CN107340331A - True time delay for platy structure detection is without frequency dispersion SH0Ripple phased array system - Google Patents

True time delay for platy structure detection is without frequency dispersion SH0Ripple phased array system Download PDF

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CN107340331A
CN107340331A CN201611003486.XA CN201611003486A CN107340331A CN 107340331 A CN107340331 A CN 107340331A CN 201611003486 A CN201611003486 A CN 201611003486A CN 107340331 A CN107340331 A CN 107340331A
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mrow
msub
ripple
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mfrac
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王文韬
李惠
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Harbin Institute of Technology
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Harbin Institute of Technology
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    • GPHYSICS
    • G01MEASURING; TESTING
    • G01NINVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N29/00Investigating 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
    • G01N29/04Analysing solids
    • G01N29/041Analysing solids on the surface of the material, e.g. using Lamb, Rayleigh or shear waves
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01NINVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N29/00Investigating 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
    • G01N29/04Analysing solids
    • G01N29/06Visualisation of the interior, e.g. acoustic microscopy
    • G01N29/0654Imaging
    • G01N29/069Defect imaging, localisation and sizing using, e.g. time of flight diffraction [TOFD], synthetic aperture focusing technique [SAFT], Amplituden-Laufzeit-Ortskurven [ALOK] technique
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01NINVESTIGATING OR ANALYSING MATERIALS BY DETERMINING THEIR CHEMICAL OR PHYSICAL PROPERTIES
    • G01N29/00Investigating 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
    • G01N29/44Processing the detected response signal, e.g. electronic circuits specially adapted therefor
    • G01N29/4409Processing the detected response signal, e.g. electronic circuits specially adapted therefor by comparison
    • G01N29/4427Processing the detected response signal, e.g. electronic circuits specially adapted therefor by comparison with stored values, e.g. threshold values

Abstract

A kind of true time delay for platy structure detection is without frequency dispersion SH0Ripple phased array system, including:Controller, multichannel D/A converter, multi-wafer SH ripple phased array probes, multichannel relay, multichannel analog/digital conversion capture card, imaging display, multi-wafer SH0Voltage signal is converted into fluctuation signal by inverse piezoelectric effect and ejected in the structure by ripple phased array probe, and the fluctuation signal that damage reflects is converted into electric signal according to direct piezoelectric effect in the reception stage;The transmission signal of multichannel D/A converter is connected to multi-wafer SH by multichannel relay in launching phase0On ripple phased array probe, and after launching phase terminates, by multi-wafer SH0Ripple phased array probe is connected on multichannel analog/digital conversion capture card, and echo-signal is damaged for gathering;Due to SH0The non-Dispersion of ripple in itself, the damage of system of the invention to platy structure detect, and improve spatial domain resolution ratio, the signal of amplification damage reflection.

Description

True time delay for platy structure detection is without frequency dispersion SH0Ripple phased array system
Technical field
Patent of the present invention is related to a kind of true time delay for platy structure detection without frequency dispersion SH0Ripple phased array system.
Background technology
Ordinary ultrasonic detection is the Structure Damage Identification of single probe, and what is obtained is one-dimensional signal, in single measurement In can not intuitively be imaged, and Multi probe composition phased array detection method structural damage can be detected and is imaged.It is super For sound phased array damage check originating from the phased-array radar in military affairs, the two is all based on Huygen's principle realization:One hair Penetrate and receive ultrasound beamformer and be used for damage check, one is used for target tracking using electromagnetic wave.The probe of ultrasonic phase array is It is made up of one group of piezoelectric transducer (PZT) unit independent of each other, ultrasound can independently be launched and be received to each unit Ripple, the pumping signal postponed by respective different time causes transmitting ultrasonic wave phase difference each other, so that each array element The ripple launched is superimposed to form the wave surface focused on directionality and wave beam for detecting in media as well.And in directional antenna beam After running into damage, its fluctuation signal reflected can be received by phased array probe, enter according to corresponding focusing rule Row delay disposal and superposition, realize phased array imaging.Compared with traditional ultrasound injury detection technique, ultrasonic phase array probe energy The wave beam of flexible deflection focusing is produced, is realized to by the scanning of geodesic structure or component, detection range is wide, and detection speed is fast, can be with Detection is difficult to approach, the undetectable region of conventional Ultrasound, realizes the detection to labyrinth and component and blind zone position defect. Pass through the control to local wafer cell pumping signal, it is possible to achieve high speed that conventional Ultrasound can not be realized, comprehensive, multi-angle Dynamic focusing scanning.
Phased array probe linear array major parameter is as shown in Figure 1.Wherein, N is linear array chip number, and w is single Piezoelectric patches array element width, l are single piezoelectric patches array element length, and e is the spacing space between array element, a centers between array element and array element Away from a=w+e, whole array total length is D=(N-1) d+w, also referred to as the array element aperture of ultrasonic phase array linear array.
To there is detection range in conventional ultrasonic wave phased array small in the detection to platy structure, and decay is big, and efficiency is low, difficult With intuitively by plate the problems such as damage imaging.And guided wave is different from normal ultrasound waves in plate, due to being limited by plate up-and-down boundary Make, guided wave can propagate farther distance without obvious signal attenuation in plate, be very suitable for carrying out long range labyrinth damage Triage is surveyed.But Lamb wave is frequency dispersion in plate, its velocity of wave changes, mode ratio with the conversion of specimen thickness and signal frequency Normal ultrasound waves are complicated and various modal couplings, as shown in Figure 2.
The content of the invention
Based on above weak point, the present invention proposes a kind of true time delay for platy structure detection without frequency dispersion SH0Ripple phase Array 1 system is controlled, can more accurately identify damage position and shape in plate, while expand the scope of damage check.
