Research ArticleWave-Blocking Characteristics of CorrugatedPlates under Explosion

Guoliang Yang,1,2 Shuai Feng ,1 and Wenjia Huang 1

1School of Mechanics and Civil Engineering, China University of Mining and Technology (Beijing), Beijing 100083, China2State Key Laboratory of Explosion and Science and Technology, Beijing Institute of Technology, Beijing 100081, China

Correspondence should be addressed to Shuai Feng; sqt1700602057@student.cumtb.edu.cn

Received 22 June 2019; Revised 29 December 2019; Accepted 22 January 2020; Published 29 February 2020

Academic Editor: Hamid Toopchi-Nezhad

Copyright © 2020Guoliang Yang et al.0is is an open access article distributed under the Creative CommonsAttribution License,which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Corrugated-board explosion-proof wall is the main means to prevent explosion shock wave damage, and it is important to studythe effect of different corrugated plates on the shock wave. Using a high-speed schlieren experimental system and an airoverpressure test system, the wave-blocking characteristics of different forms of corrugated plates are comprehensively studied.0e schlieren images were used to analyze the influence that the corrugation shape of a corrugated plate has on the shock wavepropagation characteristics. 0e results show that the reflection process of the triangular-, trapezoidal-, and half-cylindrical-shaped corrugated plates exhibit differences. 0e number of reflected waves from the triangular corrugated plate is much greaterthan that from the other corrugated plates, and it will consume more energy. 0e diffraction wave-front velocity has a trend ofinitially decreasing and then increasing and is also reduced by different degrees by the reflection. Comparative analysis of theschlieren images and the air shock wave overpressure test shows that plates corrugated with different corrugation shapes decreasethe diffraction overpressure peak and exhibit a hysteresis.

1. Introduction

Blast explosions cause a huge impact in the production andlife of our modern society. 0e human body, however, has avery limited tolerance for the shock waves emanating fromthe explosion product. Specifically, an overpressure ex-ceeding just 0.2 atm (20 kPa) will exert a bad effect on thehuman body, while few can survive a shock wave exceedingone atmospheric pressure (101 kPa) [1]. 0us, protectionfrom shock waves has always been an important issue. Inrecent years, scholars at home and abroad have studiedshock waves and protection therefrom mainly throughmodel experiments [2, 3] and numerical simulations [4–8].Chen et al. [9] numerically simulated the shock wave field ofspherical charge explosion in air and quantitatively studiedthe power parameters such as peak overpressure, specificimpulse, and positive pressure action time of the shock wave.Zhang et al. [10] studied the influence of wall height, pro-portional explosion distance and explosive position on theoverpressure distribution, and fitted the formula for

calculating the overpressure after the wall. Nian et al. [11]carried out numerical simulation analysis on the trans-mission and diffraction effects of flexible explosion-proofwalls, compared the variation characteristics of pressurewaveforms, and obtained the distribution law of the pressurefield behind the wall. Ma et al. [12] and Zong and Bai [13]proposed the design of a specially shaped explosion-proofwall of a new structure and studied the wave-breakingperformance and the propagation law of the shock wave bynumerical calculation. Yu et al. [14] studied the dynamicresponse of a trapezoidal corrugated-board explosion wallunder blast loading by ANSYS/LS-DYNA finite elementsimulation software, analyzed the influence of materialstrain rate effect, and compared the stress distribution anddisplacement time history curve of different width walls. Shiet al. [15] analyzed the failure mechanisms of three sizes oftrapezoidal corrugated-board explosion wall under differentexplosion loads, obtained a prediction formula for theuniform pressure–impulse (P-I) curve of different explo-sion-proof walls by fitting, and predicted the antiexplosion

HindawiShock and VibrationVolume 2020, Article ID 5895812, 8 pageshttps://doi.org/10.1155/2020/5895812

ability of the trapezoidal corrugated-board explosion-proofwall.

