CN1828288A - Guide-wave detection method for fluid pipe with adhesive and elastic cladding - Google Patents

Abstract

Wherein, arranging a set of length-shrink piezoelectric ceramic pieces on pipe outside wall symmetrically; exciting with 50MHz sample rate and receiving single axial-symmetrical ultrasonic waveguide non-interferential L(0, 2) mode as a branch of L(0, 2) by a piezoelectric transducer with attenuation less than 6dB/m, variable rate of group velocity less than 0.000m. This invention is fit to long distance, fast, on-line and undamaged detection.

Description

A kind of method that band viscoelastic coating liquid-filling pipe guided wave is detected

Technical field

The present invention relates to a kind of method with the detection of viscoelastic coating liquid-filling pipe guided wave, the decay that utilizes excitation frequency to be controlled at longitudinal mode is lower than 6dB/m, group velocity is lower than in the scope of 0.0003m with the absolute value of frequency change rate, sampling rate is that the 6dB bandwidth of the pumping signal of 50MHz is controlled less than single undisturbed L (0,2) the undisturbed L (0 of single rotational symmetry supersonic guide-wave of the bandwidth of one of mode branch, 2) component of mode belongs to technical field of nondestructive testing with the method for viscoelastic coating liquid-filling pipe Non-Destructive Testing.

Background technology

At present, the research that utilizes supersonic guide-wave to carry out the defect of pipeline detection has obtained bigger progress.But be mainly used in the defects detection of individual layer pipeline, liquid-filling pipe and band clad pipeline at present, when selecting the ultrasonic guided wave detecting pipeline, only consider mode frequency dispersion size usually, or only consider the decay of ripple.Yet, owing in engineering reality, in factories and miness such as chemical industry, thermoelectricity, water supply and heat supply, be commonly used to carry liquid mediums such as chemical products, water.The corrosion of medium is washed away and is made the tube wall attenuate in the pipe, and exposed for a long time corrosion or the extraneous damage that is vulnerable to humid air, soil of tube wall causes pipeline leakage and pipe explosion accident, thereby cause the heavy economic losses and the wasting of resources.In order to protect pipeline not corroded or external force is damaged,, often adhere to one deck viscoelastic coating at inner and outer walls of pipeline to ensure the pipeline security of operation and to prolong pipeline serviceable life.But because the existence of viscoelastic coating, liquid in pipe, make conventional lossless detection method such as ultrasonic, eddy current, magnetic and ray etc. fast and effeciently to carry out defects detection to these long distance band viscoelastic coating liquid-filling pipes in labour.

Compare with the better simply pipeline of structure such as individual layer pipeline, the propagation characteristic of supersonic guide-wave is complicated more in the band viscoelastic coating liquid-filling pipe, chooses the defects detection that suitable supersonic guide-wave mode is used for such pipeline and seems very important.Liu Zenghua etc. rolled up in 3 phases " mechanical engineering journal " at 2006 42 and have delivered one piece of article about supersonic guide-wave longitudinal mode Propagation Characteristics in liquid-filling pipe.Mainly study the propagation characteristic of longitudinal mode in the liquid-filling pipe, the detectability of undisturbed L (0,2) mode component has been analyzed, and utilized excitation of length-expanding and contracting piezoelectric sheet and receiving transducer.But do not provide the undisturbed L (0 that is fit to defect of pipeline, 2) the concrete parameter of mode component, and when viscoelastic coating appears in pipeline, the undisturbed L (0 that is fit to detection, 2) frequency band of mode component and the also corresponding variation that taken place that decays, undisturbed L (0,2) the mode component that is fit to defective in the detection liquid-filling pipe might not be fit to the defects detection in the viscoelastic coating liquid-filling pipe.J.L.Barshinger has studied the possibility of defective in the detection band viscoelastic coating pipeline of high-order longitudinal mode in PhD dissertation " Guided wave propagation in pipes with viscoelastic coatings " in 2002, but it is not analyzed the detectability of low frequency L (0,2) mode.At present, because theoretical and experimental analysis difficulty, still nobody carried out correlative study to one of supersonic guide-wave mode longitudinal mode in band viscoelastic coating liquid-filling pipe defects detection both at home and abroad.Behind viscoelastic coating pipeline topping up, except considering that longitudinal mode portion of energy in communication process is absorbed the caused decay in back by clad, need also to consider that liquid in the pipe absorbs the influence that produced to the portion of energy of longitudinal mode and to L (0,2) the mode branch phenomenon that mode produced, because mode branch phenomenon, make that the longitudinal mode propagation characteristic of low frequency is comparatively complicated, and because band viscoelastic coating liquid-filling pipe complex structure, the longitudinal mode signal that receives is also complicated, in addition, when pipeline being carried out the guided wave detection, because axisymmetry mode can produce MODAL TRANSFORMATION OF A when fault location reflects, some easily are mistaken for flaw echo from the conversion mode that fault location reflects, and bring difficulty for the quantity of defective and the identification of position.Therefore, when such pipeline is detected, need to select decay and frequency dispersion little, propagation distance is far away, to the strong longitudinal mode of ducted defects detection ability, otherwise the waveform complexity that receives, be difficult to analyze, can not grow distance detecting, insensitive to defective, and need to adopt that effective ways eliminate that the MODAL TRANSFORMATION OF A phenomenon produced to defects count and axial location location influence.

Summary of the invention

The objective of the invention is to grow distance in order to solve the viscoelastic coating liquid-filling pipe, fast, comprehensively, present situation in the labour Non-Destructive Testing, for to assessing in the health status and the serviceable life of band viscoelastic coating liquid-filling pipe, a kind of method with the detection of viscoelastic coating liquid-filling pipe guided wave has been proposed, based on theoretical analysis to longitudinal mode, select decay to be lower than 6dB/m, group velocity is lower than 0.0003m with the absolute value of frequency change rate, sampling rate is that the 6dB bandwidth of the pumping signal of 50MHz is controlled less than single undisturbed L (0,2) component of the undisturbed L of single rotational symmetry supersonic guide-wave (0, the 2) mode of the bandwidth of one of mode branch is to defects detection such as band viscoelastic coating liquid-filling pipe inside and outside crackle and corrosion.

Device of the present invention is referring to Fig. 1, comprise: length-expanding and contracting piezoelectric ring 1, function generator 2, power amplifier 3, switch 4, digital oscilloscope 6 and computing machine 7 etc., the piezoelectric ceramic ring 1 that is formed in parallel by a group length concertina type piezoelectric ceramic piece is installed on the band viscoelastic coating liquid-filling pipe 5, be connected with switch 4, switch 4 is connected with power amplifier 3 with digital oscilloscope 6, the output terminal of function generator 2 is connected with the input end of power amplifier 3, and computing machine 7 is connected with digital oscilloscope 6.

