CN112903157B - Stress monitoring method of circular tube type structure based on longitudinal mode ultrasonic guided waves - Google Patents

Stress monitoring method of circular tube type structure based on longitudinal mode ultrasonic guided waves Download PDF

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CN112903157B
CN112903157B CN202110071976.8A CN202110071976A CN112903157B CN 112903157 B CN112903157 B CN 112903157B CN 202110071976 A CN202110071976 A CN 202110071976A CN 112903157 B CN112903157 B CN 112903157B
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stress
phase velocity
ultrasonic guided
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circular tube
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CN112903157A (en
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刘金霞
付琳娜
崔志文
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Jilin University
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01L—MEASURING FORCE, STRESS, TORQUE, WORK, MECHANICAL POWER, MECHANICAL EFFICIENCY, OR FLUID PRESSURE
    • G01L1/00—Measuring force or stress, in general
    • G01L1/25—Measuring force or stress, in general using wave or particle radiation, e.g. X-rays, microwaves, neutrons
    • G01L1/255—Measuring force or stress, in general using wave or particle radiation, e.g. X-rays, microwaves, neutrons using acoustic waves, or acoustic emission
    • 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
    • G01N29/04—Analysing solids
    • G01N29/07—Analysing solids by measuring propagation velocity or propagation time of acoustic waves
    • 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
    • G01N29/04—Analysing solids
    • G01N29/12—Analysing solids by measuring frequency or resonance of acoustic waves
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N2291/00—Indexing codes associated with group G01N29/00
    • G01N2291/01—Indexing codes associated with the measuring variable
    • G01N2291/011—Velocity or travel time
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N2291/00—Indexing codes associated with group G01N29/00
    • G01N2291/01—Indexing codes associated with the measuring variable
    • G01N2291/014—Resonance or resonant frequency
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N2291/00—Indexing codes associated with group G01N29/00
    • G01N2291/02—Indexing codes associated with the analysed material
    • G01N2291/023—Solids
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01N—INVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N2291/00—Indexing codes associated with group G01N29/00
    • G01N2291/02—Indexing codes associated with the analysed material
    • G01N2291/028—Material parameters
    • G01N2291/02827—Elastic parameters, strength or force

Abstract

The utility model provides a stress monitoring method of tubular structure based on longitudinal mode supersound guided wave, includes: calculating a phase velocity frequency dispersion curve equation of the circular tube type structure and a curve equation of the phase velocity change value of the circular tube type structure along with the change of frequency; selecting the mode and frequency of the ultrasonic guided wave; calculating a relation curve of frequency-stress-phase velocity change of the ultrasonic guided wave under different stress effects; calculating a slope-frequency relation curve; establishing a sensor array; obtaining the phase velocity and the phase velocity change of the ultrasonic guided wave mode; and (5) obtaining corresponding stress through analysis and calculation, and realizing stress monitoring. The method provides reliable basis for selecting the mode and frequency of the ultrasonic guided wave, reasonably selects the monitoring mode according to the concrete monitoring requirement of the actual engineering, achieves the purpose of stress monitoring according to the analysis result, can timely discover pipeline damage and potential threats, and guarantees the safety of the engineering structure.

Description

Stress monitoring method of circular tube type structure based on longitudinal mode ultrasonic guided waves
Technical Field
The disclosure relates to the technical field of stress monitoring, in particular to a stress monitoring method of a circular tube type structure based on longitudinal mode ultrasonic guided waves.
Background
At present, the circular tube type structure is widely applied to pipeline transportation and engineering communication, however, most pipelines are in a harsh natural environment, such as stress release and environmental temperature change, and stress or deformation is easily generated. If the magnitude and direction of the stress can be measured before the pipeline is damaged and preventive measures are taken, the hidden danger caused by the influence of high risk factors on long-distance pipeline transportation can be eliminated.
Disclosure of Invention
The purpose of the present disclosure is to provide a stress monitoring method for a circular tube type structure based on longitudinal mode ultrasonic guided waves, which can solve one or more of the above-mentioned problems in the prior art.