The technology used in the present invention is as follows:A kind of true time delay for platy structure detection is without frequency dispersion SH0Ripple phased array System, including:Controller, multichannel D/A converter, multi-wafer SH ripple phased array probes, multichannel relay, multichannel Analog/digital conversion capture card, imaging display,
Controller electric signal connecting multi-channel D/A converter, multichannel D/A converter pass through multichannel relay electricity Signal connects multi-wafer SH ripple phased array probes;
Multi-wafer SH ripples phased array probe by multichannel relay electric signal connecting multi-channel analog/digital conversion capture card, Multichannel analog/digital conversion capture card electric signal connects controller, controller electric signal connection imaging display;
The transmission signal of different passages is converted into analog voltage signal to drive multi-wafer by multichannel D/A converter Single mode SH0Ripple phased array probe;Multi-wafer SH0Voltage signal is converted into fluctuating by ripple phased array probe by inverse piezoelectric effect Signal ejects in the structure, while will damage the fluctuation signal conversion reflected according to direct piezoelectric effect in the reception stage Into electric signal;The analog electrical signal of the damage reflection echo of different passages is changed into control by multichannel analog/digital conversion capture card Device data signal;The transmission signal of multichannel D/A converter is connected to multi-wafer SH by multichannel relay in launching phase0 On ripple phased array probe, and after launching phase terminates, by multi-wafer SH0Ripple phased array probe is connected to multichannel analog and turned Change on capture card, echo-signal is damaged for gathering;Wherein described multi-wafer single mode SH0Ripple phased array probe includes pressing one The multiple d to form a line are spaced calmly36Type piezoelectric patches;
Controller is configured to the parameter of test specimen and calculates the transmission signal of different time delay, multi-wafer SH0 Ripple phased array probe includes multiple piezoelectric sensor units, is formed a line by order from top to bottom at regular intervals, and pass through Excited in the narrow-band impulse pumping signal one-time detection of the 3 cycles Hanning window amplitude modulation of different time delay, sent out respectively simultaneously Go out respective SH0Ripple, different SH0The wave surface of ripple is superimposed, and is prolonged by adjusting the time between different piezoelectric sensor units Late, its ultrasonic wave excited can be superimposed to form new wave surface in media as well, and focus at default focus P, and amplify SH0 This amplitude without single mode signals in frequency of ripple, so as to realize single mode SH in physical field0Wave beam deflection, focus on, the work(of scanning Energy;After running into damage reflection echo, all piezoelectric sensor units are receiving signal simultaneously, carry out weight to it by controller Structure is imaged after determining damage position, calculating, and the time delay by adjusting different excitation signal realizes that platy structure is region-wide Single mode SH0Ripple orientation fixed point scanning, so as to realize the purpose of damage check.
The present invention also has following technical characteristic:
1st, the detection range of the system is, according to d36Without frequency dispersion SH caused by type piezoelectric patches0The acoustic pressure of ripple, angular relationship meter Calculation obtains single d36- 6dB the angle thetas of type piezoelectric patches0=30 °, wherein, AmaxWhat is represented is most loud caused by single d36 chips Pressure amplitude value,Represent amplitude during maximum sound pressure half;
Multiple d36Type piezoelectric patches from top to bottom by array is arranged in order into after, disclosure satisfy that all multiple d36Type pressure The region of -6dB the criterions of electric piece is effective detection region, then effective coverage is the superposition in single first region that shakes, effective detection area Domain, which has a generally triangular shape, to be expanded outwardly, and its top closest approach is h apart from the distance of cell array center line, and focusing angle is β=2 θ0, obtained according to geometrical relationship:
2nd, true time delay is without frequency dispersion SH0Ripple phased array probe focus method is:
True time delay is without frequency dispersion SH0Ripple phased array centre frequency is 40kHz, is swashed with 3 cycle Hanning window narrow-band pings Hair is without frequency dispersion SH0Ripple carries out the damage check of platy structure, wherein, the pumping signal of unit is V (t- δn), reference voltage Pumping signalH (t) is He Wei Saden step letters Number, the H (t)=1 as t >=0;Work as t<H (t)=0 when 0, Np=3, fc=40kHz;Without frequency dispersion SH0The group velocity c of rippleSH,0(t- δnH)=[(t)] it is each piezoelectricity blade unit initial signal,p(t) it is wave field strength signal at focus P:
Ann)=cos (2 γ), γn=arccos (Fcos (θF)/rn) (5)
Wherein,Represent focus point with it is every Individual d36Type piezoelectric patches distance, focus position is relative to each d36The deviation angle γ of type piezoelectric patchesn=arccos (Fcos θF/rn), d between array36The delay of type piezoelectric patches pumping signal is δn, a is the distance of two phased array unit centers, and F is focal length, θF It is the deviation angle of focus, Ann) represent the different d in array on the focus point direction36Type piezoelectric patches excites initial Sound pressure,For acoustic pressure attenuation coefficient, t0It is a sufficiently large constant to ensure time delay not for negative.
3rd, true time delay is without frequency dispersion SH0Ripple phased array imaging method is:
It is θ to be located at angled, distance RdPoint D at have a damage, the focus of phase array focusing is at P, different d36Type pressure The ripple that electric piece is sent stack result S at point DD(t) shown in equation below, wherein dnFor n-th of d36Type piezoelectric patches to damage position D distance is put, its size is calculated by geometrical relationship:
Reflection echo is propagated back to m-th of d of phased array36The ripple signal of type piezoelectric patches is:
M-th of d36Type piezoelectric patches is after echo-signal is received, by fluctuation signal Sr(t) it is converted into Vr(t), and then pass through Equation below assembles each signal according to time delay, so that it is determined that the position of damage and degree;
When focus position overlaps with defective locations, focusing angle θFd, and focal length F=Rd, injury region produces very strong Without frequency dispersion SH0Wave reflection echo, assembling signal VR(t) amplitude can get maximum.
The present invention has the advantages that and advantage:To steel box girder bridge panel, pressure vessel, pipe damage, aircraft In the damage check of the platy structures such as covering, composite structure, detection range is wide, damage sensitivity is high, imaging is directly perceived, detection Efficiency high.Patent of the present invention by real time related method thereof realize physics sound field focusing without frequency dispersion SH0Ripple phased array skill Art, different from the single later stage mathematics virtual focusing method excited, the present invention can really inspire directionality in the structure Without frequency dispersion SH0Ripple wave beam, and flexibly realize the true effects such as scanning, deflection and focusing.The technology can significantly strengthen signal Signal to noise ratio, by without frequency dispersion SH0The deflection of wave beam and the spatial resolution for focusing on lifting damage check, improve detection essence Degree.Produce directionality focus on without frequency dispersion SH0Wave beam, and by reflecting no frequency dispersion SH0The strong and weak position to damage of ripple signal Put and judged with size.
Brief description of the drawings
Fig. 1 is the geometric parameter figure of linear array;
Fig. 2 is SH ripples and the dispersion curve figure of Lamb wave group velocity and the thick product of frequency;
Fig. 3 is true time delay without frequency dispersion SH0Ripple ultrasonic phase array detection process and hardware connection diagram;
Fig. 4 is d36Polarised direction, cut direction and the deformation schematic diagram of piezoelectric patches;
Fig. 5 is single d36Piezoelectric sensor unit produces wave field situation;
Fig. 6 is single d36Piezoelectric sensor unit produces the amplitude of different modalities ripple;
Fig. 7 is true time delay without frequency dispersion SH0The detection zone schematic diagram of ripple phased array system;
Fig. 8 is true time delay without frequency dispersion SH0The geometric properties of ripple phased array system detection zone;
Fig. 9 is true time delay without frequency dispersion SH0Ripple phased array pumping signal, synthesis wave surface and focus point schematic diagram;
Figure 10 is true time delay without frequency dispersion SH0Ripple ultrasonic phase array focuses on and reflection echo schematic diagram;
Figure 11 is true time delay without frequency dispersion SH0Ripple control battle array simulates wave field schematic diagram, focus point 100mm, 0 °;
Figure 12 is true time delay without frequency dispersion SH0Ripple phased array simulates wave field schematic diagram, focus point 100mm, 15 °;
Figure 13 is true time delay without frequency dispersion SH0Schematic diagram is built and tested to ripple phased array system;
Figure 14 is under lossless case, and true time delay is without frequency dispersion SH0The actually detected result figures of ripple phased array wave field LDV, focus point 100mm,0°;
Figure 15 is under lossless case, and true time delay is without frequency dispersion SH0The actually detected result figures of ripple phased array wave field LDV, focus point 100mm,15°;
Figure 16 is under lossless case, and true time delay is without frequency dispersion SH0The actually detected result figures of ripple phased array wave field LDV, focus point 100mm,30°;
Figure 17 is in the case of damaging, and true time delay is without frequency dispersion SH0The actually detected result figures of ripple phased array wave field LDV, focus point 100mm,0°;
Figure 18 is in the case of damaging, and true time delay is without frequency dispersion SH0The actually detected result figures of ripple phased array wave field LDV, focus point 100mm,15°;
Figure 19 is in the case of damaging, and true time delay is without frequency dispersion SH0The actually detected result figures of ripple phased array wave field LDV, focus point 100mm,30°;
Figure 20 is the location drawing that region damage is detected under degree of impairment;
Figure 21 is under degree of impairment, and true time delay is without frequency dispersion SH0The signal and original reference signal that ripple phased array receives Figure;
Figure 22 is under degree of impairment, is had, the difference signal figure in the case of not damaged;
Figure 23 is under degree of impairment, and true time delay is without frequency dispersion SH0The damage check result figure of ripple phased array;
Embodiment
Below according to the citing of explanation accompanying drawing, the present invention will be further described:
Embodiment 1
A kind of true time delay of damage check for platy structure is without frequency dispersion SH0Ripple phased array system, as shown in figure 3, bag Include:Controller 1, multichannel D/A converter 2, multi-wafer SH ripples phased array probe 3, multichannel relay 4, multichannel analog Conversion capture card 5, imaging display 6,
The electric signal connecting multi-channel D/A converter 2 of controller 1, multichannel D/A converter 2 passes through multichannel relay The electric signal of device 4 connection multi-wafer SH ripples phased array probe 3;
Multi-wafer SH ripples phased array probe 3 passes through the electric signal connecting multi-channel analog/digital conversion capture card of multichannel relay 4 5, the electric signal of multichannel analog/digital conversion capture card 5 connection controller 1, the electric signal of controller 1 connection imaging display 6.
The transmission signal of different passages is converted into analog voltage signal to drive multi-wafer by multichannel D/A converter Single mode SH0Ripple phased array probe;Multi-wafer SH0Voltage signal is converted into fluctuating by ripple phased array probe by inverse piezoelectric effect Signal ejects in the structure, while will damage the fluctuation signal conversion reflected according to direct piezoelectric effect in the reception stage Into electric signal;The analog electrical signal of the damage reflection echo of different passages is changed into control by multichannel analog/digital conversion capture card Device data signal;The transmission signal of multichannel D/A converter is connected to multi-wafer SH by multichannel relay in launching phase0 On ripple phased array probe, and after launching phase terminates, by multi-wafer SH0Ripple phased array probe is connected to multichannel analog and turned Change on capture card, echo-signal is damaged for gathering;Wherein described multi-wafer single mode SH0Ripple phased array probe includes pressing one The multiple d to form a line are spaced calmly36Type piezoelectric patches.
Controller is configured to the parameter of test specimen and calculates the transmission signal of different time delay, multi-wafer SH0 Ripple phased array probe includes multiple piezoelectric sensor units, is formed a line by order from top to bottom at regular intervals, and pass through Excited in the narrow-band impulse pumping signal one-time detection of the 3 cycles Hanning window amplitude modulation of different time delay, sent out respectively simultaneously Go out respective SH0Ripple, according to Huygen's principle, different SH0The wave surface of ripple is superimposed, by adjusting different piezoelectric sensings Time delay between device unit, its ultrasonic wave excited can be superimposed to form new wave surface in media as well, and focus on default At focus P, and amplify SH0This amplitude without single mode signals in frequency of ripple, so as to realize single mode SH in physical field0Wave beam is inclined Turn, focus on, the function of scanning;After running into damage reflection echo, all piezoelectric sensor units are receiving signal simultaneously, pass through Controller is imaged after it being reconstructed determination damage position, calculating.Realized by the time delay for adjusting different excitation signal The region-wide single mode SH of platy structure0Ripple orientation fixed point scanning, so as to realize the purpose of damage check.
1st, wherein, SH is produced0The piezoelectric chip of ripple is characterized as:
New d36Piezoelectric smart material is not common d31Type lead zirconate titanate (PbZr (Ti) O3, PZT) but PMN-PT (Pb(Mg1/3Nb2/3)O3–PbTiO3), and in order to realize the property of the piezoelectric patches, need in [011] direction polarization, and (011) plane cutting.When it is by voltage drive, caused be deformed into diagonally is stretched and shunk, so as in x Direction and y directions produce detrusion, inspire SH0Ripple.Common d31Piezoelectric patches and new d36Piezoelectric patches polarised direction, cutting side Deformation is as shown in Figure 4 under to, voltage drive.
By common d31Piezoelectric patches, d36Type piezoelectric patches crystal growth direction is set to Z axis.Common d31The cutting side of piezoelectric patches To for (001) plane cutting, it is deformed into along x-axis and y-axis stretching, extension and shunk under voltage drive.But d36Piezoelectric patches polarization side To [011], cut direction is (011) plane, and its projection is it can be seen that be rhombus on original XOY plane, as shown in Figure 4. Therefore piezo-electric crystal stretching, extension and shrinkage direction are original X-axis and Y-axis, are produced corresponding to two diagonals of itself piezoelectric patches Raw stretching, extension and contraction.And for processed d36For piezoelectric patches, under its local coordinate system on 1 axle and 2 axles caused by be A pair of detrusion, so as to produce the shearing wave in plane in the structure.
D herein36The piezoelectric equations and d of piezoelectric patches36Piezoelectric patches piezoelectric modulus matrix is:
Wherein, SijFor strain tensor, VjFor electric displacement vector, TklFor stress tensor, EkFor electric-field intensity,For piezoelectricity Elastic compliances, djklFor piezoelectric constant,For free dielectric constant.Wherein, d36Item is changed into non-zero from 0, and is much larger than d31And d32, therefore the SH without frequency dispersion can be produced while Lamb wave is produced0Ripple.
Using the LISA run on GPU to single d36The wave field of piezoelectric patches carries out numerical simulation.The size of plate be 500mm × 500mm × 1.6mm, wave-field simulation result is as shown in figure 5, it can be seen that the new d36Piezoelectric patches 0 ° in plate and 90 ° of horizontal shear wave (SH that can nearby produce vertical transmission direction0Ripple), Lamb wave is mainly produced on 45 ° of directions.And its Centrosymmetric characteristic is presented in caused wave field, i.e. three direction displacements are:U (x, y)=- u (- x ,-y), v (x, y)=- v (- X ,-y), w (x, y)=w (- x ,-y).
Obtained by analog result, single d36Piezoelectric patches is after voltage drive, the SH in its all directions0Ripple, Lamb wave S0 Component and A0The amplitude of component is as shown in Figure 6.The amplitude of all directions ripple is different, and the shape of bunge bedstraw herb is presented, wherein without Frequency dispersion SH0Ripple is meets symmetric and anti-symmetric property simultaneously, and Lamb wave is then centrosymmetric, if produced in first quartile Then third quadrant can also produce compressional wave to compressional wave, at the same second and fourth quadrant produce tensile wave.And due to former piezoelectricity Coefficient matrix d[011]Middle d32Item is much larger than d31Item (see formula (2)), therefore first quartile and third quadrant S0And A0The amplitude of ripple will More than the second quadrant and the amplitude of fourth quadrant.
2nd, true time delay is without frequency dispersion SH0The detection range of ripple phased array is:
In order that ultrasonic phase array can preferably detect damage, it is necessary to strengthen main lobe, the generation of graing lobe is eliminated or reduces, Avoid influenceing the flaw detection of main lobe, while determine effective detection region.The delimitation in effective detection region typically follows -6dB criterions, i.e., It is required that in detection zone, sound pressure amplitude caused by each array element is more than the 50% of its acoustic pressure maximum, meets the region of this condition The referred to as effective detection region of ultrasonic phase array wafer array.There are two equivalent Jiao different from single mode Lamb wave phased array Point, no frequency dispersion SH0Ripple phased array produces the centre symmetry of wave field due to piezoelectric patches, and multiple piezoelectric patches are combined into linear symmetric After phased array, the focus that two focusing effects differ is had.As shown in fig. 7, focus F is due to the symmetrical of linear phase controlled array Property and by Lamb disturb it is smaller, and F ' be then because in first quartile, its focus condition it is larger by the interference of Lamb wave, because The damage check effect of this two focuses is not fully identical.Therefore the frequency of selection appropriate excitation signal is needed, reduces Lamb The interference of ripple, realize preferably Detection results.
According to d36Without frequency dispersion SH caused by type piezoelectric patches0Single d can be calculated in acoustic pressure-angular relationship of ripple36Type pressure - 6dB the angle thetas of electric piece0=30 °.Wherein, AmaxWhat is represented is maximum sound pressure amplitude caused by single d36 chips,Represent most Amplitude during big acoustic pressure half.
In d36Type piezoelectric patches is arranged in after array, disclosure satisfy that all d36The region of -6dB the criterions of type piezoelectric patches For effective detection region, then effective coverage is the superposition in single first region that shakes, as shown in Figure 7.Triangle is presented in effective detection region Shape expands outwardly, and the distance of its top closest approach distance arrays center line is h, and focusing angle is the θ of β=20, as shown in figure 8, root Understood according to geometrical relationship:
3rd, true time delay is without frequency dispersion SH0Ripple phased array probe focus method is:
True time delay is without frequency dispersion SH0Ripple phased array centre frequency is 40kHz, is swashed with 3 cycle Hanning window narrow-band pings Hair is without frequency dispersion SH0Ripple carries out the damage check of platy structure, as shown in Figure 9.Wherein, each d36The pumping signal of type piezoelectric patches is V(t-δn), reference voltage pumping signal V (t)=[(t-Npfc1-cos2 π fctNpsin2 π fcy, Ht are He Wei Sadens to H (t)-H Jump function (Heaviside function), the H (t)=1 as t >=0;Work as t<H (t)=0 when 0, Np=3, fc=40kHz.Nothing Frequency dispersion SH0The group velocity c of ripplesH, S0(t-δn)=V [H (t)] is each d36Type piezoelectric patches initial signal, Sp(t) it is at focus P Wave field strength signal:
Ann)=cos (2 γ), γn=arccos (Fcos (θF)/rn) (16)
Wherein,Represent focus point with it is every Individual wafer distance, focus position relative to each chip deviation angle γn=arccos (Fcos θF/rn), swash between array It is δ to encourage signal delayn, a is two d36The distance at type piezoelectric patches center, F are focal lengths, θFIt is the deviation angle of focus, Ann) Represent the different d in array on the focus point direction36The initial sound pressure that type piezoelectric patches excites,For acoustic pressure Attenuation coefficient, t0It is a sufficiently large constant to ensure that time delay is not negative.
