The direcrional characteristics of a spark source of acoustic waves in a solid are studied experimentally' The
angular dependence of the ampiituJes of longitudinal and shear waves and of Rayleigh surface waves is
inuestigated for two principal discharge geometries. A qualitative interpretation of the observed dependences
is given

S.V. Korolev (7122038)

Victor V. Krylov (1252356)

English

Loughborough University Institutional Repository

   This item was submitted to Loughborough’s Institutional Repository (https://dspace.lboro.ac.uk/) by the author and is made available under the following Creative Commons Licence conditions.      For the full text of this licence, please go to: http://creativecommons.org/licenses/by-nc-nd/2.5/  .on the aeoustic radiation on the basis of numericalLlculations in the investigated situation.The authors are gzateful to V. A. Gushchinfor suppilnng the program used to calculate theiryaroAynitmic characteristics of a collapslng biob'r )trre i-uPortance of collapse-t)pe Processes for the scitationof acoustic oscillatj-oN by vortex disturbalces in a stratifiedledirn sas first noted in Ref. 6 (see also Ref' 7)'1A, V. !\rrduev, rt0cean noiserrr ilt: Ocem Acoustics [in Russian],L. l.l. Brekhovskiftr (ed.), Nauka, l{oscon (197a)' p'p' 615-692'2 G. L 3arenblatr IzY. Akad. Nauk SSSR Fiz' At!' ok€lm &, 195(1e78).3 v. S. Haderich, v. I' Ni.neshov, and A. f . Stetser*o, Dyneicsof Internal Hixing irr a Stratified Hedim [in Russian],liaukova hoka' Kiev (1988)'tv. A. Gushchin, Z!r' vychisl. llat' ilat. TLz. 2L, I'oo3 (1981)'s S. o. B"lotrerkovskii ild v' A. Gsbchin, Modeling of Certai'nviscoE Fluid llovs, Pr€print of the CooPuting Center of t})eAcade8y of sciences of tlle USSR [in Russia]' vTs AN SssR (1982).6 t. M. I,yushev ad A. T. Skortsov, Akust. Zh. 3]}, 843 (1984)[Sov. Phys. Acoust. i9, 503 (1984)].? L. tt. Lyrohev ad A. T. Skvortsov, t'Somd radi'ation byloslized vortices in a slightly coupressible nediw (review)rIAbllst. z}r. 3\,769 (1988) [Sov. fhyE. Acost' 3!' *t (1988)]'I u. :. tigttttill, ?roc. R. Soc. Lndon Ser. A 9., 1 (1954)'I L, H. Srekhovskikh and v. S, Goncbarov, ilectmics of contimaand llave D;mmics, SP=inger-Verla8, BerlirrNew lork (1985)'roH. E. c'oldstein, Aeroacoustics, Hccraw-Hill, Nev York (1976)'118. ?. Denidovich and I' A. Ha!o.r' Fud@entals of CorPutationalHatheoatics [in Russbn], Nauka' Hoscow (1970).12A, A. Sanarskii, Theory of Difference Schems [in Russian]tllauka, Hoscov (1983).r3yr. P. Doronin (ed.), Physics of tJre ocea lin Russian],GidroE€teoizdat, Leningrad (1978).Translated try J. S. WoodDirectivity patterns of a spark source of acoustic waves in a solidS. V. Korolev and V. V. KrylovPhysics Department, M. V' Lomonosou State Uniuenity, Moscow{Submitted February 13, 1989)Akust. Zh. 36,4247 {January-February 1990)The direcrional characteristics of a spark source of acoustic waves in a solid are studied experimentally' Theangular dependence of the ampiituJes of longitudinal and shear waves and of Rayleigh surface waves isinuestigated for two principal discharge geometries. A qualitative interpretation of the observed dependencesis given.The iast few years have witnessed a heightenedinterest in various noncontact methods for the -gen-epation of sound. in solid's: electroma$netie,1r2Iaser,3-5 and other methods. One of the morepromising noncontact methods, proposed quite re-cently, ll tfre so-caued spark method'- 9r the gen-eration of sound in sob-ds by electrical breakdownof the surfaee air layer. 