According to one aspect of the disclosure, a stress monitoring method for a circular tube type structure based on longitudinal mode ultrasonic guided waves is provided, which includes the following steps:
calculating a phase velocity dispersion curve equation of the circular tube type structure and a curve equation of the phase velocity change value of the circular tube type structure along with the change of frequency based on an ultrasonic guided wave theory of a sound-elastic theory;
selecting the mode and frequency of ultrasonic guided waves suitable for stress monitoring according to an oil filling model of a circular tube type structure in a single-layer pipeline by combining a phase velocity dispersion curve equation and a curve equation of the change value of the phase velocity along with the change of the frequency;
calculating a relation curve of frequency-stress-phase velocity change of the ultrasonic guided waves in the circular tube type structure under different stress effects;
calculating a slope-frequency relation curve of the ultrasonic guided waves in the circular tube type structure under different stress effects;
establishing an ultrasonic guided wave sensor array suitable for stress monitoring according to the model characteristics of an oil filling model of a circular tube type structure in a single-layer pipeline;
recording and storing ultrasonic guided wave signals received by each sensor in the sensor array to obtain the phase velocity and the phase velocity change of the ultrasonic guided wave mode;
the corresponding stress is obtained by analyzing and calculating the phase velocity and the phase velocity change of the ultrasonic guided wave mode, the relation curve of the frequency-stress-phase velocity change and the relation curve of the slope-frequency, so that the stress monitoring is realized.
Compared with the prior art, the technical scheme provided by the disclosure has the following beneficial effects: by analyzing the frequency dispersion curve of the phase velocity of the circular tube type structure under the oil-filled model in the single-layer pipeline and the change curve of the phase velocity change value along with the frequency, a reliable basis is provided for selecting the mode and the frequency of the ultrasonic guided wave, the monitoring mode is reasonably selected according to the actual engineering concrete monitoring requirement, the purpose of stress monitoring is achieved according to the analysis result, the pipeline damage and the potential threat can be found in time, and the safety of the engineering structure is guaranteed.
In addition, in the technical solutions of the present disclosure, the technical solutions can be implemented by adopting conventional means in the art, unless otherwise specified.
Drawings
In order to more clearly illustrate the technical solutions of the embodiments of the present disclosure, the drawings needed to be used in the description of the embodiments are briefly introduced below, and it is obvious that the drawings in the following description are some embodiments of the present disclosure, and it is obvious for those skilled in the art to obtain other drawings based on the drawings without creative efforts.
Fig. 1 is a flowchart of a stress monitoring method for a circular tube-shaped structure based on longitudinal mode ultrasonic guided waves according to an embodiment of the present disclosure.
Fig. 2 is a phase velocity dispersion curve of each mode of ultrasonic guided waves in a circular tube type structure under the oil-filled model in the single-layer pipeline according to an embodiment of the present disclosure.
Fig. 3 is a curve of a phase velocity variation value of a circular tube-shaped structure of 3-mode ultrasonic guided waves with frequency variation under an oil-filled model in a single-layer pipeline according to an embodiment of the present disclosure.
Fig. 4 is a schematic diagram of a group of sensor arrays according to an embodiment of the present disclosure.
Fig. 5 is a relationship curve of frequency-stress-phase velocity changes under different stresses when the 3-mode ultrasonic guided wave provided by the embodiment of the present disclosure is in a horizontal section of a dispersion curve.
Fig. 6 is a frequency-slope relationship curve under different stress effects when the 3-mode ultrasonic guided wave is in the horizontal section of the dispersion curve according to an embodiment of the present disclosure.
Detailed Description
To make the objects, technical solutions and advantages of the embodiments of the present disclosure more clear, the technical solutions of the embodiments of the present disclosure will be described clearly and completely with reference to the drawings in the embodiments of the present disclosure, and it is obvious that the described embodiments are some, but not all embodiments of the present disclosure. All other embodiments, which can be derived by a person skilled in the art from the embodiments disclosed herein without making any creative effort, shall fall within the protection scope of the present disclosure.