The method that band viscoelastic coating liquid-filling pipe guided wave is detected of the present invention realizes by following steps:

(1) if viscoelastic coating at pipeline outer wall, then encloses viscoelastic coating along the circumferential local strip off one of pipeline, at the circumferential uniform a plurality of length-expanding and contracting piezoelectric sheets of strip off place; If viscoelastic coating at inner-walls of duct, then directly is distributed on pipeline outer wall with piezoelectric ceramic piece.But no matter viscoelastic coating is at internal layer or skin, and detection method is the same.The length direction of piezoelectric ceramic piece is parallel with conduit axis, and polarised direction is along the piezoelectric ceramic piece thickness direction, and the upper and lower surface of piezoelectric ceramic piece is an electrode.Each piezoelectric patches also is unified into a piezoelectric ceramic ring 1.This piezoelectric ceramic ring 1 had both encouraged transducer, made receiving transducer again;

(2) produce the narrow-band impulse that centre frequency is adjustable by function generator 2, the decay that excitation frequency is controlled at longitudinal mode is lower than 6dB/m, group velocity is lower than 0.0003m with the absolute value of frequency change rate, sampling rate is that the 6dB bandwidth of the pumping signal of 50MHz is controlled the bandwidth less than one of single undisturbed L (0,2) mode branch;

(3) pumping signal is carried out power amplification through power amplifier 3; By switch 4 excitation piezoelectric ceramic rings 1, excitation undisturbed L (0,2) mode component in band viscoelastic coating liquid-filling pipe 5;

(4) Ji Li undisturbed L (0,2) signal of mode component is propagated in band viscoelastic coating liquid-filling pipe 5, after defective and pipe end reflection, by switch 4, piezoelectric ceramic ring 1 is received signal again, show at digital oscilloscope 6, and store computing machine 7 into by ethernet port;

(5) under other constant conditions, change the centre frequency of narrow-band impulse, encourage same undisturbed L (0,2) mode component.This frequency control is lower than 6dB/m in the decay of longitudinal mode, and group velocity is lower than 0.0003m with the absolute value of frequency change rate, and sampling rate is that the 6dB bandwidth of the pumping signal of 50MHz is controlled the bandwidth less than one of single undisturbed L (0,2) mode branch.Obtain another time domain waveform;

(6) time location to all echoes before the end face echo in the different signal of two frequencies receiving compares, if an echo appears in the time location of echo same time location in another signal in the signal, can determine that this echo is a flaw echo, if the time location of echo same time location in another signal does not occur in the signal, can determine that then this echo is a conversion mode, does not consider.For the flaw echo of determining, multiply by the group velocity value of undisturbed L (0,2) mode component by the travel-time of flaw echo, and divided by 2, be in the band viscoelastic coating liquid-filling pipe defective apart from the axial location of piezoelectric ceramic ring 1, thereby determine the number and the axial location of defective.

The design concept of lossless detection method of the present invention is: choose the longitudinal mode that is fit to band viscoelastic coating liquid-filling pipe defects detection, need analyze the frequency dispersion and the attenuation characteristic of longitudinal mode theoretically, to determine the frequency range of longitudinal mode.This frequency range is controlled at decay and is lower than 6dB/m, and group velocity is lower than 0.0003m with the absolute value of frequency change rate, and sampling rate is that the 6dB bandwidth of the pumping signal of 50MHz is controlled the bandwidth less than one of single undisturbed L (0,2) mode branch.

Utilize global matrix method, longitudinal mode propagation characteristic in the band viscoelastic coating liquid-filling pipe is analyzed, at first consider the situation of viscoelastic coating at pipeline outer wall at this.Stress and displacement expression formula obtain a stack features equation according to stress and displacement boundary conditions then when utilizing the Navier equation to obtain longitudinal mode to propagate in viscoelastic coating, hollow pipe and liquid.

(1) stress and displacement expression formula in the viscoelastic coating:

$\left\{\begin{array}{c}{u}_r^v=[-{\mathrm{\&alpha;}}_1{A}_1{H}_1^1\left({\mathrm{\&alpha;}}_{1}r\right)-{\mathrm{\&alpha;}}_1{A}_2{H}_1^2\left({\mathrm{\&alpha;}}_{1}r\right)+B_{1}k{H}_1^1\left({\mathrm{\&beta;}}_{1}r\right)+B_{2}k{H}_1^2\left({\mathrm{\&beta;}}_{1}r\right)]e^{i(\mathrm{kz}-\mathrm{\&omega;t})}\\ u_z^v=[-k{A}_1{H}_0^1\left({\mathrm{\&alpha;}}_{1}r\right)-k{A}_2{\mathrm{<figure-callout\; id="0"\; label="H"\; filenames="A20061007288100193.png"\; state="\{\{state\}\}">H</figure-callout>}}_0^2\left({\mathrm{\&alpha;}}_{1}r\right)-B_1{\mathrm{\&beta;}}_1{\mathrm{<figure-callout\; id="0"\; label="H"\; filenames="A20061007288100193.png"\; state="\{\{state\}\}">H</figure-callout>}}_0^1\left({\mathrm{\&beta;}}_{1}r\right)-{\mathrm{<figure-callout\; id="2"\; label="B"\; filenames="A20061007288100193.png"\; state="\{\{state\}\}">B</figure-callout>}}_2{\mathrm{\&beta;}}_1{\mathrm{<figure-callout\; id="0"\; label="H"\; filenames="A20061007288100193.png"\; state="\{\{state\}\}">H</figure-callout>}}_0^2\left({\mathrm{\&beta;}}_{1}r\right)]e^{i(\mathrm{kz}-\mathrm{\&omega;t})}\end{array}\right.---\left(1\right)$

$\left\{\begin{array}{c}{\mathrm{\&sigma;}}_{\mathrm{rr}}^v={\mathrm{\&mu;}}_1\left\{\begin{array}{c}{A}_1[(k^2-{\mathrm{\&beta;}}_1^2){\mathrm{<figure-callout\; id="0"\; label="H"\; filenames="A20061007288100193.png"\; state="\{\{state\}\}">H</figure-callout>}}_0^1\left({\mathrm{\&alpha;}}_{1}r\right)+2\frac{{\mathrm{\&alpha;}}_1}{r}{H}_1^1\left({\mathrm{\&alpha;}}_{1}r\right)]+\\ A_2[(k^2-{\mathrm{\&beta;}}_1^2){\mathrm{<figure-callout\; id="0"\; label="H"\; filenames="A20061007288100193.png"\; state="\{\{state\}\}">H</figure-callout>}}_0^2\left({\mathrm{\&alpha;}}_{1}r\right)+2\frac{{\mathrm{\&alpha;}}_1}{r}{H}_1^2\left({\mathrm{\&alpha;}}_{1}r\right)]+\\ B_1[2k{\mathrm{\&beta;}}_1{\mathrm{<figure-callout\; id="0"\; label="H"\; filenames="A20061007288100193.png"\; state="\{\{state\}\}">H</figure-callout>}}_0^1\left({\mathrm{\&beta;}}_{1}r\right)-2\frac{k}{r}{H}_1^1\left({\mathrm{\&beta;}}_{1}r\right)]+\\ B_2[2k{\mathrm{\&beta;}}_1{\mathrm{<figure-callout\; id="0"\; label="H"\; filenames="A20061007288100193.png"\; state="\{\{state\}\}">H</figure-callout>}}_0^2\left({\mathrm{\&beta;}}_{1}r\right)-2\frac{k}{r}{H}_1^2\left({\mathrm{\&beta;}}_{1}r\right)]\end{array}\right\}{e}^{i(\mathrm{kz}-\mathrm{\&omega;t})}\\ {\mathrm{\&sigma;}}_{\mathrm{rz}}^v={\mathrm{\&mu;}}_1\left[\begin{array}{c}-2k{\mathrm{\&alpha;}}_1{A}_1{H}_1^1\left({\mathrm{\&alpha;}}_{1}r\right)-2k{\mathrm{\&alpha;}}_1{A}_2{H}_1^2\left({\mathrm{\&alpha;}}_{1}r\right)+\\ B_1(k^2-{\mathrm{\&beta;}}_1^1)H_1^1\left({\mathrm{\&beta;}}_{1}r\right)+B_2(k^2-{\mathrm{\&beta;}}_1^2)H_1^2\left({\mathrm{\&beta;}}_{1}r\right)\end{array}\right]e^{i(\mathrm{kz}-\mathrm{\&omega;t})}\end{array}\right.---\left(2\right)$