At present, there exists much research on protectionfrom explosive air shock waves. But most of the currentresearch focuses on the process of shock wave transmission,and few scholars have studied the wave-blocking charac-teristics of the corrugated plate itself. Furthermore, apressure field comprehensive test system was used to ex-plode experiments on different forms of corrugated steelplates, where visualization of the air shock wave propagationprocess was obtained with schlieren images. 0e wave-blocking characteristics of different forms of corrugated steelplate for explosion shock waves were studied, and thepropagation law of reflection and diffraction was analyzed.

2. System and Scheme

2.1. Experimental System. 0e explosion wave field andpressure field comprehensive experimental test systemcomprised a high-speed schlieren experimental system andan air shock wave overpressure test system. 0e compre-hensive experimental system is shown in Figure 1. 0eoptical components in the system consisted of a laser, twoplane mirrors (plane mirrors 1 and 2), two concave mirrors(concave mirrors 1 and 2), and a beam expander. 0e lightsource emitted by the laser became divergent light afterpassing through the beam expander. 0e light was thenreflected by plane mirror 1 and concave mirror 1 to becomeparallel light carrying the flow field information. 0is par-allel light was focused on the edge of the blade by a com-bination of concave mirror 2 and parallel mirror 2. 0eblade, placed before the high-speed camera, removed someof the focused light that was ultimately captured by the high-speed camera to obtain a schlieren image [16]. 0e corru-gated steel plates were placed horizontally within the parallellaser flow field. 0e shock wave generated by the shockdevice impacts the air and changes the air density, where-upon the overpressure was measured via the pressure sensorof the air overpressure test system placed on the back of thesteel plate. 0e high-speed camera located behind the knifeedge possessed a shooting speed of 100,000 frames persecond. Because a detonating tube was used as the shockdevice, the explosive equivalent is small and no protectivedevice was needed for the camera.

2.2. Experimental Scheme. Seven types of corrugated steelplates were designed according to the purpose of the ex-periment, which are shown in Figure 2.0ere were two typessteel plates, transverse (named FS, FY, and FT in Figure 2(a))and vertically (named RS, RY, RT, and RC in Figure 2(b)).0ecorrugated shapes are trapezoidal (including FT and RT),triangular (including FS and RS), semicylindrical (includingFY and RY), and noncorrugated (including RC). 0e sampleswere made by pressing and welding a steel plate (1.5mmthick). 0ese samples were then used for the reflection anddiffraction experiments.

In the reflection experiment, because observation of thereflection portion was desired, it was necessary to arrange

lateral corrugations, so that the parallel light could berecorded by the camera. If the corrugations were notarranged laterally for this experiment, the corrugated plateitself would block the parallel light and restrict observationof the reflection process. In addition, the transverse cor-rugated steel plates were designed to increase the plate areain order to eliminate diffraction interference. 0e plate sizeswith transverse corrugations were 18 cm long and 18 cmhigh.

In the diffraction experiment, the main purpose was toobserve the overall diffraction process. 0erefore, verticalcorrugated steel plates with a height of 5 cm and a length of18 cm were designed with triangular, half-cylindrical, andtrapezoidal shapes and no corrugations (RS, RY, RT, and RC,respectively, in Figure 2(b)). To ensure that the steel platewas firmly fixed on the horizontal test bench under theaction of the shock wave, the lower end of the corrugatedsteel plate was welded to a footing, which was fixed to thebench.

Because the schlieren observation system has a smallobservation range, a large-volume explosive was not used forthis work. Instead, a detonating tube was used as the shockdevice initiating the explosion shock wave and the explosiveproduct. In this experiment, a detonating tube with a lengthof 60 cm was used as the explosive, with a twisted enameledwire inserted as a detonating probe. 0e detonator had apower of 2200W and was electrically detonated. 0e shockwave excitation end was placed 3 cm in front of the center ofthe steel plate test piece.

When performing the reflection experiment, the testpieces FT, FS, and FY were placed parallel to the optical flowfield, so that the high-speed camera could observe thespecific reflection process. 0is arrangement solved theproblem of the test piece corrugation itself by blockingthe optical path and preventing observation of the actualreflection. When performing the diffraction experiment, thetest pieces RS, RY, RT, and RC were placed as in the reflectionexperiment. In this way the high-speed camera could obtain

Computer

High-speedcamera

BladeReflector

Detonatingtube

Detonator

Concavemirror

Oscilloscope

Chargeamplifier

Lasertransmitter

Beamexpander

Reflector Pressuresensor

Corrugatedsteelplate

Figure 1: Schematic diagram of the comprehensive experimentaltest system.