Example (b):
fig. 1 shows a stress monitoring method for a circular tube-shaped structure based on longitudinal mode ultrasonic guided waves according to an embodiment of the present disclosure, which includes the following steps:
s101: calculating a phase velocity dispersion curve equation of the circular tube type structure and a curve equation of the phase velocity change value of the circular tube type structure along with the change of frequency based on an ultrasonic guided wave theory of a sound-elastic theory;
in an alternative embodiment, the equation for calculating the phase velocity dispersion curve of the circular tube-shaped structure and the equation for calculating the phase velocity variation of the circular tube-shaped structure with respect to the variation of frequency include,
deducing the propagation behavior of the ultrasonic guided wave in the circular tube type structure based on the ultrasonic guided wave theory of the acoustoelastic theory to obtain a coefficient matrix of a characteristic equation set, and obtaining a frequency dispersion curve equation of the phase velocity based on the coefficient matrix of the characteristic equation set;
and (3) making a difference between the phase velocity after stress is applied and the phase velocity when no stress is applied to obtain a curve equation of the change value of the phase velocity along with the change of the frequency.
Because the acoustic-elastic effect is very small, the difference between the dispersion curve of the ultrasonic guided wave and the dispersion curve when the stress is zero is not obvious, in the embodiment, the difference between the phase velocity when the non-zero stress is applied and the phase velocity when the stress is not applied is adopted to obtain the curve of the phase velocity change along with the frequency change, so as to represent the propagation characteristic of the ultrasonic guided wave after the stress is applied.
In an optional embodiment, deriving a propagation behavior of the ultrasonic guided wave in the circular tube type structure based on an ultrasonic guided wave theory of a acoustoelastic theory to obtain a coefficient matrix of a characteristic equation set, and obtaining a dispersion curve equation of the phase velocity based on the coefficient matrix of the characteristic equation set includes:
the propagation of the ultrasonic waveguide in the elastic layer under the action of prestress satisfies the following dynamic wave equation:
Figure BDA0002905356500000041
wherein, sigma represents stress, rho represents density, U represents displacement, and t is a time variable;
based on the acoustoelastic theory, the medium under the action of uniaxial stress is equivalent to transverse isotropy, the equivalent elastic modulus is,
Figure BDA0002905356500000042
the other modulus of elasticity not given is 0;
wherein A, B and C are third-order elastic constants, T represents uniaxial stress, λ and μ are lame coefficients, ν is poisson's ratio, ν ═ λ/2(λ + μ), E is young's modulus, and E ═ 3 λ +2 μ) μ/(λ + μ);
based on the acoustic-elastic theory, the isotropic medium under the action of uniaxial stress can be approximately equivalent to a transverse isotropic medium, so that a circular tube type structure under the action of axial stress is obtained and can be equivalent to a transverse isotropic tube type structure with a symmetric axis along the axial direction;
in a cylindrical coordinate system r, theta and z, r is a radial direction, z is an axial direction, and theta is an angle; from the stress-displacement relationship of the transversely isotropic medium,
Figure BDA0002905356500000051
in the formula, σrr、σθθ、σzz、σrz、σθzAnd σrθIs the stress in cylindrical coordinates;
displacement of
Figure BDA0002905356500000052
The expression of (a) is as follows,
Figure BDA0002905356500000053
substituting the formulas (2), (3) and (4) into the formula (1) to obtain the following equation satisfied by the transverse isotropic medium represented by displacement potential,
Figure BDA0002905356500000054
Figure BDA0002905356500000055
Figure BDA0002905356500000056