4th, true time delay is without frequency dispersion SH0Ripple phased array imaging method is:
It is θ to be located at angled, distance RdPoint D at have a damage, the focus of phase array focusing is at P, different d36Type pressure The ripple that electric piece is sent stack result S at point DD(t) it is wherein d shown in formula (4)nFor n-th of d36Type piezoelectric patches to damage position D distance is put, its size is calculated by geometrical relationship:
Reflection echo is propagated back to m-th of d of phased array36The ripple signal of type piezoelectric patches is:
M-th of d36Type piezoelectric patches is after echo-signal is received, by fluctuation signal Sr(t) it is converted into Vr(t), and then pass through Restructing algorithm formula (11) assembles each signal according to time delay, so that it is determined that the position of damage and degree.
When focus position overlaps with defective locations, focusing angle θFd, and focal length F=Rd, injury region produces very strong Without frequency dispersion SH0Wave reflection echo, assembling signal VR(t) amplitude can get maximum.
Embodiment 2
Using the LISA numerical simulations run on GPU, model is size 800mm × 500mm × 1.6mm aluminium sheet, Young Modulus is 71.0GPa, and Poisson's ratio ν is 0.33, density 2700kg/m3.The d that 16 sizes are 7 × 7 × 0.5mm36Type piezoelectric patches is every The individual phased array system at intervals of 1mm compositions positioned at center.Pumping signal is that 16 Hanning windows with different time delay are adjusted Make 3 cycle narrow band signals (tone-burst signal).
The time delay of 16 piezoelectric patches calculates according to the delay formula of embodiment 1 respectively, it is focused on 100mm, 0 ° Place, because without frequency dispersion SH0Ripple is the ripple in plane, therefore only show the displacement in the x directions in plane and y directions in fig. 11 Component map.It can be seen that the true time delay is without frequency dispersion SH0Ripple phased array is very strong to displacement in y, it was demonstrated that without frequency dispersion SH0Ripple Very strong focus beam is formd, serves enhancing without frequency dispersion SH0The purpose of ripple detection.In addition, it should be noted that producing Without frequency dispersion SH0D while ripple36Type phased array also generates the Lamb wave of frequency dispersion, wherein S simultaneously really0Ripple and A0Wave component Mark is in fig. 11.As interference ripple, the Lamb wave of frequency dispersion has very strong amplitude in first quartile and third quadrant, therefore needs Select the second quadrant carry out damage check, or selection appropriate excitation signal by its with without frequency dispersion SH0Ripple is split, and prevents ripple Shape aliazing effect damage check effect.
Similar, time delay is adjusted, then SH ripples phase array focusing is at 100mm, 15 ° of F, such as Figure 12 institutes Show.Described in as discussed above, due to the symmetry of time delay and the symmetry of SH ripples, d36Phased array can be simultaneously first Quadrant and the second quadrant form two focuses.But due to d36The directionality and Central Symmetry property of piezoelectric patches itself, it first The Focus Club of quadrant is disturbed by the Lamb wave of frequency dispersion, and the second quadrant focus then because the Lamb wave amplitude of frequency dispersion is smaller and Be interfered very little, can obtain more preferable damage check result.
Embodiment 2
Experimental study is carried out to SH ripple ultrasonic phase arrays damage detection system, using the data of American National instrument NI companies Acquisition system and LabVIEW soft ware platforms are built, and carry out damage check using laser vibration measurer.
It is similar with true time delay single mode Lamb wave phased array, in onesize 914.4mm × 914.4mm × 1.6mm aluminium D is pasted on plate36Piezoelectric patches phased array, aluminium sheet suspension is on the ceiling with isolation vibration and the influence of noise, and in detected area Reflection paster is pasted on domain to strengthen laser reflection signal, improves signal to noise ratio.Wherein it should be noted that due to d36Type piezoelectricity Piece has directionality in itself, it is therefore desirable to which mark point when being dispatched from the factory according to it is strictly arranged, and spacing is that 1mm compositions are phased Battle array, is allowed to produce equidirectional no frequency dispersion SH0Ripple.D in experiment36Piezoelectricity chip size is identical with common PZT sizes, all for 7mm × 7mm × 0.5mm, as shown in figure 13.Equally in plate center, tow sides are pasted for excitation direction without frequency dispersion SH0Wave beam Active phased array and passive phased array for reception signal.In order to prevent no frequency dispersion SH0The A of ripple and frequency dispersion0The aliasing of ripple bag Phenomenon, different ripple bags are better discriminated between, the centre frequency of narrow-band ping is adjusted to 40kHz, output channel and input are logical The sample frequency in road is 1MHz.
(1) result of the test in the case of not damaged
In the case of undamaged, to true time delay without frequency dispersion SH0Ripple active phased array produces wave field and studied, due to PSD-400 laser vibration measurers can only measure the Vibration Condition in 1 dimension z directions, and without frequency dispersion SH0Ripple vibration is in-plane moving, therefore Focus condition directly can not be obtained by LDV laser vibration measurers, can only be by detecting true time delay without frequency dispersion SH0Ripple active phased array The Lamb wave secondary lobe ejected is calculated.