2 Shock and Vibration

images from the side angle. 0is arrangement was moreintuitive to observe how the shock wave generated by theexplosion acted on the steel plate to generate diffraction andenabled recording of the complete diffraction process.

A piezoelectric pressure sensor (CY-YD-202 made byWuxi Shiao Technology Co., Ltd.) was placed horizontally5 cm behind the center of the steel plate and connected to theamplifier and oscilloscope. 0e trigger voltage was loweredto 20mV, ensuring that a good electrical signal curve couldbe obtained. 0e measurable pressure range of the pressuresensor was 0–10MPa, the sensitivity of the charge amplifierwas K� 10mV/pC, and the sensitivity coefficient of thesensor was Sq� 36.79 pC/MPa.

0e number of image frames obtained by the high-speedcamera was set by the software, and an image was recordedevery 10 μs.

3. Results and Analysis

3.1. Reflection Process of Explosion Shock. During the re-flection process, the shock wave follows the law of reflection,where the angle of reflection is equal to the angle of inci-dence.0e different corrugation shapes will change the angleof incidence to form different angles of reflection. Figure 3shows a comparison of the reflection processes of the tri-angular (FS, Figure 3(a)), half-cylindrical (FY, Figure 3(b)),and trapezoidal (FT, Figure 3(c)) corrugated steel plates.

As shown in Figure 3, the initial stage of the reflectionprocess is similar for the three corrugation shapes on the steelsheets. At t� 130μs after detonation, the shock wave istransmitted to the plate surface for all samples, and the tri-angular corrugated plate produces a reflected wave whosecenter is the apex of the triangle. 0e inner side surface of thetriangle also causes reflection, and the reflected wave inside thetwo adjacent corrugations exhibits a symmetric shape. Finally,the reflection from the outer side surface of the triangle by-passes the corrugation and continues to propagate outward.Unlike the triangular corrugated plate, for the half-cylindrical

corrugated plate, the wavefront generated by the explosionalmost simultaneously reaches the flat surface between thecorrugations and the corrugation surface. Upon reflection ofthe shock wave, the central angle of the reflected wave is larger.0e shockwave of the trapezoidal corrugated plate also reachesthe plate surface at t� 130μs and forms a larger reflected wave,but the center angle of the reflected wave is moderate. Whent� 170μs, it can be seen that regular reflection waves appear infront of the different corrugated plates, and the reflected waveson the inner sides of the two adjacent corrugations nearest theexplosion gradually approach each other. In addition, thereflected waves from the ground can be observed at this time.Observing the images obtained at t� 260 and 450μs, the re-flections produced by the different corrugation shapes began toexhibit differences. As seen for triangular corrugations inFigure 3(a), the shock waves reflected by the inner side of theapex angle continue to propagate and then propagate again tothe inner side of the apex angle, whereupon they experiencemultiple oblique reflections. As shown by t� 260μs, at leastthree reflection ripples are generated in the space between thetriangular ripples. 0e reflection angle of the reflected wave isgradually perpendicular to the inner side, and slowly spreadsoutward. As seen for half-cylindrical corrugations inFigure 3(b), the shock wave reflected by the half-cylindricalcorrugation is again reflected by the half-cylindrical corru-gation. 0e angle of reflection changes gradually and, becausethe corrugations are half-cylindrical, the repeated reflectionsare not as numerous as that of the triangular. As shown byt� 260μs, there are two reflected waves between the circularripples. After several reflections, the reflected shock wavesfrom the half-cylindrical corrugation expand outward. As seenfor the trapezoidal corrugations in Figure 3(c), the reflectionprocess is more similar to that of the simplified half-cylindricalcorrugated plate than that of the triangular corrugated plate.0is similarity is owing to the overall similarity and circularreflection. However, owing to the existence of the upper flatbase on the trapezoid corrugation shape, there exists a greaterchance of vertical reflection that results in fewer reflections

(a) (b)

Figure 2: Corrugated steel plate test pieces used for (a) reflection testing with transverse corrugations shaped as trapezoidal (FT, left),triangular (FS, middle), and half-cylindrical (FY, right) and for (b) diffraction testing with vertical corrugations shaped as triangular (RS,upper left), half-cylindrical (RY, lower left), trapezoidal (RT, upper right), and noncorrugated (RC, lower left).

