiangjie times;
beta-helix angle;
R a -average value of inner and outer diameters of circular tube; ω—angular frequency.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202310903662.9A CN117113746A (en) | 2023-07-23 | 2023-07-23 | Spiral guided wave dispersion curve solving method based on periodic boundary conditions |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202310903662.9A CN117113746A (en) | 2023-07-23 | 2023-07-23 | Spiral guided wave dispersion curve solving method based on periodic boundary conditions |
Publications (1)
| Publication Number | Publication Date |
|---|---|
| CN117113746A true CN117113746A (en) | 2023-11-24 |
Family
ID=88799245
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN202310903662.9A Pending CN117113746A (en) | 2023-07-23 | 2023-07-23 | Spiral guided wave dispersion curve solving method based on periodic boundary conditions |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN117113746A (en) |
Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN117594170A (en) * | 2024-01-17 | 2024-02-23 | 中国石油大学(华东) | Method and system for analyzing guided wave dispersion of plate-shell structure under temperature-stress coupling effect |
| CN117648584A (en) * | 2024-01-26 | 2024-03-05 | 中国石油大学(华东) | Guided wave mode classification method and system based on displacement vector similarity |
| CN117594170B (en) * | 2024-01-17 | 2024-04-26 | 中国石油大学(华东) | Method and system for analyzing guided wave dispersion of plate-shell structure under temperature-stress coupling effect |
-
2023
- 2023-07-23 CN CN202310903662.9A patent/CN117113746A/en active Pending
Cited By (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN117594170A (en) * | 2024-01-17 | 2024-02-23 | 中国石油大学(华东) | Method and system for analyzing guided wave dispersion of plate-shell structure under temperature-stress coupling effect |
| CN117594170B (en) * | 2024-01-17 | 2024-04-26 | 中国石油大学(华东) | Method and system for analyzing guided wave dispersion of plate-shell structure under temperature-stress coupling effect |
| CN117648584A (en) * | 2024-01-26 | 2024-03-05 | 中国石油大学(华东) | Guided wave mode classification method and system based on displacement vector similarity |
| CN117648584B (en) * | 2024-01-26 | 2024-04-30 | 中国石油大学(华东) | Guided wave mode classification method and system based on displacement vector similarity |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| O'donoghue et al. | The development and validation of a dynamic fracture propagation model for gas transmission pipelines | |
| Demma et al. | Scattering of the fundamental shear horizontal mode from steps and notches in plates | |
| Castaings et al. | Finite element model for waves guided along solid systems of arbitrary section coupled to infinite solid media | |
| Nguyen et al. | Numerical modeling of three-dimensional open elastic waveguides combining semi-analytical finite element and perfectly matched layer methods | |
| Belogol'Skii et al. | Pressure dependence of the sound velocity in distilled water | |
| CN108168746A (en) | Pipe is in the ultrasonic inspection system and method for uniaxial stress | |
| Hsu et al. | Mandrel effects on the dipole flexural mode in a borehole | |
| Wang et al. | A generalized model for space-coiling resonators | |
| Gallezot et al. | A modal approach based on perfectly matched layers for the forced response of elastic open waveguides | |
| Li et al. | Stress measurement for steel slender waveguides based on the nonlinear relation between guided wave group velocity and stress | |
| CN108469298A (en) | A kind of standing wave tube vector hydrophone calibration low frequency modification method | |
| CN117113746A (en) | Spiral guided wave dispersion curve solving method based on periodic boundary conditions | |
| Zhu et al. | Evaluation of cross-sectional deformation in pipes using reflection of fundamental guided-waves | |
| CN111060043B (en) | Ultrasonic thickness measurement method based on temperature compensation | |
| Zheng et al. | Effects of concrete on propagation characteristics of guided wave in steel bar embedded in concrete | |
| Khan et al. | Measurement of dynamic properties of stiff specimens using ultrasonic waves | |
| CN204571965U (en) | One joins water flooding well pipe external flux ultrasonic doppler measurements instrument | |
| Eybpoosh et al. | Investigation on the effects of environmental and operational conditions (EOC) on diffuse-field ultrasonic guided-waves in pipes | |
| CN114910753B (en) | Acoustic wave transmission device and detection method for GIL fault location | |
| Barshinger et al. | Ultrasonic guided wave propagation in pipes with viscoelastic coatings | |
| Periyannan et al. | Temperature dependent E and G measurement of materials using ultrasonic guided waves | |
| Ismaine et al. | New spectral displacement post-processing approach for modeling ultrasonic guided waves | |
| CN105548356A (en) | Method for detecting defects of small-bending-radius bend pipe with girth joint based on T-mode guided waves | |
| Sanderson et al. | The reflection of guided waves from multiple flaws in pipes | |
| Cui et al. | Excitation mechanisms and dispersion characteristics of guided waves in multilayered cylindrical solid media |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination |