Nonlinear Acoustic Waves in Micro-inhomogeneous Solids PDF
Preview Nonlinear Acoustic Waves in Micro-inhomogeneous Solids
Nonlinear Acoustic Waves in Micro-inhomogeneous Solids Nonlinear Acoustic Waves in Micro-inhomogeneous Solids VENIAMIN E. NAZAROV AND ANDREY V. RADOSTIN Institute of Applied Physics of the Russian Academy of Sciences (IAP RAS), Russia Thiseditionfirstpublished2015 ©2015JohnWiley&SonsLtd Registeredoffice JohnWiley&SonsLtd,TheAtrium,SouthernGate,Chichester,WestSussex,PO198SQ,UnitedKingdom Fordetailsofourglobaleditorialoffices,forcustomerservicesandforinformationabouthowtoapplyforpermissiontoreuse thecopyrightmaterialinthisbookpleaseseeourwebsiteatwww.wiley.com. TherightoftheauthortobeidentifiedastheauthorofthisworkhasbeenassertedinaccordancewiththeCopyright,Designs andPatentsAct1988. Allrightsreserved.Nopartofthispublicationmaybereproduced,storedinaretrievalsystem,ortransmitted,inanyformorby anymeans,electronic,mechanical,photocopying,recordingorotherwise,exceptaspermittedbytheUKCopyright,Designs andPatentsAct1988,withoutthepriorpermissionofthepublisher. 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LibraryofCongressCataloging-in-PublicationData Nazarov,V.E.(VeniaminEvgen?evich),author. Nonlinearacousticwavesinmicro-inhomogeneoussolids/V.E.NazarovandA.V.Radostin. pagescm Includesbibliographicalreferencesandindex. ISBN978-1-118-45608-8(cloth) 1. Nonlinearacoustics.2. Elasticwavepropagation.3. Elasticsolids.4. Inhomogeneousmaterials. 5. Microstructure. I.Radostin,A.V.(AndreiViktorovich),author.II.Title. QC244.2.N392015 534′.22–dc23 2014023107 AcataloguerecordforthisbookisavailablefromtheBritishLibrary. ISBN:9781118456088 Setin10/12ptTimesLTStdbyLaserwordsPrivateLimited,Chennai,India 1 2015 Contents Preface ix I. Introduction 1 I.1 NonlinearityofGasesandLiquids 2 I.2 NonlinearityofHomogeneousSolids 2 I.3 Micro-inhomogeneousSolids.GeneralConsiderations 6 References 9 1. NonlinearWaveProcessesinHomogeneousMedia 11 1.1 AProgressiveApproximationApproach:TheSecondHarmonic GenerationinanUnboundedMedium 14 1.2 GenerationoftheWaveataDifferenceFrequency:ParametricArray, DegenerateInteractionofWaves 15 1.3 GenerationoftheWaveatSecondHarmonicFrequencyinResonators 17 1.4 SimpleWavesandFormationofDiscontinuities 19 1.5 ExactSolutionsoftheBurgersEquation 25 1.6 NonlinearWaveProcessesinRelaxingMedia 27 1.7 SphericalandCylindricalWaves 32 References 34 2. PhysicalModelsandMechanismsoftheStructureNonlinearityof Micro-inhomogeneousMediawithCracksandCavities 37 2.1 ContactMechanismofNonlinearityforCrackswithRoughand SmoothSurfaces 38 2.2 CapillaryandViscousMechanismsofNonlinearityforCracksPartially FilledwithLiquid 43 2.2.1 TheEquilibriumStateofaCrackPartiallyFilledwithLiquid 43 2.2.2 TheEquationofStateforaCrackPartiallyFilledwitha PerfectLiquid 45 2.2.3 TheEquationofStateforaCrackPartiallyFilledwitha ViscousLiquid 46 2.3 AcousticNonlinearityofPorousWater-likeMaterialswithCylindrical CavitiesPartiallyFilledwithViscousLiquid 50 2.4 AnAdhesionMechanismofHystereticNonlinearityforCracks 58 References 63 vi Contents 3. ElasticWavesinMediawithStrongAcousticNonlinearity 65 3.1 NonlinearPropagationandInteractionofAcousticWavesinMedia withCracksPossessingAdhesion 65 3.2 AcousticWavesinMediawithBimodularNonlinearity 68 3.3 AcousticWavesinMediawithBimodularNonlinearityandLinear Dissipation 70 3.4 DoublingofAcousticWaveFrequencybyaNonlinearLayer 76 3.5 PropagationofHigh-FrequencyPulsesinMediawithDissipative Nonlinearity 79 3.6 InteractionofCounter-PropagatingAcousticWavesinMediawith DissipativeNonlinearity 80 References 81 4. WaveProcessesinMicro-inhomogeneousSolidswithHysteretic Nonlinearity 83 4.1 HystereticEquationsofStateforSolids:PhenomenologicalModels 84 4.2 NonlinearWavesinanUnboundedMedium 88 4.2.1 PropagationofUnipolarAcousticPulses 95 4.2.2 Self-DemodulationofHigh-FrequencyAcousticPulses 96 4.2.3 