Shock and Vibration 3

than observed for half-cylindrical corrugations. As shown byt� 260μs, there is only one reflected wave between trapezoidalripples.

In general, the reflection of shock waves exhibited dif-ferent reflection effects from the differently shaped corru-gated steel sheets. Owing to the shape of the triangularcorrugated steel plate, increasingly complex reflectionprocesses will emerge between the two adjacent corruga-tions, which will consume the energy of the shock wave anddelay its propagation. 0e half-cylindrical corrugated steelsheets will form more reflections because of the larger re-flection angle, but the small corrugation height restricts theformation of complex multiple reflections. 0e trapezoidalcorrugated steel plate has a flat-topped corrugation similarto a noncorrugated steel plate, which is more prone toordinary regular reflections. However, because of the exis-tence of the angled sides of the trapezoid, complex reflec-tions between two adjacent corrugations will occur to someextent. 0e complex reflection process between these ad-jacent trapezoidal corrugations consumes the energy of theincident shock wave and increases the reflection processtime, causing hysteresis of the diffraction.

3.2. Diffraction Process of Explosion Shock. Figure 4 showsthe diffraction process of the explosion shock wave acting on

the noncorrugated (RC, Figure 4(a)), triangular (RS,Figure 4(b)), half-cylindrical (RY, Figure 4(c)), and trape-zoidal (RT, Figure 4(d)) steel plates. 0e overall diffractionpropagation process for the four different corrugationshapes is similar, but the specific details are different. Foreach type of corrugated steel plate, we obtained a specificschlieren image at four time points (60, 160, 220, and 320 μs)for observation.

0e observations in Figure 4 show that the differentshapes of the corrugated steel plates induce differentpropagation states upon the diffraction shock wave gener-ated by the explosion. Analysis of the schlieren images att� 160 and 220 μs after detonation shows that the diffractionwavefront of the triangular steel plate (Figure 4(b)) is smallerthan that of the other corrugated shapes, and the wavefronttransmits for smaller distances.0is is because the triangularsteel plate forms a more complex reflection process forincident overpressure, increasing the reflection time anddelaying the vertical diffraction propagation. Differentcorrugation shapes have different effects on the diffraction.Table 1 shows the distances of the diffracted shock wavesfrom different corrugated plates at 160 μs and 220 μs. FromTable 1, we know the wavefront propagation distances forthe different metal sheets are ordered as RS<RY<RT<RC.0is result indicates that the triangular corrugatedplate exhibits the most delayed diffraction, followed by

t = 130μs t = 170μs t = 260μs t = 450μs

(a)

t = 130μs t = 170μs t = 260μs t = 450μs

(b)

t = 130μs t = 170μs t = 260μs t = 450μs

(c)

Figure 3: Reflection process of the explosion shock wave on the transverse corrugated steel plate with (a) triangular (FS), (b) half-cylindrical(FY), and (c) trapezoidal (FT) corrugations.

4 Shock and Vibration

half-cylindrical corrugated plates, trapezoidal corrugatedplates, and, finally, noncorrugated plates.

In addition, it can be seen in Figure 4(a) that in additionto the reflected shock waves from the ground and from theoriginal steel plate and the newly formed diffraction shockwave, many other shock waves are present in the circle. 0isis because the shock wave generated by the explosion is not asingle shock wave but is composed of a group of shockwaves. 0us, there are many outwardly diffusing wavefrontsin the outermost shock wave that can be observed. Whenthe shock wave is diffracted, it gradually spreads backward tothe corrugated steel plate. When the shock wave reaches the

horizontal plane, it interacts with the ground to form aMachshock wave that gradually propagates to the back of thecorrugated steel plate.

