Mathematical-Numerical Modelling of Ultrasonic Scattering Data from a Closed Obstacles and Inverse Analysis

Volodymyr Emets, Jan Rogowski

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ISBN/ISSN:

978-83-7837-564-7

DOI:

Wydawnictwo:

Akademicka Oficyna Wydawnicza EXIT Andrzej Lang

Rok wydania:

2015

Liczba stron:

271

XML:ISBN/ISSN:

ONIX MARC21

Bibliografia:

Emets, Volodymyr; Rogowski, Jan. Mathematical-Numerical Modelling of Ultrasonic Scattering Data from a Closed Obstacles and Inverse Analysis. Red. . : Akademicka Oficyna Wydawnicza EXIT Andrzej Lang, 2015, 271 s. ISBN 978-83-7837-564-7

Bibliografia refWorks:

RT Book, Whole

SR Electronic(1)

A1 Emets, V.

A1 Rogowski, J.

T1 Mathematical-Numerical Modelling of Ultrasonic Scattering Data from a Closed Obstacles and Inverse Analysis

PB Akademicka Oficyna Wydawnicza EXIT Andrzej Lang

YR 2015

SN 978-83-7837-564-7

Bibliografia BibTex:

@Book{ 149656, author = "Emets, Volodymyr and Rogowski, Jan", editor = "", title = "Mathematical-Numerical Modelling of Ultrasonic Scattering Data from a Closed Obstacles and Inverse Analysis", publisher = "Akademicka Oficyna Wydawnicza EXIT Andrzej Lang", year = "2015", address = "", isbn = "978-83-7837-564-7" }

Bibliografia endNote:

TY - BOOK

AU - Emets, Volodymyr

AU - Rogowski, Jan

ED -

TI - Mathematical-Numerical Modelling of Ultrasonic Scattering Data from a Closed Obstacles and Inverse Analysis

PB - Akademicka Oficyna Wydawnicza EXIT Andrzej Lang

CY -

PY - 2015

SN - 978-83-7837-564-7

ER -

Netografia (standard APA):

Emets, Volodymyr; Rogowski, Jan. Mathematical-Numerical Modelling of Ultrasonic Scattering Data from a Closed Obstacles and Inverse Analysis [baza danych online] : Akademicka Oficyna Wydawnicza EXIT Andrzej Lang, 2015 [dostęp: 24 08 2024]. Dostęp w Ibuk Libra: https://libra.ibuk.pl/reader/mathematical-numerical-modelling-of-ultrasonic-scattering-data-from-a-volodymyr-emets-jan-rogowski-149656.

modelowanie matematyczne, modelowanie numeryczne

In this work the methods of analysis and models of the direct and inverse elastic waves scattering problems for the local objects located in a uniform background are presented. The work is based on the concept of using of the sounding field freque...

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ISBN/ISSN:

978-83-7837-564-7

DOI:

Wydawnictwo:

Akademicka Oficyna Wydawnicza EXIT Andrzej Lang

Rok wydania:

2015

Liczba stron:

271

XML:ISBN/ISSN:

ONIX MARC21

Spis treści niedostępny

Preface

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

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Mathematical-Numerical Modelling of Ultrasonic Scattering Data from a Closed Obstacles and Inverse Analysis

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