in the formula, C11、C13、C33、C44And C66Is the elastic constant of the stress-induced anisotropic medium,
Figure BDA0002905356500000057
ψ and χ denote displacement potentials of the P wave, SV wave and SH wave, respectively, z denotes the axial direction of the cylindrical coordinate system,
Figure BDA0002905356500000058
represents the Laplace operator;
the axial symmetry mode heuristic solution form of the displacement potential in the frequency wave number domain is as follows,
Figure BDA0002905356500000059
in the formula, R1、R2、B1And B2Is an unknown coefficient, K0And I0The order of the order is 0 Bessel function, M is a radial virtual wave number, and r represents the radial direction of a cylindrical coordinate system;
substituting the tentative solution into the formula (5) and the formula (6), and making the determinant of the coefficient matrix in the formula obtained after substitution be zero to obtain the P-SV wave displacement potential as follows,
Figure BDA0002905356500000061
the displacement potential of the SH wave is obtained as,
χ＝[R3K0(M3r)+B3I0(M3r)]， (10)
in the formula, the radial imaginary wave number M1、M2Is the solution of equation when the determinant of coefficient matrix in formula (1) and formula (2) is equal to zero, the radial imaginary wave number M3 is the solution of equation when the determinant of coefficient matrix in formula (3) is equal to zero, R is the value of the coefficient matrix in formula (3)3And B3Is an unknown coefficient, a1And a2Is a proportionality coefficient;
substituting the P-SV wave displacement potential and the SH wave displacement potential into a formula (3) and a formula (4) to respectively obtain a displacement component u of the column coordinaterAnd stress component σrrAnd σrzAs follows below, the following description will be given,
ur＝[-K1(M1r)]q1R1+[I1(M1r)]q1B1+[-K1(M2r)]q2R2+[I1(M2r)]q2B2，
Figure BDA0002905356500000062
σrz＝Q3[-K1(M1r)]R1+Q3[I1(M1r)]B1-Q4[K1(M2r)]R2+Q4[I1(M2r)]B2， (11)
in the formula, the coefficient qiAnd Qi(i is 1, 2, 3, 4) is,
q1＝M1(1+a1ikz)，
q2＝M2(a2+ikz)，
q3＝ikz-a1M1 2，
q4＝a2ikz-M2 2，
Q1＝[(C11M1)q1+ikzC13q3]，
Q2＝[(C11M2)q2+ikzC13q4]，
Q3＝M1(2ikz-M1 2a1-kz 2a1)C44，
Q4＝M2(2ikza2-kz 2-M2 2)C44，
wherein, K0And I0Is a Bessel function of order 0, K1And I1Is a Bessel function of order 1, kzIs the wave number of the ultrasonic guided wave;
assuming that oil is an ideal fluid, the expressions of the isotropic displacement and pressure of the fluid medium in the round pipe are as follows:
Ur f＝{B0[I0(krr)+krI1(krr)]+C0[K0(krr)-krK1(krr)]}-Pf＝ω2ρfluid[B0I0(krr)+C0K0(krr)] (12)
in the formula of Ur fDenotes a displacement, PfRepresenting the pressure, pfluidIs the corresponding density of the liquid, B0Is an unknown coefficient of the fluid, C0Is a coefficient, k, related to the sound sourcerIs the radial imaginary wave number of the fluid, omega is the angular frequency;
boundary conditions are introduced, namely an oil filling model in a single-layer pipeline is as follows,
Figure BDA0002905356500000071
Figure BDA0002905356500000072
in the formula, u represents displacement, and a and b are the outer surface radiuses of the circular tube layer and the oil layer respectively;
respectively substituting the displacement and stress expressions of the ultrasonic guided waves in the oil layer and the circular tube layer, namely a formula (11) and a formula (12), into a boundary condition formula (13) to obtain a characteristic equation set as follows:
[D]·{A}＝0， (14)
wherein [ D ]]For the coefficient matrix of the characteristic equation set, { A } is a matrix containing all unknown amplitudes { R }1，B1，R2，B2，B0The vector of (c);
making the characteristic equation set have non-zero solution, even if the coefficient matrix of the characteristic equation set is zero, the expression is as follows:
[D]＝0， (15)
thereby obtaining the wave number k of the ultrasonic guided wavezThe expressions for angular frequency ω and phase velocity v, i.e., the dispersion curve equation for phase velocity, are as follows:
Figure BDA0002905356500000073
where v is the phase velocity, ω is the angular frequency, kzIs the wavenumber of the ultrasonic guided wave.