3.3.Wave Velocity. To study the propagation characteristicsof diffraction shock waves from the different steel plates, thediffraction wave velocity was further analyzed and the dif-fraction law of the explosion shock wave was compared forthe different steel plates.

To extract the shock wave-frontal velocity, Yang et al.proposed that the leading edge of the shock wavefront is

t = 60μs t = 160μs t = 220μs t = 320μs

(a)

t = 60μs t = 160μs t = 220μs t = 320μs

(b)

t = 60μs t = 160μs t = 220μs t = 320μs

(c)

t = 60μs t = 160μs t = 220μs t = 320μs

(d)

Figure 4: Diffraction process of the explosion shock wave on the vertical corrugated steel plate with (a) no corrugations (RC), (b) triangular(RS), (c) half-cylindrical (RY), and (d) trapezoidal (RT) corrugations.

Table 1: Distance between diffraction wave and corrugated plate.

No corrugations (RC) Triangular (RS) Half-cylindrical (RY) Trapezoidal (RT)t� 160 μs 3.2mm 2mm 2.8mm 2.3mmt� 220 μs 12.5mm 6mm 11.8mm 8mm

Shock and Vibration 5

smooth, thus making it easy to obtain the displacement andspeed of the shock wave [16]. 0e impact of the explosiveproduction on the shock wave transmission is relativelysmall and therefore was not studied here. For each of thedifferently shaped corrugation steel plates, the schlierenimages after the diffraction process were analyzed, where theinterval between each adjacent image was Δt� 10 μs. 0erecording was started with the top and back of the steel platechosen as the coordinate origin.0e horizontal positions of aspecific diffraction wavefront in two adjacent pictures arelabeled x1 and x2, and thus the horizontal displacementdifference is ΔX � x2 − x1 and the horizontal velocity of thewavefront is V � ΔX/Δt. Using these calculated values, thediffraction shock wave velocity and displacement versustime is plotted (Figure 5).

From Figure 5, we can determine how the wave velocityand displacement changes over time. When analyzing thewavefronts from the different steel plates at the same timeafter detonation, the position of the wavefront propagation isdifferent. 0e displacement of the wavefront from the tri-angular (RS) steel plate is always the smallest, followed inincreasing displacement by the half-cylindrical (RY), trape-zoidal (RT), and noncorrugated (RC) steel plates. 0is indi-cates that the diffraction shock wave generated by theexplosion will have delayed diffraction on different corrugatedplates. 0e diffraction shock wave transmission of the tri-angular (RS) steel plate is the most obvious, which is con-sistent with the results of the diffraction process (Section 3.2).

Observing the wavefront velocity curve in Figure 5, it isseen that the wave velocity of the diffraction propagation forsteel plates with different-shaped corrugations is basicallyregular. 0e law is that, after the diffraction occurs, the wavevelocity of the shock wave will initially decrease and thenexhibit an increasing trend. 0is behavior is because, as theshock wave is diffracted, the propagation distance increasesand the energy is slowly consumed and the propagation speedis reduced. However, at about 250 μs, the transmitted dif-fraction shock wave and the ground action produce a Machreflection wave that interacts with the original diffractionshock wave to gradually increase the wavefront propagationspeed. At the same time, the order of the different steel platesfor initial diffraction speed is RS<RT<RY<RC, which indi-cates that the corrugated steel plates of different shapes havedifferent energy consumptions for shock waves comparedwith the noncorrugated steel plate. 0e triangular corrugatedsteel plate has the highest shock wave energy consumption, sothat the wave velocity transmitted by the diffraction is alsosmall. 0is result is also consistent with the experimentalphenomenon obtained by the reflection experiment.

3.4. Wave Overpressure. 0e original load signal was ob-tained from the oscilloscope, and the valid segment neededto obtain the required basic charge signal data was selectedand substituted into the formula [17], whereby the unpro-cessed overpressure signal data were obtained by calculation.Normalization and filter smoothing processes were per-formed on the Origin software to eliminate interferencefactors such as noise. 0e diffraction overpressure time

history curve at 5 cm behind the steel plates with fourdifferent shapes was thus obtained. Because the actual ex-perimental specimens were small in size and the signal dosewas extremely small, the overpressure value was relativelysmall. However, the overpressure results are basically in linewith the estimated situation.0e diffraction overpressure vs.time for the corrugated steel plates with different shapes isplotted in Figure 6.