When default focus point is 100mm, at 0 °, SH ripples phased array produces the z of wave field to vibration by laser vibration measurer LDV's Measurement result is as shown in figure 14.The z wherein measured according to LDV is to displacement field it can be found that the secondary lobe of Lamb wave is presented with level Line form symmetrical above and below, so as to demonstrate focus point really in 0 ° of direction.Surely time delay is without frequency dispersion SH0Default Jiao of ripple phased array Point be 100mm, and at 15 °, it can be found that the secondary lobe of Lamb wave is generated and significantly rotated, its proof is without frequency dispersion SH0What ripple focused on Direction generates upward deflection, is focused on from symmetry estimation main lobe and should be 15 °, as shown in figure 15.It is 100mm in focus, 30 ° When, as shown in figure 16, the Lamb wave secondary lobe anglec of rotation further increases, and shows no frequency dispersion SH0Ripple main lobe focus point further to Upper skew.Simultaneously as can be seen that by the new d36The d of piezoelectric patches31Xiang Buwei 0 influence, frequency dispersion be present in focus direction A0The influence of ripple, different yet with velocity of wave, it will not be to without frequency dispersion SH0The detection of ripple makes a significant impact.
(2) result of the test under degree of impairment
In addition, also to true time delay without frequency dispersion SH0Wave field of the ripple phased array damage detection system in the case where there is degree of impairment is carried out Research, it is that 12.7mm × 12.7mm permanent magnets are pasted onto 100mm by two sizes, at 0 °, for simulating degree of impairment.Pass through LDV laser vibration measurers carry out z to wave field measure, wherein different focus points in the case where there is degree of impairment wave field change as Figure 17, Shown in Figure 18 and Figure 19.It can be seen that damage can significantly influence wave field form, true time delay is without frequency dispersion SH0Ripple phased array system It is very sensitive to damaging.Its send without frequency dispersion SH0The Lamb wave of ripple and frequency dispersion can all form obvious diffusing reflection after damage is run into Echo is received by phased array element, the positions and dimensions of identification of damage.
Embodiment 3
Except the wave field measurement result in the z directions of laser vibration measurer, true time delay is controlled without frequency dispersion SH0Ripple phased array detection system The time delay sequence of system, focus point is made to be incremented to 250mm by step-length of 25mm from 50mm, focusing angle is with 15 ° from -90 ° Step-length increases to 90 °, scans whole region to be detected, using passive phased array system reception signal and determines damage position.Damage Condition of the injury condition is shown in Figure 20.The size of permanent magnet is that 38.1mm × 12.7mm is pasted onto the 150mm of aluminium sheet, at 0 °, for simulating Damage, pumping signal centre frequency 40kHz, signal sampling frequencies 1MHz.
Under health status and have respectively will be without frequency dispersion SH under damage status0The passive phase control array receiving signal storage point of ripple Analysis.The signal that sensor receives is as shown in figure 21, and the difference signal of damage signal and healthy reference signal is as shown in figure 22.Wherein By damage scattering without frequency dispersion SH0The difference signal of ripple echo can be identified for damaging reconstruct, damage check result by clear As shown in figure 23, it can be seen that non-destructive tests result and the magnet positions actually pasted and shape are all coincide very well, are shown herein The true time delay proposed is without frequency dispersion SH0Ripple phased array detecting system has good damage check ability.

Claims (4)

1. a kind of true time delay for platy structure detection is without frequency dispersion SH0Ripple phased array system, including:Controller, multichannel number/ Weighted-voltage D/A converter, multi-wafer SH ripple phased array probes, multichannel relay, multichannel analog/digital conversion capture card, imaging display, Phase is characterised by:Controller electric signal connecting multi-channel D/A converter, multichannel D/A converter pass through multichannel relay Device electric signal connects multi-wafer SH ripple phased array probes;Multi-wafer SH ripples phased array probe is connected by multichannel relay electric signal Multichannel analog/digital conversion capture card, multichannel analog/digital conversion capture card electric signal connection controller are connect, controller electric signal connects Connect imaging display;The transmission signal of different passages is converted into analog voltage signal to drive by multichannel D/A converter Multi-wafer single mode SH0Ripple phased array probe;Multi-wafer SH0Ripple phased array probe is changed voltage signal by inverse piezoelectric effect Ejected in the structure into fluctuation signal, while the fluctuation letter reflected will be damaged according to direct piezoelectric effect in the reception stage Number it is converted into electric signal;Multichannel analog/digital conversion capture card converts the analog electrical signal of the damage reflection echo of different passages Into controller data signal;The transmission signal of multichannel D/A converter is connected to more by multichannel relay in launching phase Chip SH0On ripple phased array probe, and after launching phase terminates, by multi-wafer SH0Ripple phased array probe is connected to multichannel On analog/digital conversion capture card, echo-signal is damaged for gathering;Wherein described multi-wafer single mode SH0Ripple phased array probe Including the multiple d to form a line at regular intervals36Type piezoelectric patches;
Controller is configured to the parameter of test specimen and calculates the transmission signal of different time delay, multi-wafer SH0Ripple is phased Battle array probe includes multiple piezoelectric sensor units, when being formed a line by order from top to bottom at regular intervals, and passing through different Between in the narrow-band impulse pumping signal one-time detection of 3 cycles Hanning window amplitude modulation that postpones while excited, send respectively each SH0Ripple, different SH0The wave surface of ripple is superimposed, by adjusting the time delay between different piezoelectric sensor units, its The ultrasonic wave excited can be superimposed to form new wave surface in media as well, and focus at default focus P, and amplify SH0Ripple this Amplitude without single mode signals in frequency, so as to realize single mode SH in physical field0Wave beam deflection, focus on, the function of scanning;Meet To after damage reflection echo, all piezoelectric sensor units are receiving signal simultaneously, and it is reconstructed really by controller It is imaged after determining damage position, calculating, the time delay by adjusting different excitation signal realizes the region-wide single mode of platy structure State SH0Ripple orientation fixed point scanning, so as to realize the purpose of damage check.