S102: selecting the mode and frequency of ultrasonic guided waves suitable for stress monitoring according to an oil filling model of a circular tube type structure in a single-layer pipeline by combining a phase velocity dispersion curve equation and a curve equation of the change value of the phase velocity along with the change of the frequency;
in this embodiment, a steel pipe and engine oil are selected as the oil-filled model in the single-layer pipeline, wherein the outer diameter of the steel pipe is 720mm, the inner diameter is 698mm, and various attribute parameters of the selected steel pipe and engine oil are shown in table 1.
Figure BDA0002905356500000081
TABLE 1
Specifically, referring to the attached fig. 2 in the specification, a phase velocity dispersion curve of each mode ultrasonic guided wave in a round pipe type structure under an oil filling model in a single-layer pipeline is shown. As can be seen from FIG. 2, the 3-mode ultrasonic guided wave has good non-frequency dispersion in the horizontal section with the low frequency of 4KHz to 6KHz, has obvious speed change, and is suitable for stress monitoring.
Referring to the attached figure 3 of the specification, a curve of a phase velocity change value of a circular tube type structure of 3-mode ultrasonic guided waves under an oil-filled model in a single-layer pipeline along with the change of frequency is shown. As can be seen from FIG. 3, when a force of 100MPa to 200MPa is applied, the velocity change of the 3-mode ultrasonic guided wave in the horizontal section is obvious, and the frequency is low, so that the method is suitable for stress detection.
In the embodiment, by combining the curves of the attached fig. 2 and the attached fig. 3 in the specification, the mode of the ultrasonic guided wave suitable for stress monitoring is 3 modes, and the frequency is between 4KHz and 6 KHz.
S103: calculating a relation curve of frequency-stress-phase velocity change of the ultrasonic guided waves in the circular tube type structure under different stress effects;
in an alternative embodiment, referring to the attached figure 5 of the specification, the relationship curve of the frequency-stress-phase velocity change of the ultrasonic guided wave under different stresses in the circular tube type structure is calculated as follows,
obtaining corresponding frequency and phase velocity under stress according to a dispersion curve equation;
the phase velocity is differed from the phase velocity when no stress is applied, so that the phase velocity change is obtained;
and obtaining a frequency-stress-phase velocity change curve according to the frequency, the stress and the corresponding phase velocity change.
S104: calculating a slope-frequency relation curve of the ultrasonic guided waves in the circular tube type structure under different stress effects;
in an alternative embodiment, referring to fig. 6 of the specification, a formula for calculating a slope-frequency relation curve of the ultrasonic guided wave in the circular tube type structure under different stress is as follows,
Figure BDA0002905356500000091
where k (ω) is the slope of the phase velocity change value with stress, Δ v is the phase velocity change value, and T is the applied stress.
S105: establishing an ultrasonic guided wave sensor array suitable for stress monitoring according to the model characteristics of an oil filling model of a circular tube type structure in a single-layer pipeline;
in an alternative embodiment, the sensor array comprises a plurality of sets of sensors arranged axially along the circular tube-type structure, and referring to the description of fig. 4, a set of sensors in the sensor array is shown. The sensor set comprises at least one transmitting end and at least one receiving end. Referring to the description and shown in fig. 4, the sensor at the lowest end is the transmitting end, and the rest are the receiving ends.
S106: recording and storing ultrasonic guided wave signals received by each sensor in the sensor array to obtain the phase velocity and the phase velocity change of the ultrasonic guided wave mode;
s107: the corresponding stress is obtained by analyzing and calculating the phase velocity and the phase velocity change of the ultrasonic guided wave mode, the relation curve of the frequency-stress-phase velocity change and the relation curve of the slope-frequency, so that the stress monitoring is realized.
According to the stress monitoring method of the circular tube type structure based on the longitudinal modal ultrasonic guided waves, a frequency dispersion curve of the phase velocity of the circular tube type structure under an oil-filled model in a single-layer pipeline and a change curve of a phase velocity change value along with the frequency are analyzed, a reliable basis is provided for selecting the mode and the frequency of the ultrasonic guided waves, the monitoring mode is reasonably selected according to the actual engineering concrete monitoring requirement, the purpose of stress monitoring is achieved according to the analysis result, pipeline damage and potential threats can be found in time, and the safety of the engineering structure is guaranteed.
