Treść książki
Przejdź do opcji czytnikaPrzejdź do nawigacjiPrzejdź do informacjiPrzejdź do stopki
Preface
9
onesystemofmomentequationsisinvestigated,towhichsomeinverse
problemsconsideredintheworkarereduced.Theuniquenesstheoremsof
theshapedeterminationfromthescatteringamplitudesofelasticwaves
areconsideredandtheintegralrepresentationsforthescatteringampli-
tudesofthelongitudinalandthetransversalwavesareconstructed.
Chapter2isdevotedtothemathematicalmodelsofSHwavescat-
teringbyanelasticthin-walledinclusions.Theinclusionisreplacedby
theeffectiveboundaryconditionthatallowstosimplifycalculationsof
thescatteredfieldsignificantly.Usingtheproposedmodels,aproblem
isreducedtothehypersingularintegralequationsthataresolvedby
usingoftheWiener-Hopftechnique.Inordertoinvestigatethevalidity
ofthemathematicalmodels,theresultsobtainedarecomparedwiththe
exactsolutionfortheinfinitethinlayer.Theanalyticalsolutionsofthe
hypersingularintegralequationsarecomparedwiththenumericalso-
lutions.Thealgorithmbasedontheanalyticalsolutionscanbeusedas
aprogrammingtoolinnondestructivetestingofelasticmaterialswith
athinplaneinclusionsofarbitrarystiffness.Inthissectiontheelasto-
dynamicstressconcentrationnearthetipsofathin-walledinclusionof
weakrigiditysubjectedtoanincidentharmonichigh-frequencySHwave
istreatedalso.
Chapter3isdevotedtotheasymptoticinversescatteringproblem
foraplanecrack.Integralequationsrelativetounknowndisplacements
jumpsfortheproblemofelasticwavescatteringbyacrackareob-
tained.Theseequationsarevaluablebecausetheycontaininevident
formthesymbolsoftheirkernels,andunknownfunctionshavethephys-
icalsense.Thenumericalsolutionsofobtainedequationsaredescribed.
Forapenny-shapeandatunnelcracks,aproblemisreducedtosolving
oflinearquasi-regularsystemsofalgebraicequations.Inacase,whena
crackformisnotcircular,asolutionissearchedintheformoftheexpan-
sionsbytheGaussbeams.Thisleadstoalgebraicsystemsofequations
withmatrixes,thataresymmetricandhaveprevalenttermsonthedi-
agonal.Theresultsobtainedinthissectionareusedhenceforthformod-
elingofthescatteringdata.Amethodfordeterminationofdimensions
oftheplanetunnelcracksisconstructed.Themethodisbasedonusing
ofinformationabouttheRayleighsurfacewavestravellingbetweenthe
twocracktips.Otherimportantproblem,i.e.problemofdetermination
oftheelasticallydeformingstateofelasticmediumfromacousticemis-
sionsignals,generatedbynew-createdtunnelcrackofnormalloading,
isconsidered.AproblemisreducedtosolvingoftheFredholmintegral
equationofthefirstkind.Andfinally,severalapproximatemethodsfor