Nonlinear Acoustical Imaging

111 Pages·2021·4.49 MB·English

by  Woon Siong Gan

Woon Siong Gan
Nonlinear
Acoustical
Imaging
Nonlinear Acoustical Imaging
Woon Siong Gan
Nonlinear Acoustical
Imaging
WoonSiongGan
AcousticalTechnologiesSingaporePteLtd.
Singapore,Singapore
ISBN978-981-16-7014-5 ISBN978-981-16-7015-2 (eBook)
https://doi.org/10.1007/978-981-16-7015-2
©SpringerNatureSingaporePteLtd.2021
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Tomyparents
Foreword
Nonlinearityinacousticsisusuallysomethingthatistobeavoided.Forinstance,the
nonlineardistortioninamusicreproductionsystemindicatesapossibledamagein
maybetheamplifierorloudspeaker.Thisdistortionappearsdisturbingtous,butit
doesalsocontaininformationaboutthestructuralinhomogeneities—likecracks.
Thisisoneexampleofwhenanonlinearityinacousticsyieldsinformationabout
a material or medium. It also introduces the importance in that a small inhomo-
geneity may result in a heavily nonlinear distortion. Nonlinear acoustic imaging
doesnotfollowthesamerulesandguidelinesasnormallinearacousticimaging.For
example,materialdisturbanceswhichareordersofmagnitudesmallerinsizethan
theacousticwavelengthdonothaveanimpactinthelineartechniques,butcangive
clearindicationsusingnonlinearacousticmethods.
ThisiswhyWoonSiongGanistreatingthesubjectofnonlinearacousticimaging
inthisspecificallydedicatedbook,despitethathehasgivenanextensiveoverviewof
thelinearaspectsinthepreviouslypublishedbookAcousticalImaging:Techniques&
Applications(2012).
This book presented the equations and basics of the nonlinear acoustics, its
pertinent phenomena and how these are used in imaging techniques for different
applications.
The subject of nonlinear acoustic imaging techniques is relatively new and has
notbeenextensivelycoveredinpreviousbooks.Itisadifficultsciencetodelveinto,
especiallywhilemostacousticcoursesteachonlythelinearacoustics.Thisisperhaps
completelynatural,asthemoveintononlinearstudiesisnotalwaysquickandeasy
sincesomeoftheacceptedconceptionsneedtobeelaborated.
WoonSiongGanhas,duringthelastyears,beenprolificinsharingafractionofhis
deepanddiverseknowledgethroughpublishingthefollowingbooks:NewAcoustics
Based on Metamaterials (2018); Gauge Invariance Approach to Acoustic Fields
(2019); Signal Processing and Image Processing for Acoustical Imaging (2020);
TimeReversalAcoustics(2021).
The titles and the contents of all these books show the nature of Woon Siong
Ganthroughhowheconnectsthetopicalbroadspectrumallthewayfromthemost
vii
viii Foreword
fundamentalsciencetousefulapplicationpractices—ashehasdonealsointhishis
latestveryvaluablebook.
ClaesHedberg
Professor,BlekingeInstitute
ofTechnology
Karlskrona,Sweden
Preface
Tostudynonlinearacousticalimaging,oneneedstounderstandindepththephysics
ofnonlinearacoustics.Hence,itisnecessarytostartwiththetheoreticalfoundation
ofnonlinearacoustics.Themostpopularequationofnonlinearacoustics,theKZK
equation only accounts for diffraction, nonlinearity and absorption in directional
soundbeams.Thereareseveralotheraspectsofnonlinear acousticswhicharenot
coveredbythisequation.Anexampleisthecurvilinearpathofhighintensityacoustic
wavefields.Toaccountforthecurvilinearpath,thecurvilinearspacetimecoordinates
have to be used. The most well-known application of curvilinear spacetime is the
general theory of relativity by Albert Einstein to account for the curvilinear path
ofthenonlineargravitationalfield.Thecurvilinearspacetimeapproachstartswith
theintrinsicnonlinearnatureoftheprobleminsteadofextendingthelinearcaseto
nonlinearitybyaddingonhigher-ordertermswhichisstillanapproximation.
Twowell-knownunsolvedproblemsofnonlinearacoustics,turbulenceandsono-
luminescencearephasetransitioninnature.Totreatphasetransitionproblem,statis-
ticalmechanicshastobeusedtostudythecriticalpointofphasetransitionandthe
singularitybehaviourofthetransportpropertiesoftheregionsurroundingthecritical
point.SofarthemostacceptabletheoriesofturbulencearethatduetoKolmogorov
whichisastatisticaltheoryandstatisticalmechanicshastobeused.Theothertheory
is that of the description of turbulence as a critical phenomenon, a form of phase
transitionandthesolvingofthesingularityproblemofthecorrelationlengthatthe
criticalpointbytheuseofrenormalizationgroupmethodwhichisusedinstatistical
mechanics.
Gaugetheoryisusefulforsolvingseveralproblemsinnonlinearacousticssuch
as multiple scattering, diffraction and electron–phonon interaction. The symmetry
usedingaugetheorycansimplifyseveralcomplexitiesinnonlinearacoustics.Also
theusualmethodusedforelectron–phononinteractionismanybodytheoryofDirac
whichcanhandleonlyuptothesecond-orderterm.Beyondthat,divergenceoccurs,
and there are infinities terms. With the use of gauge theory, the renormalization
methodcancancelofftheinfinitiesterms.
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x Preface
Duringthelastfortyyears,severalformatsofnonlinearacousticalimaginghave
beendevelopedsuchasharmonicsimaging,fractalimaging,B/Anonlinearparam-
eteracousticalimaging,non-classicalnonlinearacousticalimagingandmodulation
method in nonlinear acoustical imaging. The advantages of nonlinear acoustical
imaging are high sensitivity and higher image resolution. They can be applied to
non-destructivetesting,medicalultrasoundandunderwateracoustics.
Singapore WoonSiongGan
September2021
Contents
1 IntroductiontoNonlinearAcoustics ............................ 1
1.1 Introduction ............................................. 1
1.2 ConstitutiveEquations .................................... 2
1.3 PhenomenainNonlinearAcoustics ......................... 2
References .................................................... 2
2 NonlinearAcousticWaveEquationsforSoundPropagation
inFluidsandinSolids ......................................... 3
2.1 NonlinearAcousticWaveEquationsinFluids ................ 3
2.1.1 TheWesterveltEquation[1] ......................... 4
2.1.2 TheBurgers’Equation[2] ........................... 4
2.1.3 KZKEquation ..................................... 5
2.1.4 NonlinearAcousticWaveEquationsforSound
PropagationinSolids ............................... 6
References .................................................... 7
3 StatisticalMechanicsApproachtoNonlinearAcoustics ........... 9
3.1 Introduction ............................................. 9
3.2 StatisticalEnergyAnalysisisTransportTheory ............... 10
3.3 StatisticalEnergyAnalysis ................................ 12
3.4 TransportTheoryApproachtoPhaseTransition .............. 14
References .................................................... 15
4 CurvilinearSpacetimeAppliedtoNonlinearAcoustics ............ 17
4.1 IntroductionandMeaningofCurvilinearSpacetime ........... 17
4.2 PrincipleofGeneralCovariance ............................ 18
4.3 ContravariantandCovariantFour-Vectors .................... 19
4.4 ContravariantTensorsandCovariantTensors ................. 20
4.5 TheCovariantFundamentalTensorgμν ...................... 21
4.6 EquationofMotionofaMaterialPointintheGravitational
Field ................................................... 22
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