(2) stress and displacement expression formula in the hollow pipe:

$\left\{\begin{array}{c}{u}_r=[-{\mathrm{\&alpha;}}_2{A}_3{H}_1^1\left({\mathrm{\&alpha;}}_{2}r\right)-{\mathrm{\&alpha;}}_2{A}_4{H}_1^2\left({\mathrm{\&alpha;}}_{2}r\right)+B_{3}k{H}_1^1\left({\mathrm{\&beta;}}_{2}r\right)+B_{4}k{H}_1^2\left({\mathrm{\&beta;}}_{2}r\right)]e^{i(\mathrm{kz}-\mathrm{\&omega;t})}\\ u_z=[-k{A}_3{H}_0^1\left({\mathrm{\&alpha;}}_{2}r\right)-k{A}_4{\mathrm{<figure-callout\; id="0"\; label="H"\; filenames="A20061007288100193.png"\; state="\{\{state\}\}">H</figure-callout>}}_0^2\left({\mathrm{\&alpha;}}_{2}r\right)-B_3{\mathrm{\&beta;}}_2{\mathrm{<figure-callout\; id="0"\; label="H"\; filenames="A20061007288100193.png"\; state="\{\{state\}\}">H</figure-callout>}}_0^1\left({\mathrm{\&beta;}}_{2}r\right)-B_4{\mathrm{\&beta;}}_2{\mathrm{<figure-callout\; id="0"\; label="H"\; filenames="A20061007288100193.png"\; state="\{\{state\}\}">H</figure-callout>}}_0^2\left({\mathrm{\&beta;}}_{2}r\right)]e^{i(\mathrm{kz}-\mathrm{\&omega;t})}\end{array}\right.---\left(3\right)$

$\left\{\begin{array}{c}{\mathrm{\&sigma;}}_{\mathrm{rr}}^v={\mathrm{\&mu;}}_2\left\{\begin{array}{c}{A}_3[(k^2-{\mathrm{\&beta;}}_2^2){\mathrm{<figure-callout\; id="0"\; label="H"\; filenames="A20061007288100193.png"\; state="\{\{state\}\}">H</figure-callout>}}_0^1\left({\mathrm{\&alpha;}}_{2}r\right)+2\frac{{\mathrm{\&alpha;}}_2}{r}{H}_1^1\left({\mathrm{\&alpha;}}_{2}r\right)]+\\ A_4[(k^2-{\mathrm{\&beta;}}_2^2){\mathrm{<figure-callout\; id="0"\; label="H"\; filenames="A20061007288100193.png"\; state="\{\{state\}\}">H</figure-callout>}}_0^2\left({\mathrm{\&alpha;}}_{2}r\right)+2\frac{{\mathrm{\&alpha;}}_2}{r}{H}_1^2\left({\mathrm{\&alpha;}}_{2}r\right)]+\\ B_3[2k{\mathrm{\&beta;}}_2{\mathrm{<figure-callout\; id="0"\; label="H"\; filenames="A20061007288100193.png"\; state="\{\{state\}\}">H</figure-callout>}}_0^1\left({\mathrm{\&beta;}}_{2}r\right)-2\frac{k}{r}{H}_1^1\left({\mathrm{\&beta;}}_{2}r\right)]+\\ B_4[2k{\mathrm{\&beta;}}_1{\mathrm{<figure-callout\; id="0"\; label="H"\; filenames="A20061007288100193.png"\; state="\{\{state\}\}">H</figure-callout>}}_0^2\left({\mathrm{\&beta;}}_{2}r\right)-2\frac{k}{r}{H}_1^2\left({\mathrm{\&beta;}}_{2}r\right)]\end{array}\right\}{e}^{i(\mathrm{kz}-\mathrm{\&omega;t})}\\ {\mathrm{\&sigma;}}_{\mathrm{rz}}^v={\mathrm{\&mu;}}_1\left[\begin{array}{c}-2k{\mathrm{\&alpha;}}_2{A}_3{H}_1^1\left({\mathrm{\&alpha;}}_{2}r\right)-2k{\mathrm{\&alpha;}}_2{A}_4{H}_1^2\left({\mathrm{\&alpha;}}_{2}r\right)+\\ B_3(k^2-{\mathrm{\&beta;}}_2^2)H_1^1\left({\mathrm{\&beta;}}_{2}r\right)+B_4(k^2-{\mathrm{\&beta;}}_2^2)H_1^2\left({\mathrm{\&beta;}}_{2}r\right)\end{array}\right]e^{i(\mathrm{kz}-\mathrm{\&omega;t})}\end{array}\right.---\left(4\right)$

(3) stress and displacement expression formula in the liquid:

$\left\{\begin{array}{c}{\mathrm{\&sigma;}}_{\mathrm{rr}}^f=2{\mathrm{\&mu;}}_3\left\{\begin{array}{c}[\frac{1}{2}(k^2-{\mathrm{\&beta;}}_3^2)J_0\left({\mathrm{\&alpha;}}_{3}r\right)+\frac{{\mathrm{\&alpha;}}_3}{r}{J}_1\left({\mathrm{\&alpha;}}_{3}r\right)]A_3+\\ [-\mathrm{ik}{\mathrm{\&beta;}}_3^2{J}_0\left({\mathrm{\&beta;}}_{3}r\right)+\frac{\mathrm{ik}{\mathrm{\&beta;}}_3}{r}{J}_1\left({\mathrm{\&beta;}}_{3}r\right)]B_5\end{array}\right\}{e}^{i(\mathrm{kz}-\mathrm{\&omega;t})}\\ {\mathrm{\&sigma;}}_{\mathrm{rz}}^f={\mathrm{\&mu;}}_3[-2\mathrm{ik}{\mathrm{\&alpha;}}_3{J}_1\left({\mathrm{\&alpha;}}_{3}r\right)A_5-({\mathrm{\&beta;}}_3^2-k^2)J_1\left({\mathrm{\&beta;}}_{3}r\right)B_5]e^{i(\mathrm{kz}-\mathrm{\&omega;t})}\end{array}\right.---\left(6\right)$