6-d Foremost among theadvantages of this gbneration technique over othernoncont;ct nethods, e.g. ' over the laser method'is the simplicity of impiementation, compactness 'low cost, and higher Lfficiency. According to Ref'?, the principal inechanism of the spark gener^ationof r"on-=ti" wlves in a solid is the exposure of itssurface to the strong divergent air shock producedby expansion of the discharge plasma' Since theciraracteristie duration of the air-shock pulse nearthe diseharge zone can be fairiy small (of the orderof a few teis of nanoseconds); the excited shockpulses can also be very short. e This means that-the spark method can be used for spectral measu?e-ments of the parameters of solids, in particular forultrasonic spectroscopy and nondestructive testing'Among the most important properties of anyacoustic wave source are its directivity patterns'In applieation to the spark generation of sound'the iirst experimental study of the angular depen-dence of the red'iatdd fieid was reported in Ref ' 6'However, the measurements in Ref. 6 were cariedout oniy for longitudinal waves and oniy with elec-trical discharge directly on the sample' In thepresent articie we give the results of detailed ex-perimental investigations of the directional charac-ieristics of a spaik souree of acoustic waves in asolid. We discuss the angular dependence of theamplitudes of both longitudinal and shear waves 'and also of Rayieigh surfaee waves for various dis-charge geometries and parameters' The knowledgeof tir-esJdependences is essentiai to the practicaiuti[zation of the method in various applications'It also lends deeper insight into the nature of thespark sound souree in solids 'The experiments were caried out with analuminum sample in the shape of a haif-disk of diam-eter 190 Erm and thickness 30 mm. Electrical dis-charge took place both on the metal sample- itself 6 ' 7and 6n an auxitiary grounded electrode. T-s It isimportant to note thal the use of an auxiliary elec-trode permits fuil implementation of the noncontactmethod of sound genlration without detracting fromthe purity of the lurface; the sample can be eithera metal or a dielectric in this case.The experimental arangement is shownschematically in Fig' 1' The high dc voltage souree1 generates approximately 2.? kV. The storage21 Sov. Phys. Acoust. 36{1 ), Jan'-Feb' 1 99O OO38-562)U9O/O1 OO21-O4 $03.OO O 1 990 Americsn lnstitute of Physics 21EIG. 1. EJcpetjrental arrangeDent.JU AU n, AegFIG. 2. Dilectivity Patterns of longitudinal acoustie waves gen-elated by discharge on the sample (curves l-4) and by disclurgeon the auxiliary electrode (d = 0.8 tB' curves 5-7) for aeapacitanee C = 5?OO,pF. 1) h = 0.2 @; 2) 0'3 m; 3) 0.8 no;4) 0.8 m; 5) 2 m; 6) I o; 7) 0.5 E.capacitor C is charged through the current-iimitingresistor R = 10 M o. The value of the capacitanceC was varied in the interval from 100 pF to 35'000pF during the measurements. The resistance R'ihe eapacitance C, and the breakdown *it g"p formeda relaxation oscillator, whose frequency was variedfrom a few hertz to several kilohertz during theexperiments. The oscilloscope sweep was triggered.synchronously with electrical breakdown from thecapacitative divider Cr, Cz.The main bronze discharge electrode Er hada roundoff radius -0.3mmand was situated at adistanqs h frnm the surface of the sample 2. Thevalue of h was varied by means of a micrometerdrive, whjch had an error of approximateiy 0.03 mm.The auxiliary grounded electrode Ez (whenused) was aiways situated at the same distance hfrom the surface of the samFle as the main eleetrodeE r ; the spacing d of the electrodes was fixed ata value of approximatelY 0.8 mm.The excited longitudi.nal acoustic wave pulseswere reeeived by the circular piezoeeramic wafers3 of diameter 15 mm with a center frequency of 2Sov. Phvs- Acoust. 36('l ), Jan.-Feb. 1 990-rI{Hz and by a Uthium niobate wafer of dimensions6 ' 8 mm2 with a center frequency of 5 MHz.Piezoceramic wafers of dimensions 6 x 10 mm2 witha center frequency of 5 MHz were used to recordthe shear waves. The received longitudinal andshear waves were identified by the pulse delay times.The piastic coupling biock 4, wtrich had the sameradius of curvature as the aiuminum sample, wasused to ensure smooth displacement of the trans-ducers aiong the perirneter of the sampie. Epoxyresin was used to form an acoustic bond betweenthe coupling block and the sample.The wideband preamplifier 5 with a low noiselevel and a gain of 60 dB was housed in a commonmetal easing with the