2. a kind of true time delay for platy structure detection according to claim 1 is without frequency dispersion SH0Ripple phased array system, its It is characterised by:The detection range of the system is, according to d36Without frequency dispersion SH caused by type piezoelectric patches0The acoustic pressure of ripple, angular relationship meter Calculation obtains single d36- 6dB the angle thetas of type piezoelectric patches0=30 °, wherein, AmaxWhat is represented is most loud caused by single d36 chips Pressure amplitude value,Represent amplitude during maximum sound pressure half;
<mrow> <mo>-</mo> <mn>6</mn> <mi>d</mi> <mi>B</mi> <mo>=</mo> <mn>20</mn> <mi>l</mi> <mi>g</mi> <mfrac> <msub> <mi>A</mi> <msub> <mi>&amp;theta;</mi> <mn>0</mn> </msub> </msub> <msub> <mi>A</mi> <mi>max</mi> </msub> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow>
Multiple d36Type piezoelectric patches from top to bottom by array is arranged in order into after, disclosure satisfy that all multiple d36Type piezoelectric patches The regions of -6dB criterions be effective detection region, then effective coverage is the superposition in single first region that shakes, and effective detection region is in Existing triangle expands outwardly, and its top closest approach be h apart from the distance of cell array center line, and focusing angle is the θ of β=20, root Obtained according to geometrical relationship:
3. a kind of true time delay for platy structure detection according to claim 1 is without frequency dispersion SH0Ripple phased array system, its It is characterised by, true time delay is without frequency dispersion SH0Ripple phased array probe focus method is:
True time delay is without frequency dispersion SH0Ripple phased array centre frequency is 40kHz, is excited with 3 cycle Hanning window narrow-band pings without frequency Dissipate SH0Ripple carries out the damage check of platy structure, wherein, the pumping signal of unit is V (t- δn), reference voltage excitation letter NumberH (t) is He Wei Saden jump functions, when t >= H (t)=1 when 0;Work as t<H (t)=0 when 0, Np=3, fc=40kHz;Without frequency dispersion SH0The group velocity c of rippleSH, S0(t-δn)=V [H (t) it is] each piezoelectricity blade unit initial signal, Sp(t) it is wave field strength signal at focus P:
<mrow> <msub> <mi>S</mi> <mi>p</mi> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>n</mi> <mo>=</mo> <mo>-</mo> <mrow> <mo>(</mo> <mi>N</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>/</mo> <mn>2</mn> </mrow> <mrow> <mi>n</mi> <mo>=</mo> <mrow> <mo>(</mo> <mi>N</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>/</mo> <mn>2</mn> </mrow> </munderover> <mfrac> <mrow> <msub> <mi>A</mi> <mi>n</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>&amp;gamma;</mi> <mi>n</mi> </msub> <mo>)</mo> </mrow> </mrow> <msqrt> <msub> <mi>r</mi> <mi>n</mi> </msub> </msqrt> </mfrac> <mo>&amp;CenterDot;</mo> <msub> <mi>S</mi> <mn>0</mn> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>-</mo> <mfrac> <msub> <mi>r</mi> <mi>n</mi> </msub> <mi>c</mi> </mfrac> <mo>-</mo> <msub> <mi>&amp;delta;</mi> <mi>n</mi> </msub> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>4</mn> <mo>)</mo> </mrow> </mrow>
Ann)=cos (2 γ), γn=arccos (Fcos (θF)/rn) (5)
<mrow> <msub> <mi>&amp;delta;</mi> <mi>n</mi> </msub> <mo>=</mo> <mfrac> <mi>F</mi> <msub> <mi>c</mi> <mrow> <mi>S</mi> <mi>H</mi> </mrow> </msub> </mfrac> <mo>{</mo> <mn>1</mn> <mo>-</mo> <msup> <mrow> <mo>&amp;lsqb;</mo> <mn>1</mn> <mo>+</mo> <msup> <mrow> <mo>(</mo> <mfrac> <mrow> <mi>n</mi> <mi>a</mi> </mrow> <mi>F</mi> </mfrac> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>-</mo> <mn>2</mn> <mfrac> <mrow> <mi>n</mi> <mi>a</mi> </mrow> <mi>F</mi> </mfrac> <msub> <mi>sin&amp;theta;</mi> <mi>F</mi> </msub> <mo>&amp;rsqb;</mo> </mrow> <mrow> <mn>1</mn> <mo>/</mo> <mn>2</mn> </mrow> </msup> <mo>}</mo> <mo>+</mo> <msub> <mi>t</mi> <mn>0</mn> </msub> <mo>,</mo> <mi>w</mi> <mi>h</mi> <mi>e</mi> <mi>n</mi> <mi> </mi> <mi>n</mi> <mo>=</mo> <mn>0</mn> <mo>,</mo> <mo>&amp;PlusMinus;</mo> <mn>1</mn> <mo>,</mo> <mo>&amp;PlusMinus;</mo> <mn>2</mn> <mo>,</mo> <mo>...</mo> <mo>&amp;PlusMinus;</mo> <mfrac> <mrow> <mo>(</mo> <mi>N</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> <mn>2</mn> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>6</mn> <mo>)</mo> </mrow> </mrow>
<mrow> <msub> <mi>&amp;delta;</mi> <mi>n</mi> </msub> <mo>=</mo> <mfrac> <mi>F</mi> <msub> <mi>c</mi> <mrow> <mi>S</mi> <mi>H</mi> </mrow> </msub> </mfrac> <mo>{</mo> <mn>1</mn> <mo>-</mo> <msup> <mrow> <mo>&amp;lsqb;</mo> <mn>1</mn> <mo>+</mo> <msup> <mrow> <mo>(</mo> <mfrac> <mrow> <mo>(</mo> <mi>n</mi> <mo>+</mo> <mn>0.5</mn> <mo>)</mo> <mi>a</mi> </mrow> <mi>F</mi> </mfrac> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>-</mo> <mn>2</mn> <mfrac> <mrow> <mo>(</mo> <mi>n</mi> <mo>+</mo> <mn>0.5</mn> <mo>)</mo> <mi>a</mi> </mrow> <mi>F</mi> </mfrac> <msub> <mi>sin&amp;theta;</mi> <mi>F</mi> </msub> <mo>&amp;rsqb;</mo> </mrow> <mrow> <mn>1</mn> <mo>/</mo> <mn>2</mn> </mrow> </msup> <mo>}</mo> <mo>+</mo> <msub> <mi>t</mi> <mn>0</mn> </msub> <mo>,</mo> <mi>w</mi> <mi>h</mi> <mi>e</mi> <mi>n</mi> <mi> </mi> <mi>n</mi> <mo>=</mo> <mo>&amp;PlusMinus;</mo> <mn>1</mn> <mo>,</mo> <mo>&amp;PlusMinus;</mo> <mn>2</mn> <mo>,</mo> <mo>...</mo> <mo>&amp;PlusMinus;</mo> <mfrac> <mi>N</mi> <mn>2</mn> </mfrac> </mrow>
Wherein,Represent focus point and each d36 Type piezoelectric patches distance, focus position is relative to each d36The deviation angle γ of type piezoelectric patchesn=arccos (Fcos θF/rn), Pumping signal delay is δ between arrayn, a is two d36The distance at type piezoelectric patches center, F are focal lengths, θFIt is the deviation angle of focus Degree, Ann) represent the different d in array on the focus point direction36The initial sound pressure that type piezoelectric patches excites,For acoustic pressure attenuation coefficient, t0It is a sufficiently large constant to ensure time delay not for negative.