In the formula, A ₁, A ₂, A ₃, A ₄, A ₅, B ₁, B ₂, B ₃, B ₄And B ₅Be undetermined coefficient; ${\mathrm{\&alpha;}}_1^2=\frac{{\mathrm{\&omega;}}^2}{c_{L1}^2}-{\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="A20061007288100193.png"\; state="\{\{state\}\}">k</figure-callout>}}^2,$ ${\mathrm{\&alpha;}}_2^2=\frac{{\mathrm{\&omega;}}^2}{{\mathrm{<figure-callout\; id="2"\; label="c\; L"\; filenames="A20061007288100193.png"\; state="\{\{state\}\}">c</figure-callout>}}_L^2}-{\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="A20061007288100193.png"\; state="\{\{state\}\}">k</figure-callout>}}^2,$ ${\mathrm{\&alpha;}}_3^2=\frac{{\mathrm{\&omega;}}^2}{c_{L3}^2}-{\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="A20061007288100193.png"\; state="\{\{state\}\}">k</figure-callout>}}^2,$ ${\mathrm{\&beta;}}_1^2=\frac{{\mathrm{\&omega;}}^2}{c_{T1}^2}-{\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="A20061007288100193.png"\; state="\{\{state\}\}">k</figure-callout>}}^2,$ ${\mathrm{\&beta;}}_2^2=\frac{{\mathrm{\&omega;}}^2}{{\mathrm{<figure-callout\; id="2"\; label="c\; T"\; filenames="A20061007288100193.png"\; state="\{\{state\}\}">c</figure-callout>}}_T^2}-{\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="A20061007288100193.png"\; state="\{\{state\}\}">k</figure-callout>}}^2,$ ${\mathrm{\&beta;}}_3^2=\frac{{\mathrm{\&omega;}}^2}{c_{T3}^2}-{\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="A20061007288100193.png"\; state="\{\{state\}\}">k</figure-callout>}}^2,$ c _T1, c _T2And c _T3Be respectively the transverse wave speed of viscoelastic coating, hollow pipe and liquid; c _L1, c _L2And c _L3Be respectively the longitudinal wave velocity of viscoelastic coating, hollow pipe and liquid; μ ₁, μ ₂And μ ₃Be respectively the Lame constant of viscoelastic coating, hollow pipe and liquid; K is a wave number; H is the Hankel function; J is the Bessel function; R is a radius, and z is an axial location; ω is the circular frequency of ripple.Subscript f, v be express liquid and viscoelastic coating respectively.

Stress and displacement boundary conditions in the band viscoelastic coating liquid-filling pipe have:

(1) viscoelastic coating outside surface (r=r ₁):

$\left\{\begin{array}{c}{\left({\mathrm{\&sigma;}}_{\mathrm{rr}}^v\right)}_{r=r_1}=0\\ {\left({\mathrm{\&sigma;}}_{\mathrm{rz}}^v\right)}_{r=r_1}=0\end{array}\right.---\left(6\right)$

(2) interface (r=r of pipeline and viscoelastic coating ₂):

$\left\{\begin{array}{c}{\left(u_r\right)}_{r={\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="A20061007288100193.png"\; state="\{\{state\}\}">r</figure-callout>}}_2}={\left(u_r^v\right)}_{r=r_2}\\ {\left(u_z\right)}_{r={\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="A20061007288100193.png"\; state="\{\{state\}\}">r</figure-callout>}}_2}={\left(u_z^v\right)}_{r=r_2}\\ {\left({\mathrm{\&sigma;}}_{\mathrm{rr}}\right)}_{r={\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="A20061007288100193.png"\; state="\{\{state\}\}">r</figure-callout>}}_2}={\left({\mathrm{\&sigma;}}_{\mathrm{rr}}^v\right)}_{r=r_2}\\ {\left({\mathrm{\&sigma;}}_{\mathrm{rz}}\right)}_{r={\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="A20061007288100193.png"\; state="\{\{state\}\}">r</figure-callout>}}_2}{=\left({\mathrm{\&sigma;}}_{\mathrm{rz}}^v\right)}_{r=r_2}\end{array}\right.---\left(7\right)$

(3) interface (r=r of pipeline and liquid ₃):

$\left\{\begin{array}{c}{\left(u_r\right)}_{r=r_3}={\left(u_r^f\right)}_{r=r_3}\\ {\left(u_z\right)}_{r=r_3}={\left(u_z^f\right)}_{r=r_3}\\ {\left({\mathrm{\&sigma;}}_{\mathrm{rr}}\right)}_{r=r_3}={\left({\mathrm{\&sigma;}}_{\mathrm{rr}}^f\right)}_{r=r_3}\\ {\left({\mathrm{\&sigma;}}_{\mathrm{rz}}\right)}_{r=r_3}{=\left({\mathrm{\&sigma;}}_{\mathrm{rz}}^f\right)}_{r=r_3}\end{array}\right.---\left(8\right)$

Utilization is set up a stack features equation with the top offset and the stress condition of continuity, and the matrix form of equation is:

$\left[\begin{array}{cccccccccc}{D}_{11}& D_{12}& D_{13}& D_{14}& 0& 0& 0& 0& 0& 0\\ D_{21}& D_{22}& D_{23}& D_{24}& 0& 0& 0& 0& 0& 0\\ D_{31}& D_{32}& D_{33}& D_{34}& D_{35}& D_{36}& D_{37}& D_{38}& 0& 0\\ D_{41}& D_{42}& D_{43}& D_{44}& D_{45}& D_{46}& D_{47}& D_{48}& 0& 0\\ D_{51}& D_{52}& D_{53}& D_{54}& D_{55}& D_{56}& D_{57}& D_{58}& 0& 0\\ D_{61}& D_{62}& D_{63}& D_{64}& D_{65}& D_{66}& D_{67}& D_{68}& 0& 0\\ 0& 0& 0& 0& D_{75}& D_{76}& D_{77}& D_{78}& D_{79}& D_{7\left(10\right)}\\ 0& 0& 0& 0& D_{85}& D_{86}& D_{87}& D_{88}& D_{89}& D_{8\left(10\right)}\\ 0& 0& 0& 0& D_{95}& D_{96}& D_{97}& D_{98}& D_{99}& D_{9\left(10\right)}\\ 0& 0& 0& 0& D_{\left(10\right)5}& D_{\left(10\right)6}& D_{\left(10\right)7}& D_{\left(10\right)8}& D_{\left(10\right)9}& D_{\left(10\right)\left(10\right)}\end{array}\right]\left\{\begin{array}{c}{A}_1\\ A_2\\ B_1\\ B_2\\ A_3\\ A_4\\ B_3\\ B_4\\ A_5\\ {\mathrm{<figure-callout\; id="5"\; label="B"\; filenames="A20061007288100181.png"\; state="\{\{state\}\}">B</figure-callout>}}_5\end{array}\right\}=0---\left(9\right)$

For making formula (9) that untrivialo solution be arranged, its determinant of coefficient is necessary for zero.That is:

$\left|\begin{array}{cccccccccc}{D}_{11}& D_{12}& D_{13}& D_{14}& 0& 0& 0& 0& 0& 0\\ D_{21}& D_{22}& D_{23}& D_{24}& 0& 0& 0& 0& 0& 0\\ D_{31}& D_{32}& D_{33}& D_{34}& D_{35}& D_{36}& D_{37}& D_{38}& 0& 0\\ D_{41}& D_{42}& D_{43}& D_{44}& D_{45}& D_{46}& D_{47}& D_{48}& 0& 0\\ D_{51}& D_{52}& D_{53}& D_{54}& D_{55}& D_{56}& D_{57}& D_{58}& 0& 0\\ D_{61}& D_{62}& D_{63}& D_{64}& D_{65}& D_{66}& D_{67}& D_{68}& 0& 0\\ 0& 0& 0& 0& D_{75}& D_{76}& D_{77}& D_{78}& D_{79}& D_{7\left(10\right)}\\ 0& 0& 0& 0& D_{85}& D_{86}& D_{87}& D_{88}& D_{89}& D_{8\left(10\right)}\\ 0& 0& 0& 0& D_{95}& D_{96}& D_{97}& D_{98}& D_{99}& D_{9\left(10\right)}\\ 0& 0& 0& 0& D_{\left(10\right)5}& D_{\left(10\right)6}& D_{\left(10\right)7}& D_{\left(10\right)8}& D_{\left(10\right)9}& D_{\left(10\right)\left(10\right)}\end{array}\right|=0---\left(10\right)$

Following formula is the dispersion equation of longitudinal mode in the band viscoelastic coating topping up body pipeline.Every formula that embodies of determinant is seen appendix in the equation.When liquid was the non-viscous flow moving medium, dispersion equation was reduced to 9 * 9 determinant.