piezoceramic plate. Thisa"rangement made it possible to lower the strayelectromagnetic noise level and, accordingly, to en-hanee the acculacy of the measurements. Theamptified signal was subsequently transmitted tothe high-pass filter 6, which lowered the noiselevel of the spark discharge, and then to the inputof the oscilloscope ?.The directivity patterns of the Rayleigh sur-face waves excited by the spark di.scharge lYereinvestigated on a sample in the form of an aluminumdisk of diemeter 300 mm and thickness 18 mm. Break-down took place both on the sample and on theauxiliary eieetrode. The Rayleigh waves were re-ceived by a standard wedge transducer, to whichwas attached a piezoeeramic wafer of diameter 15mm with a center frequency-of 2 MHz.Figure 2 shows the angular dependence of theamplitudes of the eiectrical signals U g(0) corre-sponding to the generated longitudinal acoustic wavesof frequency 2 MHz (curves 1-3 and 5-?) for vari-ous values of the capacitance C and the electrodeheight h. Curve 4 was plotted from measurementusing the lithium niobate wafer with a center fre-quency of 5 MHz. It follows from Fig. 2 that thedirectivity maxima are oriented in the direction ofthe normal to the surface both for discharge onthe sampie (curves 1-4) and for discharge on theauxiliary electrode (curves 5-?), and tbe angulardependenees themselves are similar in ail cases.tiJ0 60 I' degFIG. 3, DirectiviEy patterns of shear acoustic waves generatedby discharge on the sasple (curves 1-3) md by discharge on theauiliary electrode (d = 0.8 ro, cuwes 4-5). 1) C = 5200 pF,h = o.4m; 2) c = 5200 pFr h = o.8xm; 3) C - 351000 pF, h = 0.8m; 3) C = 5200pF, h = 2 m; 5) C = 5?OO PF, h = 0.5 m; 6)C = 35,000 pF, h = 0.5 m.208/\ "'r' Uo-t\YAf ,'"'{-!- \i/"iq)$,i/ !.d-r3:fu*-*r'b-rIfx rr- JL!\4 \*{-a to. tR\r-1't\ \\J- t ah'\22 S. V. Korolev and V. V. Krylov 22Figure 3 shows the dj-rectivity patterns of the' generated shear acoustic waves of frequency 5 MHzfor various values of the capacitance C and theheight h. We see that the angular dependencesfor shear waves U1(8) have a more complicated shapethan in the case of longitudinal waves. The posi-tions of the maxima depend on the discbargetechnique: The maxima for discharge on the sampleare observed at angles 0 'v 40o for ali vaiues ofC, and the maxima for diccharge on the auxiliaryeiectrode are strifted toward larger angles 8. Ac-cording to s5rmmetry considerations, wtren the airshock is incident on the surface of the sample, shearwaves should not be excited in the direction of thenormal to the surfaee (0 = 0). In the experiment,however, nonzero ninima were observed at 0 = 0,evidently because of the influence of deviations ofthe aetual experimental geometry from the ideal sym-metrical case.Measurements of the directivity patterns ofRayleigh waves generated in a spark discharge showethat the patterns are isotropic within the measure-ment error iimits for all the experimental valuesof C and h, both for discharge on the sampie andfor discharge on the auxiliary electrode. We havetherefore omitted them here.The directivity patterns of elastic waves gen-erated by a spark discharge can be calculated quan-titativeiy, i.n prineiple, by solving the problem ofthe refraction of a strong divergent shock waveat the interface between a gas and a iinearly elastiesolid. Since this problem laeks a rigorous solution,we restrict the ensuing discussion to a quaUtativeinterpretation of the plotted experimental curvesof U g,1(s).For thjs purpose, we associate the effect ofthe shock wave on the surface of the soiid witha eertain effective normal force Fn, whieh dependson the distance p from the epicenter and on thetime, whereupon the generation of elastic wavesin a solid half-space can be redueed to the axisym-metrical Lamb probiem ro,1: for the effective forceFn(t, p). The dependence of this force on thecoordinates and on the time must clearly exhibita lagged (wave) behavior Fn(t, p) = Fn[t - p/v(p)],being deterrnined by the path traced by the shockwave on the plane. Introducing the height I ofthe lower boundary of the discharge zone abovethe plane and the d.istance r = (p2 + 9.2)\12 fromthe lower boundary of the discharge zone to theobservation point, we see at once that the veiocityv( p ) of the pulse representing the effective normaiforce along the surface is related to the veiocityv(r) of the spherical shock front .by the equationv( p) = d pi dt =, v(r) (l + h2 lo2)tlz. In turn,v(r) .u (E/po )1/?r- s/2, u'here E is the electricaldischarge energ'y spent in generation of the shockwave, and po is the equiLibrium air density. 