Through the above description of the embodiments, those skilled in the art will clearly understand that each embodiment can be implemented by software plus a necessary general hardware platform, and certainly can also be implemented by hardware. With this understanding in mind, the above-described technical solutions may be embodied in the form of a software product, which can be stored in a computer-readable storage medium such as ROM/RAM, magnetic disk, optical disk, etc., and includes instructions for causing a computer device (which may be a personal computer, a server, or a network device, etc.) to execute the methods described in the embodiments or some parts of the embodiments.
Finally, it should be noted that: the above examples are only intended to illustrate the technical solutions of the present disclosure, not to limit them; although the present disclosure has been described in detail with reference to the foregoing embodiments, it should be understood by those of ordinary skill in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some technical features may be equivalently replaced; and such modifications or substitutions do not depart from the spirit and scope of the corresponding technical solutions of the embodiments of the present disclosure.

Claims (6)

1. The stress monitoring method of the circular tube type structure based on the longitudinal mode ultrasonic guided wave is characterized by comprising the following steps of:
calculating a phase velocity dispersion curve equation of the circular tube type structure and a curve equation of the phase velocity change value of the circular tube type structure along with the change of frequency based on an ultrasonic guided wave theory of a sound-elastic theory;
selecting the mode and frequency of the ultrasonic guided wave suitable for stress monitoring according to an oil filling model of the circular tube type structure in the single-layer pipeline by combining the phase velocity dispersion curve equation and the curve equation of the phase velocity change value along with the change of the frequency;
calculating a relation curve of frequency-stress-phase velocity change of the ultrasonic guided waves in the circular tube type structure under different stress effects;
calculating a slope-frequency relation curve of the ultrasonic guided waves in the circular tube type structure under different stress effects;
establishing an ultrasonic guided wave sensor array suitable for stress monitoring according to the model characteristics of the oil filling model of the circular tube type structure in the single-layer pipeline;
recording and storing ultrasonic guided wave signals received by each sensor in the sensor array to obtain the phase velocity and the phase velocity change of an ultrasonic guided wave mode;
analyzing and calculating the phase velocity and the phase velocity change of the ultrasonic guided wave mode, the relation curve of the frequency-stress-phase velocity change and the relation curve of the slope-frequency to obtain corresponding stress, and realizing stress monitoring;
the ultrasonic guided wave theory based on the acoustoelastic theory calculates the phase velocity dispersion curve equation of the circular tube type structure and the curve equation of the phase velocity change value of the circular tube type structure along with the change of frequency,
deducing the propagation behavior of the ultrasonic guided wave in the circular tube type structure based on the ultrasonic guided wave theory of the acoustoelastic theory to obtain a coefficient matrix of a characteristic equation set, and obtaining a frequency dispersion curve equation of the phase velocity based on the coefficient matrix of the characteristic equation set;
the phase velocity after stress application and the phase velocity when no stress is applied are differentiated to obtain a curve equation of the change value of the phase velocity along with the change of the frequency;
the formula for calculating the relationship curve of the slope and the frequency of the ultrasonic guided wave under different stress actions in the circular tube type structure is as follows,
Figure FDA0003241241410000021
where k (ω) is the slope of the phase velocity change value with stress, Δ v is the phase velocity change value, and T is the applied stress.