When the viscoelastic layer in the formula (10) and all parameters of individual layer pipeline are exchanged, can obtain viscoelastic coating is with longitudinal mode in the viscoelastic coating liquid-filling pipe when the individual layer inner-walls of duct dispersion equation.

Formula (10) is applicable to the situation of viscoelastic coating when individual layer inner-walls of duct or outer wall.Band viscoelastic coating liquid-filling pipe as shown in Figure 2.Fig. 2 (a) be viscoelastic coating 8 outside, individual layer pipeline 9 is interior, the band viscoelastic coating liquid-filling pipe of liquid 10 in individual layer pipeline 9.Fig. 2 (b) be viscoelastic coating 8 interior, individual layer pipeline 9 outside, the band viscoelastic coating liquid-filling pipe of liquid 10 in viscoelastic coating 8.

The present invention has adopted above technical scheme, has reached following effect: (1) can grow distance detecting to band viscoelastic coating liquid-filling pipe, and can carry out detecting in labour; (2) only needing at a place transducer to be installed can carry out complete detection to the whole cross section of band viscoelastic coating liquid-filling pipe of one section longer distance, the detection efficiency height, and labour intensity is low.

Description of drawings

Fig. 1 pick-up unit schematic diagram;

Fig. 2 band viscoelastic coating liquid-filling pipe synoptic diagram;

Fig. 3 has torsion mode dispersion curve in the epoxy resin clad water-filling steel pipe;

Defective axial location synoptic diagram in Fig. 4 band epoxy resins clad water-filling steel pipe;

Fig. 5 defective schematic cross-section;

Fig. 6 pumping signal figure;

During Fig. 7 frequency 105kHz, the oscillogram that in epoxy resin clad water-filling steel pipe, receives;

During Fig. 8 frequency 120kHz, the oscillogram that in epoxy resin clad water-filling steel pipe, receives;

Among the figure, 1, piezoelectric ceramic ring, 2, function generator, 3, power amplifier, 4, switch, 5, band viscoelastic coating liquid-filling pipe, 6, digital oscilloscope, 7, computing machine, 8, viscoelastic coating, 9, the individual layer pipeline, 10, liquid, 11, circumferential defect, 12, band epoxy resins clad water-filling steel pipe, 13, epoxy resin layer, 14, steel pipe, 15, water, 16, first echo, 17, second echo, the 18, the 3rd echo, 19, the 4th echo, the 20, the 5th echo, the 21, the 6th echo.

Embodiment

Content in conjunction with the inventive method provides embodiment:

(1) the length-expanding and contracting piezoelectric sheet with the generous 20mm of being respectively of 16 lengths of a film, 4mm and 0.5mm composes in parallel a piezoelectric ceramic ring 1, circumferentially be distributed on band viscoelastic coating liquid-filling pipe 5 one ends, length direction is parallel with conduit axis, polarised direction is along the piezoelectric ceramic piece thickness direction, and the upper and lower surface of piezoelectric ceramic piece is an electrode.The length direction of piezoelectric ceramic piece is parallel with conduit axis, and each piezoelectric patches also is unified into a piezoelectric ceramic ring 1.This piezoelectric ceramic ring 1 had both encouraged transducer, made receiving transducer again.Band viscoelastic coating liquid-filling pipe 5 in the present embodiment is a band epoxy resins clad water-filling steel pipe 12, long 4m, steel pipe overall diameter 60mm, wall thickness 3.5mm, the average thick 0.24mm of epoxy resin.The longitudinal wave velocity of steel is 5960m/s, and transverse wave speed is 3260m/s, and compressional wave decay and shear wave decay are 0, and density is 7932kg/m ³The epoxy resin longitudinal wave velocity is 2532m/s, and transverse wave speed is 1114m/s, and density is 1170kg/m ³, compressional wave decays to 0.068np/wl, and shear wave decays to 0.17np/wl; The longitudinal wave velocity of water is 1500m/s, and transverse wave speed, compressional wave decay and shear wave decay are 0, and the density of water is 1000kg/m ³

According to the numerical solution to formula (10), Fig. 3 has provided the dispersion curve of longitudinal mode in the band epoxy resins clad water-filling steel pipe 12 of above-mentioned parameter.Fig. 3 (a) and Fig. 3 (b) are respectively group velocity and decay dispersion curve.The bandwidth of each undisturbed L (0,2) mode component changes in the 35-40kHz scope among the figure.At frequency band 0-0.5MHz, decay is lower than 6dB/m, group velocity is lower than 0.0003m with the absolute value of frequency change rate, the frequency range that is fit to undisturbed L (0,2) the mode component of defects detection in the band epoxy resins clad water-filling steel pipe 12 is: 93-128kHz, 144-184kHz, 205-245kHz, 264-304kHz, 319-363kHz, 386-422kHz and 446-483kHz.

In the band epoxy resins clad water-filling steel pipe 12 of above-mentioned geometry and material parameter, processed an artificial circumferential defect 11, defective axial location such as Fig. 4.Defective is 3.77m apart from band epoxy resins clad water-filling steel pipe 12 1 ends (being piezoelectric ceramic ring 1 installation place).Fig. 5 has provided the circumferential defect cross sectional representation.Wherein, be respectively epoxy resin layer 13 from outside to inside, steel pipe 14 and water 15.Circumferential defect 11 circumferential chord length 14mm, axial wide 1.1mm.Its xsect is 5.55% of a whole pipe xsect, is the non-defective that penetrates;

(2) produce the narrow-band impulse that centre frequency is adjustable by function generator 2, the type of narrow-band impulse, frequency, intensity and recurrent interval etc. all can exert an influence to supersonic guide-wave.In this enforcement, produce 20 sinusoidal signals of shaking the cycles of peak-to-peak value 150mV through the Hanning window modulation by function generator 2, the frequency of selecting has two kinds: 105kHz and 120kHz, the longitudinal mode that encourages under these two frequencies are same undisturbed L (0,2) mode component.These narrow-band impulse excitations are at interval all greater than 20ms.The frequency of these two pumping signals is lower than 6dB/m in the decay of longitudinal mode, group velocity is lower than 0.0003m with the absolute value of frequency change rate, sampling rate is that the 6dB bandwidth of the pumping signal of 50MHz is controlled the bandwidth less than one of single undisturbed L (0,2) mode branch.Sampling rate be the frequency of 50MHz be the 120kHz single audio signal as shown in Figure 6, wherein, time domain waveform is 6 (a), frequency domain figure is 6 (b), the 6dB bandwidth of pumping signal is about 12.5kHz;

(3) pumping signal is carried out power amplification through power amplifier 3, and peak-to-peak value reaches 150V; By switch 4 excitation piezoelectric ceramic rings 1, excitation undisturbed L (0,2) mode component in band epoxy resins clad water-filling steel pipe 12;