12 ' 13The pressure p(r) at the shock front is known tobe related to v(r) by the equation p(r) t povz(r) tr-3 = (p2 + L2)-312. Consequently, the forceFn(t, p), which is of the same order of magrr.itudeas p(r), must clearly decrease rapidiy as p is in-creased.* In the case of discharge on the samle it can;.. be assumed that !. = 0, and-so r = p. The veloeity[. v( p) now decreases as o-3/2 to the value of theF' sound velocity in air co (Refs. ? and 12). Ac-L eor'dingly, the pressure p( p) is proportional toi,r p-t initially and then varies .up-]. In the casei: of discharge on the auxiliary eiectrode [ = h, andS, IY--r:- Sov. Phys. Acoust. 36(1), Jan.-Feb. 1990hr.w'J0 60 8, 629FIG. 4. Calculated directivi.ty pattems of longitudirEl (cwe1) and shan (cu:se 2) eaves generated by a vertic€.l lusrpedforce ia e elastic tralf-space.the.function v(p) ^,( p2 + h2)- 3/! (1 + hzlp2)r 12 =o-s/r (1 + hzlp2 )-ti u decreases somewhat moreslowly at small values of p. More significant, how-ever, is the fact that the pressure p( p) ru (p2 +t.2)- 312 in this ease does not have a singularityin the limit p + 0, but is characterized by aplateau of-radius p', \ h in the neighborhood ofthe epieenter. In -other words, the distributedcharacter of the force source Fn(t, p) in the caseof discharge on the auxi.liary eiectrode is manifestedmore explicitiy than in the case of discharge onthe sampie, where the source can eieariy be re-garded as a point source,For comparison, Fig. 4 shows the calculateddirectivity patterns of longitudinal (curve 1) andshear (curve 2) waves generated by a vertieai lumpedforce (point source) in an elastic half-space 11 fora Poisson ratio o = 0.35, which corresponds toaluminum. We first compare the theoretical curvefor shear waves with the corresponding experi-mental curves of U1( 0) in the case of dischargedireetiy on the sample (Fig. 3, curve 1-3). Wesee that curve 2 i-n Fig. 4 and curves 1-3 in Fig.3 are quaiitatively similar, consistent with the as-sumption that the source is a point source,In the case of discharge on the auxiliary elec-trode, on the other hand, the observed ehangesin the behavior of the experimental curves (curves4-6 in Fig. 3) are obviousiy assoeiated with theiagged character of the force Fn = Fn[t - p/v( o;1,which can exert an appreciable influence in the caseof a distributed source. lndeed, according to pr€-vious experimental data,7 the veiocity of the shockwave vlr=h = 1000 mls at a height h equal (e.g.)to 0.2 mm. In accordance with the foregoing dis-cussion, the velocity of its trace on the surfacev( p) = v ly=6(1 + h?l 92)r/: can be considerablyhigher than 1000 m/s near the epicenter (at p: h).In particuiar, the velocity v(p) ean also exceedthe shear bulk wave velocity c1 in the solid (e13100 m/s for aluminum), wtr-ich evidently accountsfor the onset of the additional maxima of curves5 and 6 in Fig. 3 at 0 r ?0o. The form of theU1(e) curve (curve 4) also differs from thetheoreticai curve in Fig. 4 for an electrode heighth = 2 mm, but the pronounced maximum at largeI is not observed here. Its absence can probablybe attributed to the fact that the velocity of theshock wave is ciose to the sound veioci.ty in airco = 340 m/s as it approaches the surface in thiscase, and the velocity v( p) exceeds the velocityet only in a small neighborhood of the epicenter.We now discuss the directivity characteristicU t(e) for longitudinal waves (Fig. 2). ln thi.scase all