2. The method for monitoring stress of the circular tube type structure based on the longitudinal mode ultrasonic guided wave according to claim 1, wherein the step of deriving propagation behavior of the ultrasonic guided wave in the circular tube type structure based on the ultrasonic guided wave theory of the acoustoelastography to obtain a coefficient matrix of a characteristic equation set, and the step of obtaining a dispersion curve equation of the phase velocity based on the coefficient matrix of the characteristic equation set comprises:
the propagation of the ultrasonic waveguide in the elastic layer under the action of prestress satisfies the following dynamic wave equation:
Figure FDA0003241241410000022
wherein, sigma represents stress, rho represents density, U represents displacement, and t is a time variable;
based on the acoustoelastic theory, the medium under the action of uniaxial stress is equivalent to transverse isotropy, the equivalent elastic modulus is,
C11≈λ+2μ+2((1-4υ)B+(1-2υ)C-υA)T/E，
C22≈λ+2μ+2((1-4υ)B+(1-2υ)C-υA)T/E，
C33≈λ+2μ+2(A+(3-2υ)B+(1-2υ)C)T/E，
C12≈λ+2(-2υB+(1-2υ)C)T/E， (2)
C13≈λ+2((1-υ)B+(1-2υ)C)T/E，
C23≈λ+2((1-υ)B+(1-2υ)C)T/E，
C44≈μ+((1-2υ)B+(1-υ)A/2))T/E，
C55≈μ+((1-2υ)B+(1-υ)A/2)T/E，
C66≈μ+((1-2υ)B-υA)T/E，
C12＝C21，C13＝C31，C23＝C32，
the other modulus of elasticity not given is 0;
wherein A, B and C are third-order elastic constants, T represents uniaxial stress, λ and μ are ramei coefficients, ν is poisson's ratio, ν ═ λ/2{ λ + μ), E is young's modulus, E ═ 3 λ +2 μ) μ/{ λ + μ);
based on the acoustic-elastic theory, the isotropic medium under the action of uniaxial stress can be approximately equivalent to a transverse isotropic medium, so that a circular tube type structure under the action of axial stress is obtained and can be equivalent to a transverse isotropic tube type structure with a symmetric axis along the axial direction;
in a cylindrical coordinate system r, theta and z, r is a radial direction, z is an axial direction, and theta is an angle; from the stress-displacement relationship of the transversely isotropic medium,
Figure FDA0003241241410000031
in the formula, σrr、σθθ、σzz、σrz、σθzAnd σrθIs the stress in cylindrical coordinates;
displacement of
Figure FDA0003241241410000032
The expression of (a) is as follows,
Figure FDA0003241241410000033
substituting the formulas (2), (3) and (4) into the formula (1) to obtain the following equation satisfied by the transverse isotropic medium represented by displacement potential,
Figure FDA0003241241410000034
Figure FDA0003241241410000035
Figure FDA0003241241410000036
in the formula, C11、C13、C33、C44And C66Is the elastic constant of the stress-induced anisotropic medium,
Figure FDA0003241241410000037
ψ and χ denote displacement potentials of P-wave, SV-wave, and SH-wave, respectively, and z denotes an axis of a cylindrical coordinate systemIn the direction of the air flow,
Figure FDA0003241241410000038
represents the Laplace operator;
the axial symmetry mode heuristic solution form of the displacement potential in the frequency wave number domain is as follows,
Figure FDA0003241241410000039
in the formula, R1、R2、B1And B2Is an unknown coefficient, K0And I0The order of the order is 0 Bessel function, M is a radial virtual wave number, and r represents the radial direction of a cylindrical coordinate system;
substituting the heuristic solution into the formula (5) and the formula (6), enabling a coefficient matrix determinant in the formula obtained after substitution to be zero, obtaining the P-SV wave displacement potential as follows,
Figure FDA0003241241410000041
the displacement potential of the SH wave is obtained as,
χ＝[R3K0(M3r)+B3I0(M3r)]， (10)
in the formula, the radial imaginary wave number M1、M2Is the equation solution when the determinant of the coefficient matrix in the formula (1) and the formula (2) is equal to zero, and the radial virtual wave number M3Is the solution of the equation when the determinant of the coefficient matrix in formula (3) is equal to zero, R3And B3Is an unknown coefficient, a1And a2Is a proportionality coefficient;