(4) Ji Li longitudinal mode signal is propagated in band epoxy resins clad water-filling steel pipe 12, after defective and pipe end reflection, by switch 4, piezoelectric ceramic ring 1 is received signal again, show at digital oscilloscope 6, and store computing machine 7 into by ethernet port;

(5) during frequency 105kHz, in epoxy resin clad water-filling steel pipe 12, receive waveform such as Fig. 7.During frequency 120kHz, in epoxy resin clad water-filling steel pipe 12, receive waveform such as Fig. 8.By the time of the arrival of the reflection echo in analytic signal acceptance point, determine the axial location of circumferential defect 11 in the pipeline.As shown in Figure 7, the 3rd echo 18 is the end face echo, and first echo 16 and second echo 17 are arranged before the 3rd echo 18, and as shown in Figure 8, the 4th echo 21 is the end face echo, and the 5th echo 19 and the 6th echo 20 are arranged before the 4th echo 21.Second echo 17 is identical with the time location of the 6th echo 20, is about 1.476ms.When centre frequency is 105kHz and 120kHz, undisturbed L (0,2) group velocity of mode component all is about 3.130m/ms, can determine the distance propagated according to the velocity of wave time of multiply by, the position that obtains defective as can be known during time 1.142ms is 3.786m, with the actual range relative error of circumferential defect 11 only be 0.4%.Because second echo 17 does not occur in Fig. 8, the 6th echo 20 does not occur in Fig. 7, can be defined as changing mode, does not consider.Thereby determine the quantity and the axial location of defective.

Appendix

${\mathrm{<figure-callout\; id="11"\; label="D"\; filenames="A20061007288100191.png"\; state="\{\{state\}\}">D</figure-callout>}}_{11}=(k^2-{\mathrm{\&beta;}}_1^2){\mathrm{<figure-callout\; id="0"\; label="H"\; filenames="A20061007288100193.png"\; state="\{\{state\}\}">H</figure-callout>}}_0^1\left({\mathrm{\&alpha;}}_1{r}_1\right)+2\frac{{\mathrm{\&alpha;}}_1}{r_1}{H}_1^1\left({\mathrm{\&alpha;}}_1{r}_1\right)$

${\mathrm{<figure-callout\; id="12"\; label="D"\; filenames="A20061007288100191.png"\; state="\{\{state\}\}">D</figure-callout>}}_{12}=(k^2-{\mathrm{\&beta;}}_1^2){\mathrm{<figure-callout\; id="0"\; label="H"\; filenames="A20061007288100193.png"\; state="\{\{state\}\}">H</figure-callout>}}_0^2\left({\mathrm{\&alpha;}}_1{r}_1\right)+2\frac{{\mathrm{\&alpha;}}_1}{r_1}{H}_1^2\left({\mathrm{\&alpha;}}_1{r}_1\right)$

$D_{13}=2k{\mathrm{\&beta;}}_1{\mathrm{<figure-callout\; id="0"\; label="H"\; filenames="A20061007288100193.png"\; state="\{\{state\}\}">H</figure-callout>}}_0^1\left({\mathrm{\&beta;}}_1{r}_1\right)-2\frac{k}{r_1}{H}_1^1\left({\mathrm{\&beta;}}_1{r}_1\right)$

$D_{14}=2k{\mathrm{\&beta;}}_1{\mathrm{<figure-callout\; id="0"\; label="H"\; filenames="A20061007288100193.png"\; state="\{\{state\}\}">H</figure-callout>}}_0^2\left({\mathrm{\&beta;}}_1{r}_1\right)-2\frac{k}{r_1}{H}_1^2\left({\mathrm{\&beta;}}_1{r}_1\right)$

$D_{21}=-2k{\mathrm{\&alpha;}}_1{H}_1^1\left({\mathrm{\&alpha;}}_1{r}_1\right)$

$D_{22}=-2k{\mathrm{\&alpha;}}_1{H}_1^2\left({\mathrm{\&alpha;}}_1{r}_1\right)$

$D_{23}=(k^2-{\mathrm{\&beta;}}_1^2)H_1^1\left({\mathrm{\&beta;}}_1{r}_1\right)$

$D_{24}=(k^2-{\mathrm{\&beta;}}_1^2)H_1^2\left({\mathrm{\&beta;}}_1{r}_1\right)$

$D_{31}={\mathrm{\&mu;}}_1[(k^2-{\mathrm{\&beta;}}_1^2){\mathrm{<figure-callout\; id="0"\; label="H"\; filenames="A20061007288100193.png"\; state="\{\{state\}\}">H</figure-callout>}}_0^1\left({\mathrm{\&alpha;}}_1{r}_2\right)+2\frac{{\mathrm{\&alpha;}}_1}{r_2}{H}_1^1\left({\mathrm{\&alpha;}}_1{r}_2\right)]$

$D_{32}={\mathrm{\&mu;}}_1[(k^2-{\mathrm{\&beta;}}_1^2){\mathrm{<figure-callout\; id="0"\; label="H"\; filenames="A20061007288100193.png"\; state="\{\{state\}\}">H</figure-callout>}}_0^2\left({\mathrm{\&alpha;}}_1{r}_2\right)+2\frac{{\mathrm{\&alpha;}}_1}{r_2}{H}_1^2\left({\mathrm{\&alpha;}}_1{r}_2\right)]$

$D_{33}={\mathrm{\&mu;}}_1[2k{\mathrm{\&beta;}}_1{\mathrm{<figure-callout\; id="0"\; label="H"\; filenames="A20061007288100193.png"\; state="\{\{state\}\}">H</figure-callout>}}_0^1\left({\mathrm{\&beta;}}_1{r}_2\right)-2\frac{k}{r_2}{H}_1^1\left({\mathrm{\&beta;}}_1{r}_2\right)]$

$D_{34}={\mathrm{\&mu;}}_1[2k{\mathrm{\&beta;}}_1{\mathrm{<figure-callout\; id="0"\; label="H"\; filenames="A20061007288100193.png"\; state="\{\{state\}\}">H</figure-callout>}}_0^2\left({\mathrm{\&beta;}}_1{r}_2\right)-2\frac{k}{r_2}{H}_1^2\left({\mathrm{\&beta;}}_1{r}_2\right)]$

$D_{35}=-{\mathrm{\&mu;}}_2[(k^2-{\mathrm{\&beta;}}_2^2){\mathrm{<figure-callout\; id="0"\; label="H"\; filenames="A20061007288100193.png"\; state="\{\{state\}\}">H</figure-callout>}}_0^1\left({\mathrm{\&alpha;}}_2{r}_2\right)+2\frac{{\mathrm{\&alpha;}}_2}{r_2}{H}_1^1\left({\mathrm{\&alpha;}}_2{r}_2\right)]$

$D_{36}=-{\mathrm{\&mu;}}_2[(k^2-{\mathrm{\&beta;}}_2^2){\mathrm{<figure-callout\; id="0"\; label="H"\; filenames="A20061007288100193.png"\; state="\{\{state\}\}">H</figure-callout>}}_0^2\left({\mathrm{\&alpha;}}_2{r}_2\right)+2\frac{{\mathrm{\&alpha;}}_2}{r_2}{H}_1^2\left({\mathrm{\&alpha;}}_2{r}_2\right)]$