4. a kind of true time delay for platy structure detection according to claim 1 is without frequency dispersion SH0Ripple phased array system, its It is characterised by, true time delay is without frequency dispersion SH0Ripple phased array imaging method is:
It is θ to be located at angled, distance RdPoint D at have a damage, the focus of phase array focusing at P,
Different d36The ripple that type piezoelectric patches is sent stack result S at point DD(t) shown in equation below, wherein dnFor n-th of d36Type To damage position D distance, its size calculates piezoelectric patches by geometrical relationship:
<mrow> <msub> <mi>S</mi> <mi>D</mi> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>R</mi> <mo>=</mo> <mo>-</mo> <mrow> <mo>(</mo> <mi>N</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>/</mo> <mn>2</mn> </mrow> <mrow> <mi>R</mi> <mo>=</mo> <mrow> <mo>(</mo> <mi>N</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>/</mo> <mn>2</mn> </mrow> </munderover> <mfrac> <mrow> <mi>A</mi> <mrow> <mo>(</mo> <msub> <mi>&amp;gamma;</mi> <mi>n</mi> </msub> <mo>)</mo> </mrow> </mrow> <msqrt> <msub> <mi>d</mi> <mi>n</mi> </msub> </msqrt> </mfrac> <mo>&amp;CenterDot;</mo> <msub> <mi>S</mi> <mn>0</mn> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>-</mo> <mfrac> <msub> <mi>d</mi> <mi>R</mi> </msub> <msub> <mi>c</mi> <mrow> <mi>S</mi> <mi>H</mi> </mrow> </msub> </mfrac> <mo>-</mo> <msub> <mi>&amp;delta;</mi> <mi>n</mi> </msub> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>7</mn> <mo>)</mo> </mrow> </mrow>
Reflection echo is propagated back to m-th of d of phased array36The ripple signal of type piezoelectric patches is:
<mrow> <msub> <mi>S</mi> <mi>r</mi> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>R</mi> <mo>=</mo> <mo>-</mo> <mrow> <mo>(</mo> <mi>N</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>/</mo> <mn>2</mn> </mrow> <mrow> <mi>R</mi> <mo>=</mo> <mrow> <mo>(</mo> <mi>N</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>/</mo> <mn>2</mn> </mrow> </munderover> <mfrac> <mrow> <mi>B</mi> <mo>&amp;CenterDot;</mo> <mi>A</mi> <mrow> <mo>(</mo> <msub> <mi>&amp;gamma;</mi> <mi>n</mi> </msub> <mo>)</mo> </mrow> </mrow> <msqrt> <mrow> <msub> <mi>d</mi> <mi>n</mi> </msub> <mo>&amp;CenterDot;</mo> <msub> <mi>d</mi> <mi>m</mi> </msub> </mrow> </msqrt> </mfrac> <mo>&amp;CenterDot;</mo> <msub> <mi>S</mi> <mn>0</mn> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>-</mo> <mfrac> <mrow> <msub> <mi>d</mi> <mi>n</mi> </msub> <mo>+</mo> <msub> <mi>d</mi> <mi>m</mi> </msub> </mrow> <msub> <mi>c</mi> <mrow> <mi>S</mi> <mi>H</mi> </mrow> </msub> </mfrac> <mo>-</mo> <msub> <mi>&amp;delta;</mi> <mi>n</mi> </msub> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>8</mn> <mo>)</mo> </mrow> </mrow>
<mrow> <msub> <mi>d</mi> <mi>m</mi> </msub> <mo>=</mo> <msqrt> <mrow> <msup> <mrow> <mo>(</mo> <mi>m</mi> <mi>a</mi> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msubsup> <mi>R</mi> <mi>d</mi> <mn>2</mn> </msubsup> <mo>-</mo> <mn>2</mn> <msub> <mi>R</mi> <mi>d</mi> </msub> <mo>&amp;CenterDot;</mo> <mrow> <mo>(</mo> <mi>m</mi> <mi>a</mi> <mo>)</mo> </mrow> <mi>s</mi> <mi>i</mi> <mi>n</mi> <mrow> <mo>(</mo> <msub> <mi>&amp;theta;</mi> <mi>d</mi> </msub> <mo>)</mo> </mrow> </mrow> </msqrt> </mrow>
M-th of d36Type piezoelectric patches is receiving echo-signal by fluctuation signal Sr(t) it is converted into Vr(t), and then equation below is passed through Each signal is assembled according to time delay, so that it is determined that the position of damage and degree;
<mrow> <msub> <mi>V</mi> <mi>R</mi> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>m</mi> <mo>=</mo> <mo>-</mo> <mrow> <mo>(</mo> <mi>N</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>/</mo> <mn>2</mn> </mrow> <mrow> <mi>m</mi> <mo>=</mo> <mrow> <mo>(</mo> <mi>N</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>/</mo> <mn>2</mn> </mrow> </munderover> <msub> <mi>V</mi> <mi>r</mi> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>-</mo> <msub> <mi>&amp;delta;</mi> <mi>m</mi> </msub> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>9</mn> <mo>)</mo> </mrow> </mrow>
When focus position overlaps with defective locations, focusing angle θFd, and focal length F=Rd, the very strong nothing of injury region generation Frequency dispersion SH0Wave reflection echo, assembling signal VR(t) amplitude can get maximum.
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