substituting the P-SV wave displacement potential and the SH wave displacement potential into a formula (3) and a formula (4) to respectively obtain a displacement component u of the column coordinaterAnd stress component σrrAnd σrzAs follows below, the following description will be given,
ur＝
[-K1(M1r)]q1R1+[I1(M1r)]q1B1+[-K1(M2r)]q2R2+[I1(M2r)]q2B2，
Figure FDA0003241241410000042
σrz＝
Q3[-K1(M1r)]R1+Q3[I1(M1r)]B1-Q4[K1(M2r)]R2+Q4[I1(M2r)]B2， (11)
in the formula, the coefficient qiAnd Qi(i is 1, 2, 3, 4) is,
q1＝M1(1+a1ikz)，
q2＝M2(a2+ikz)，
q3＝ikz-a1M1 2，
q4＝a2ikz-M2 2，
Q1＝[(C11M1)q1+ikzC13q3]，
Q2＝[(C11M2)q2+ikzC13q4]，
Q3＝M1(2ikz-M1 2a1-kz 2a1)C44，
Q4＝M2(2ikza2-kz 2-M2 2)C44，
wherein, K0And I0Is a Bessel function of order 0, K1And I1Is a Bessel function of order 1, kzIs the wave number of the ultrasonic guided wave;
assuming that oil is an ideal fluid, the expressions of the isotropic displacement and pressure of the fluid medium in the round pipe are as follows:
Ur f＝{B0[I0(krr)+krI1(krr)]+C0[K0(krr)-krK1(krr)]}-Pf＝ω2ρfluid[B0I0(krr)+C0K0(krr)] (12)
in the formula of Ur fDenotes a displacement, PfRepresenting the pressure, pfluidIs the corresponding density of the liquid, B0Is an unknown coefficient of the fluid, C0Is a coefficient, k, related to the sound sourcerIs the radial imaginary wave number of the fluid, omega is the angular frequency;
boundary conditions are introduced, namely an oil filling model in a single-layer pipeline is as follows,
Figure FDA0003241241410000051
Figure FDA0003241241410000052
in the formula, u represents displacement, and a and b are the outer surface radiuses of the circular tube layer and the oil layer respectively;
respectively substituting the displacement and stress expressions of the ultrasonic guided waves in the oil layer and the circular tube layer, namely a formula (11) and a formula (12), into a boundary condition formula (13) to obtain a characteristic equation set as follows:
[D]·{A}＝0， (14)
wherein [ D ]]For the coefficient matrix of the characteristic equation set, { A } is a matrix containing all unknown amplitudes { R }1，B1，R2，B2，B0The vector of (c);
making the characteristic equation set have a non-zero solution even if the coefficient matrix of the characteristic equation set is zero, the expression is as follows:
[D]＝0， (15)
thereby obtaining the wave number k of the ultrasonic guided wavezThe expressions for angular frequency ω and phase velocity v, i.e., the dispersion curve equation for phase velocity, are as follows:
Figure FDA0003241241410000053
where v is the phase velocity, ω is the angular frequency, kzIs the wavenumber of the ultrasonic guided wave.
3. The stress monitoring method of the circular tube type structure based on the longitudinal mode ultrasonic guided wave according to claim 2, wherein the relation curve of the ultrasonic guided wave frequency-stress-phase velocity change under different stress actions in the circular tube type structure is calculated as follows,
obtaining corresponding frequency and phase velocity under stress according to the frequency dispersion curve equation;
subtracting the phase velocity from the phase velocity when no stress is applied to obtain phase velocity change;
and obtaining a frequency-stress-phase velocity change curve according to the frequency, the stress and the corresponding phase velocity change.
4. The stress monitoring method of the circular tube type structure based on the longitudinal mode ultrasonic guided wave according to claim 1, wherein the oil-filled model in the single-layer pipeline adopts a steel tube and engine oil.
5. The stress monitoring method for the circular tube type structure based on the longitudinal mode ultrasonic guided wave according to claim 1, wherein the sensor array is arranged along the axial direction of the circular tube type structure.
6. The stress monitoring method of the circular tube type structure based on the longitudinal mode ultrasonic guided wave according to claim 5, wherein the sensor array comprises at least one transmitting end and at least one receiving end.
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