$D_{37}=-{\mathrm{\&mu;}}_2[2k{\mathrm{\&beta;}}_2{\mathrm{<figure-callout\; id="0"\; label="H"\; filenames="A20061007288100193.png"\; state="\{\{state\}\}">H</figure-callout>}}_0^1\left({\mathrm{\&beta;}}_2{r}_2\right)-2\frac{k}{r_2}{H}_1^1\left({\mathrm{\&beta;}}_2{r}_2\right)]$

$D_{38}=-{\mathrm{\&mu;}}_2[2k{\mathrm{\&beta;}}_2{\mathrm{<figure-callout\; id="0"\; label="H"\; filenames="A20061007288100193.png"\; state="\{\{state\}\}">H</figure-callout>}}_0^2\left({\mathrm{\&beta;}}_2{r}_2\right)-2\frac{k}{r_2}{H}_1^2\left({\mathrm{\&beta;}}_2{r}_2\right)]$

$D_{41}=-2k{\mathrm{\&alpha;}}_1{\mathrm{\&mu;}}_1{H}_1^1\left({\mathrm{\&alpha;}}_1{r}_2\right)$

$D_{42}=-2k{\mathrm{\&alpha;}}_1{\mathrm{\&mu;}}_1{H}_1^2\left({\mathrm{\&alpha;}}_1{r}_2\right)$

$D_{43}={\mathrm{\&mu;}}_1(k^2-{\mathrm{\&beta;}}_1^2)H_1^1\left({\mathrm{\&beta;}}_1{r}_2\right)$

$D_{44}={\mathrm{\&mu;}}_1(k^2-{\mathrm{\&beta;}}_1^2)H_1^2\left({\mathrm{\&beta;}}_1{r}_2\right)$

$D_{45}=2k{\mathrm{\&alpha;}}_2{\mathrm{\&mu;}}_2{H}_1^1\left({\mathrm{\&alpha;}}_2{r}_2\right)$

$D_{46}=2k{\mathrm{\&alpha;}}_2{\mathrm{\&mu;}}_2{H}_1^2\left({\mathrm{\&alpha;}}_2{r}_2\right)$

$D_{47}=-{\mathrm{\&mu;}}_2(k^2-{\mathrm{\&beta;}}_2^2)H_1^1\left({\mathrm{\&beta;}}_2{r}_2\right)$

$D_{48}=-{\mathrm{\&mu;}}_2(k^2-{\mathrm{\&beta;}}_2^2)H_1^2\left({\mathrm{\&beta;}}_2{r}_2\right)$

$D_{51}=-{\mathrm{\&alpha;}}_1{H}_1^1\left({\mathrm{\&alpha;}}_1{r}_2\right)$

$D_{52}=-{\mathrm{\&alpha;}}_1{H}_1^2\left({\mathrm{\&alpha;}}_1{r}_2\right)$

$D_{53}={\mathrm{kH}}_1^1\left({\mathrm{\&beta;}}_1{r}_2\right)$

$D_{54}={\mathrm{kH}}_1^2\left({\mathrm{\&beta;}}_1{r}_2\right)$

$D_{55}={\mathrm{\&alpha;}}_2{H}_1^1\left({\mathrm{\&alpha;}}_2{r}_2\right)$

$D_{56}={\mathrm{\&alpha;}}_2{H}_1^2\left({\mathrm{\&alpha;}}_2{r}_2\right)$

$D_{57}={-\mathrm{kH}}_1^1\left({\mathrm{\&beta;}}_2{r}_2\right)$

$D_{58}={-\mathrm{kH}}_1^2\left({\mathrm{\&beta;}}_2{r}_2\right)$

$D_{61}=-{\mathrm{<figure-callout\; id="0"\; label="kH"\; filenames="A20061007288100193.png"\; state="\{\{state\}\}">kH</figure-callout>}}_0^1\left({\mathrm{\&alpha;}}_1{r}_2\right)$

$D_{62}=-{\mathrm{<figure-callout\; id="0"\; label="kH"\; filenames="A20061007288100193.png"\; state="\{\{state\}\}">kH</figure-callout>}}_0^2\left({\mathrm{\&alpha;}}_1{r}_2\right)$

$D_{63}=-{\mathrm{\&beta;}}_1{\mathrm{<figure-callout\; id="0"\; label="H"\; filenames="A20061007288100193.png"\; state="\{\{state\}\}">H</figure-callout>}}_0^1\left({\mathrm{\&beta;}}_1{r}_2\right)$

$D_{64}=-{\mathrm{\&beta;}}_1{\mathrm{<figure-callout\; id="0"\; label="H"\; filenames="A20061007288100193.png"\; state="\{\{state\}\}">H</figure-callout>}}_0^2\left({\mathrm{\&beta;}}_1{r}_2\right)$

$D_{65}={\mathrm{<figure-callout\; id="0"\; label="kH"\; filenames="A20061007288100193.png"\; state="\{\{state\}\}">kH</figure-callout>}}_0^1\left({\mathrm{\&alpha;}}_2{r}_2\right)$

$D_{66}={\mathrm{<figure-callout\; id="0"\; label="kH"\; filenames="A20061007288100193.png"\; state="\{\{state\}\}">kH</figure-callout>}}_0^2\left({\mathrm{\&alpha;}}_2{r}_2\right)$

$D_{67}={\mathrm{\&beta;}}_2{\mathrm{<figure-callout\; id="0"\; label="H"\; filenames="A20061007288100193.png"\; state="\{\{state\}\}">H</figure-callout>}}_0^1\left({\mathrm{\&beta;}}_2{r}_2\right)$

$D_{68}={\mathrm{\&beta;}}_2{\mathrm{<figure-callout\; id="0"\; label="H"\; filenames="A20061007288100193.png"\; state="\{\{state\}\}">H</figure-callout>}}_0^2\left({\mathrm{\&beta;}}_2{r}_2\right)$

$D_{75}={\mathrm{\&mu;}}_2[(k^2-{\mathrm{\&beta;}}_2^2){\mathrm{<figure-callout\; id="0"\; label="H"\; filenames="A20061007288100193.png"\; state="\{\{state\}\}">H</figure-callout>}}_0^1\left({\mathrm{\&alpha;}}_2{r}_2\right)+2\frac{{\mathrm{\&alpha;}}_2}{r_1}{H}_1^1\left({\mathrm{\&alpha;}}_2{r}_1\right)]$

$D_{76}={\mathrm{\&mu;}}_2[(k^2-{\mathrm{\&beta;}}_2^2){\mathrm{<figure-callout\; id="0"\; label="H"\; filenames="A20061007288100193.png"\; state="\{\{state\}\}">H</figure-callout>}}_0^2\left({\mathrm{\&alpha;}}_2{r}_1\right)+2\frac{{\mathrm{\&alpha;}}_2}{r_1}{H}_1^2\left({\mathrm{\&alpha;}}_2{r}_1\right)]$

$D_{77}={\mathrm{\&mu;}}_2[2k{\mathrm{\&beta;}}_2{\mathrm{<figure-callout\; id="0"\; label="H"\; filenames="A20061007288100193.png"\; state="\{\{state\}\}">H</figure-callout>}}_0^1\left({\mathrm{\&beta;}}_2{r}_1\right)-2\frac{k}{r_1}{H}_1^1\left({\mathrm{\&beta;}}_2{r}_1\right)]$