It can be seen from Figure 6 that the diffraction over-pressure propagation process for the different steel plates isroughly the same at equivalent points of the explosion. Allsteel plates initially experience a positive pressure and then anegative pressure and ultimately tend to a balance. 0isresult is consistent with the diffraction process seen from theschlieren images and is consistent with the law of shock wavepropagation. 0e diffraction overpressure presents twodistinct positive phase peaks initially, and the absolute valueof the negative phase is smaller than the absolute value of thepositive phase. 0ese two results are consistent with theconclusions of Mu and Wang [4].

As the diffraction overpressure propagates to the sensor,the sensormeasures two distinct positive pressure peaks.0efirst peak is the diffraction of the overpressure shock wave,and the second is the overpressure reflected by the horizontalworking surface. Shao and Zhao [5] also previously observedthis phenomenon.

Further analyzing Figure 6, it is found that the time ofarrival of the shock wave overpressure and the peak of thepositive and negative overpressure differ significantly for thedifferent steel plates. 0e peak time of the post-plate dif-fraction overpressure of the RC-, RT-, RY-, and RS-steel platesare 175, 198, 186, and 216 μs, respectively. Among thecorrugated steel plates, the peak of the diffraction over-pressure of the RS-steel plate comes at the latest. 0is isconsistent with the experimental phenomena seen in

6

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100 150 200 250Time (µs)

Disp

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300 350 400

0

20

40

60

80

100

120

Rc velocityRy velocityRs velocityRt velocity

Rs displacementRy displacementRt displacementRc displacement

Figure 5: Explosion diffraction shock wave displacement velocityversus time curve.

6 Shock and Vibration

Figure 4, and it is clear that the diffraction overpressure ofthe triangular steel plate lags behind that of the other steelplates, where the order of diffraction overpressure arrivaltime is RC, RY, RT, and RS.

Furthermore, the peak value of the diffraction over-pressure for the RS-, RT-, RY-, and RC-steel plates are 74, 78,88, and 91 Pa, respectively. It is evident that the differentshapes of the corrugated steel plates have a great influence onthe diffraction overpressure.

4. Conclusions

(1) 0e shock wave reflection process follows the law ofreflection, and different corrugation shapes can affectthe reflection process and consume more energy.Triangular corrugation reflections are more complexthan other corrugated shapes.

(2) 0e diffraction wavefront velocity has a law of ini-tially decreasing and then increasing and is alsoaffected by reflection. 0e order of the different steelplates for wavefront velocity is RS<RT<RY<RC.

(3) Compared with the vertical steel plate, the shockwave diffraction of the different corrugated steelsheets produce different degrees of hysteresis, andthe peak overpressure is correspondingly reduced. Itis not difficult to see that different corrugated steelplates do have a great influence on diffractionoverpressure, and the reduction effect of diffractionoverpressure is as follows: RS-steel plate>RT steelplate>RY steel plate>RC-steel plate. 0e experi-mental phenomenon of triangular corrugated steelplate is particularly obvious.

Data Availability

0e data used to support the findings of this study areavailable from the corresponding author upon request.

Conflicts of Interest

0e authors declare no conflicts of interest.

Authors’ Contributions

G. Y. and S. F. conceived and designed the experiments; J. Z.performed the experiments; S. F. and W. H. analyzed thedata; S. F. wrote the paper.

Acknowledgments

0is paper was supported by the opening project of the StateKey Laboratory of Explosion Science and Technology(Beijing Institute of Technology). 0e opening projectnumber was KFJJ19-10M.

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–1000 50 100 150 200 250 300 350 400 450 500 550 600

–75

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RC: 91PaRY: 88PaRT: 78PaRS: 74Pa

RC

RTRY

RS

Figure 6: Diffraction overpressure as a function of time for thevarious corrugation shapes on steel plates.

Shock and Vibration 7

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