the experimental curves decrease mono-tonically as the angle I deereases, both in the caseof discharge on the sample (curves 1-4) and in the/,tt,00,5S. V. Korolev and V. V. Krylov aacase of discharge on the auxiliary electrode (curves5-7); this result agrees with the theoretical eurvein Fig. 4, wtrich is caiculated for a lumped force.In regard to the experimental curves 1-4, this factconfirms the point character of the source in dis-charge on the sampie. On the other hand, the ab-sence of any appreciable singularities of curves5-7 can be attributed to the larger value of thelongitudinal wave velocity c g in eomparison withthe shear wave velocity (c [ = 6400 m/s for alumi-num), so that it is djffieult for the effeetive forceFn(t, p) to exhibit a lagged behavior.We note that the..point nature of the sparksource in the case of disqlnrgg on the sample hasalso been conciuded by Copper et a1.5 on the basisof a measurement of tlre angular dependence forthe generated iongitudinal waves. However, ouranal5rsis shows that measurements lirnited to longi-tudinal vraves are not sufficient for arriving at this(as it happens) correct conclusion with cer{ainty,because even i.n the case of a distributed source(for discharge on the auxiliary electrode) thedireetivity pattern for longitudinal waves (curves5-7) have a similar form. The additionaL shear wavemeasurements reported in the present study permitthe conclusion of the point character of the sparksoupce in the case of discharge on the sample tobe drawn with absolute certainty.Thus, the experimental directivity patternsobtained here for a spark source of acoustic wavesin a solid contain important information about thedistinctive features of the processes of spark soundgeneration for two principal discharge geometries.Of eourse, the measured directivity patterns canaiso be used directly in practice in connection withthe appUcation of spark sources in ultrasonic diagnos-tic problems.1D. Eutchins, J. Itu, ad K. ludgren, Hate!. Eval. g, LZ\4( 1e85).2 A. N. Vail'"v, Vestn. Mosk. Univ. Fiz- Astron. Ar 54 (1997).3 e. a. Xat.U.Lov, Usp. Fiz. liauk 147, 605 (1985) lsfl. phys.Usp. 28, 1042 ( 1985 ) j .tu. u. Xtylot, E. p. ponomrev, and T. V. Shtentselr, vestj.ilosk. Univ. Fiz. Astrcn. n, 43 (Lga6).s A. I. Kozlov and V. ?. plesskii, Fiz. Tverd. Tela (leningrad). 4, e (1e85) [Sov. n1y5. solid state 2s, 4 (1986)].- J. A. Cooper, R. J. Dertrurst, p. S. Xoody, and S. !: paLoer,_ Proc. Inst, Electr, Eng. 131, 275 (1984).7 S. V. Korolev, v. A. Krasilrnilw, and V. v. Krylov, Akust. 43.-33,774 (1987) [Sov. ptrys. Aco:sc. 33, 45I (1987]1.8 S. V. Korolev ad V- V. Xrylov, rrGeneration of elastic waves byspark breakdown of a scface gc layer,rr in: Third Scientificad Technical Conference on tie Application of l{odem }{ethodsin Nondestluctive Te_sting and Inspection fin Russian],_ Dalrstandart, Khabarovsk (1987), pp. 19O-t-91.9 S. V. Korolev and V. V.-(ryl.ov, rspark discharge n€ar a sur-face: a nen and effstive nethod for tl.e noncmtact gen_eration of Rayleig! rewesr,r il: proceeclings of tie Conferenceon Acoutoelectronic- Inf omtion-processing Devics ( Orerkassy,_ 1988) lin Rrssian], VIIfI:II, Hoscow (1988), W. ZA7_Z}8-r0I,J. Nc,acki, Ttreory of Elasticity [Russian t uo;f"tiorj, mir,- - Xoscm-(1975); Teorj.a pelzania, Arkady, Harsaw (1963).11J. E. I*rite, SeisEic ltaves: Raaliation, Transnission, and- _Attenuation, HcGrav-Eil1, Nes york (1965).12Y., B. Zel'ilovich, and yu. p. Raizer, physics of Shock iiavesand lligh Tesperature Eydrodyrrmic phaorem, Z Vols., Acadeic_-Press, Nev york (1966, 1967).t"K, A. Naugol'nykh ed N. A. Roi, Electri€l Dischr-ges intiater [in Russian], Nau.ka, Mosiow (1971).Translated by J. S. WoodSov. Phys. Acoust. 36{ 1 ), Jan.-Feb. 1 99024 S. V. Korolev and V. V. Krylov 24

Directivity patterns of a spark source of acoustic waves in a solid

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Directivity patterns of a spark source of acoustic waves in a solid

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