$D_{78}={\mathrm{\&mu;}}_2[2k{\mathrm{\&beta;}}_2{\mathrm{<figure-callout\; id="0"\; label="H"\; filenames="A20061007288100193.png"\; state="\{\{state\}\}">H</figure-callout>}}_0^2\left({\mathrm{\&beta;}}_2{r}_1\right)-2\frac{k}{r_1}{H}_1^2\left({\mathrm{\&beta;}}_2{r}_1\right)]$

$D_{79}=-2{\mathrm{\&mu;}}_3[\frac{1}{2}(k^2-{\mathrm{\&beta;}}_3^2)J_0\left({\mathrm{\&alpha;}}_3{r}_1\right)+\frac{{\mathrm{\&alpha;}}_3}{r}{J}_1\left({\mathrm{\&alpha;}}_3{r}_1\right)]$

$D_{7\left(10\right)}=-2{\mathrm{\&mu;}}_3[-\mathrm{ik}{\mathrm{\&beta;}}_3^2{J}_0\left({\mathrm{\&beta;}}_3{r}_1\right)+\frac{\mathrm{ik}{\mathrm{\&beta;}}_3}{r_1}{J}_1\left({\mathrm{\&beta;}}_3{r}_1\right)]$

$D_{85}=-2k{\mathrm{\&alpha;}}_2{\mathrm{\&mu;}}_2{H}_1^1\left({\mathrm{\&alpha;}}_2{r}_1\right)$

$D_{86}=-2k{\mathrm{\&alpha;}}_2{\mathrm{\&mu;}}_2{H}_1^2\left({\mathrm{\&alpha;}}_2{r}_1\right)$

$D_{87}={\mathrm{\&mu;}}_2(k^2-{\mathrm{\&beta;}}_2^2)H_1^1\left({\mathrm{\&beta;}}_2{r}_1\right)$

${\mathrm{<figure-callout\; id="88"\; label="D"\; filenames="A20061007288100193.png"\; state="\{\{state\}\}">D</figure-callout>}}_{88}={\mathrm{\&mu;}}_2(k^2-{\mathrm{\&beta;}}_2^2)H_1^2\left({\mathrm{\&beta;}}_2{r}_1\right)$

D ₈₉＝2ikμ ₃α ₃J ₁(α ₃r ₁)

$D_{8\left(10\right)}=({\mathrm{\&beta;}}_3^2-k^2){\mathrm{\&mu;}}_3{J}_1\left({\mathrm{\&beta;}}_3{r}_1\right)$

$D_{95}=-{\mathrm{\&alpha;}}_2{H}_1^1\left({\mathrm{\&alpha;}}_2{r}_1\right)$

$D_{96}=-{\mathrm{\&alpha;}}_2{H}_1^2\left({\mathrm{\&alpha;}}_2{r}_1\right)$

$D_{97}=k{H}_1^1\left({\mathrm{\&beta;}}_2{r}_1\right)$

$D_{98}=k{H}_1^2\left({\mathrm{\&beta;}}_2{r}_1\right)$

D ₉₉＝α ₃J ₁(α ₃r ₁)

D ₉₍₁₀₎＝ikβ ₃J ₁(β ₃r ₁)

$D_{\left(10\right)5}=-{\mathrm{<figure-callout\; id="0"\; label="kH"\; filenames="A20061007288100193.png"\; state="\{\{state\}\}">kH</figure-callout>}}_0^1\left({\mathrm{\&alpha;}}_2{r}_1\right)$

$D_{\left(10\right)6}=-\mathrm{<figure-callout\; id="0"\; label="k\; H"\; filenames="A20061007288100193.png"\; state="\{\{state\}\}">k</figure-callout>}{H}_{}^{}{}_0^2\left({\mathrm{\&alpha;}}_2{r}_1\right)$

$D_{\left(10\right)7}=-{\mathrm{\&beta;}}_2{\mathrm{<figure-callout\; id="0"\; label="H"\; filenames="A20061007288100193.png"\; state="\{\{state\}\}">H</figure-callout>}}_0^1\left({\mathrm{\&beta;}}_2{r}_1\right)$

$D_{\left(10\right)8}=-{\mathrm{\&beta;}}_2{\mathrm{<figure-callout\; id="0"\; label="H"\; filenames="A20061007288100193.png"\; state="\{\{state\}\}">H</figure-callout>}}_0^2\left({\mathrm{\&beta;}}_2{r}_1\right).$

D ₍₁₀₎₉＝-ikJ ₀(α ₃r ₁)

$D_{\left(10\right)\left(10\right)}=-{\mathrm{\&beta;}}_3^2{J}_0\left({\mathrm{\&beta;}}_3{r}_1\right)$

Claims (1)

1, a kind of method that band viscoelastic coating liquid-filling pipe guided wave is detected, it is characterized in that: the step of detection method is as follows:

1) if viscoelastic coating at pipeline outer wall, then encloses viscoelastic coating along the circumferential local strip off one of pipeline, at the circumferential uniform a plurality of length-expanding and contracting piezoelectric sheets of strip off place; If viscoelastic coating at inner-walls of duct, then directly is distributed on pipeline outer wall with piezoelectric ceramic piece; The length direction of piezoelectric ceramic piece is parallel with conduit axis, and polarised direction is along the piezoelectric ceramic piece thickness direction, and the upper and lower surface of piezoelectric ceramic piece is an electrode; Each piezoelectric ceramic piece also is unified into a piezoelectric ceramic ring (1), and this piezoelectric ceramic ring (1) had both encouraged transducer, made receiving transducer again;

2) produce the narrow-band impulse that centre frequency is adjustable by function generator (2), the decay that excitation frequency is controlled at longitudinal mode is lower than 6dB/m, group velocity is lower than 0.0003m with the absolute value of frequency change rate, sampling rate is that the 6dB bandwidth of the pumping signal of 50MHz is controlled the bandwidth less than one of single undisturbed L (0,2) mode branch;

3) pumping signal is carried out power amplification through power amplifier (3); By switch (4) excitation piezoelectric ceramic ring (1), excitation undisturbed L (0,2) mode component in band viscoelastic coating liquid-filling pipe (5);

4) Ji Li undisturbed L (0,2) signal of mode component is propagated in band viscoelastic coating liquid-filling pipe (5), after defective and pipe end reflection, by switch (4), piezoelectric ceramic ring (1) is received signal again, show at digital oscilloscope (6), and store computing machine (7) into by ethernet port;

5) under other constant conditions, change the centre frequency of narrow-band impulse, encourage same undisturbed L (0,2) mode component; This frequency control is lower than 6dB/m in the decay of longitudinal mode, group velocity is lower than 0.0003m with the absolute value of frequency change rate, sampling rate is that the 6dB bandwidth of the pumping signal of 50MHz is controlled the bandwidth less than single undisturbed L (0,2) mode branch, obtains another time domain waveform;

6) time location to all echoes before the end face echo in the different signal of two frequencies receiving compares, if an echo appears in the time location of echo same time location in another signal in the signal, can determine that this echo is a flaw echo, if the time location of echo same time location in another signal does not occur in the signal, can determine that then this echo is a conversion mode, does not consider; For the flaw echo of determining, multiply by undisturbed L (0 by the travel-time of flaw echo, 2) the group velocity value of mode component, and divided by 2, be in the band viscoelastic coating liquid-filling pipe defective apart from the axial location of piezoelectric ceramic ring (1), thereby determine the number and the axial location of defective.

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