NonlinearTravellingWavesinaRingResonator 97 4.3 VibrationsofRodsComposedofMaterialswithHysteretic NonlinearityandLinearDissipation 99 4.4 PropagationofUnipolarStrainPulsesinMediawithHysteretic NonlinearityofanArbitraryPower-Law 103 References 107 5. WaveProcessesinNonlinearMicro-inhomogeneousMediawith Relaxation 111 5.1 RheologicalModelandDynamicEquationofStateofNonlinear Micro-inhomogeneousMediawithRelaxation 112 5.1.1 SecondHarmonicGeneration 116 5.1.2 GenerationoftheDifferenceFrequencyWave 120 5.1.3 Self-DemodulationofPulseswithaHigh-FrequencyCarrier 124 5.2 EvolutionofAcousticWavesinMicro-inhomogeneousMediawith QuadraticElasticNonlinearityandRelaxation 127 5.2.1 StationarySymmetricShockWaves 127 5.2.2 EvolutionEquationsforLow-FrequencyandHigh-Frequency AcousticWaves 129 5.2.3 EvolutionofInitiallyHarmonicWaves 130 5.3 WaveProcessesinMicro-inhomogeneousElasticMediawith HystereticNonlinearityandRelaxation 132 5.3.1 EquationofStateofMicro-inhomogeneousMediumwith HystereticNonlinearityandRelaxation 133 5.3.2 NonlinearPropagationofaQuasi-HarmonicWave 133 Contents vii 5.3.3 FrequencyDependenciesofNonlinearCoefficientsfora MediumwithDefectshavingDifferentDistributionover RelaxationFrequencies 135 5.4 SimulationoftheDynamicHysteresesinMicro-inhomogeneous MediaCharacterizedbyImperfectElasticityandRelaxation 138 5.5 NonlinearWaveProcessesinMediaContainingCracksPartiallyFilled withaViscousLiquid 142 5.5.1 EquationofStateforaRodContainingCracksPartiallyFilled withaViscousLiquid 142 5.5.2 NonlinearPropagationandInteractionofElasticWavesina RodwithCracks 144 5.5.3 AnalysisoftheWaveProcessesinaRodwithIdenticalCracks 147 5.5.4 AnalysisoftheWaveProcessesinaRodwithCracks DistributedovertheRadii 148 References 150 6. WaveProcessesinPolycrystallineSolidswithDissipativeandReactive NonlinearityCausedbyDislocations 153 6.1 ModificationoftheLinearPartoftheGranato–LückeDislocation TheoryofAbsorptionandEquationofStatewithResonance DissipativeandReactiveNonlinearityforPolycrystallineSolids 154 6.2 AttenuationofHigh-FrequencyPulsesandthePhaseDelayofits CarrierFrequencyundertheActionofaLow-FrequencyWave 158 6.3 Amplitude–PhaseSelf-ActionPhenomenaintheHigh-Frequency WaveofFiniteAmplitude 160 References 163 7. ExperimentalStudiesofNonlinearAcousticPhenomenain PolycrystallineRocksandMetals 165 7.1 ExperimentalSetup 166 7.2 NonlinearShiftinResonanceFrequencyinaGlassRodwithArtificial Cracks 166 7.3 Low-FrequencyAmplitude-DependentInternalFrictionand High-FrequencyDissipativeNonlinearityofCoarse-GrainedSandstone 167 7.3.1 PhenomenaofLFHystereticNonlinearity: Amplitude-DependentLossesandShiftsofResonant Frequencies 168 7.3.2 NonlinearAttenuationofanUltrasonicPulseundertheAction ofaLFWave 173 7.4 EffectofanIntenseSoundWaveontheAcousticPropertiesofa Fine-GrainedSandstoneRodResonator 176 7.5 NonlinearAcousticPhenomenainLimestone 180 7.5.1 PhenomenaofLFHystereticNonlinearity 180 7.5.2 ManifestationoftheHFDissipativeNonlinearity 186 7.6 OscillogramsoftheFreeBoundaryNonlinearOscillationsofa MagnesiteResonator 187 viii Contents 7.7 High-FrequencyNonlinearAcousticPhenomenainMarble 189 7.7.1 AttenuationandPhaseDelayoftheCarrierFrequencyofWeak UltrasonicPulsesundertheActionofaLFPowerfulWave 189 7.7.2 Self-ActionofFinite-AmplitudeUltrasonicPulses 192 7.8 SoundbySoundDampingofPolycrystallineZinc 195 7.9 ModulationofSoundbySoundinCopperSubjectedtoDifferent DegreesofAnnealing 199 References 203 8. ExperimentalStudiesofNonlinearAcousticPhenomena inGranularMedia 205 8.1 Self-DemodulationofAcousticPulsesinPartiallyWater-Saturated RiverSand 206 8.1.1 ExperimentalSetup 206 8.1.2 ExperimentalResults 207 8.2 Self-ActionofAcousticWavesinSystemswithDissipative Nonlinearity 212 8.2.1 DescriptionoftheExperiment 213 8.2.2 AnalyticalDescriptionofthePhenomenonofSelf-Brightening 216 8.3 AmplificationofSoundbySoundinSystemswithDissipative Nonlinearity 221 8.4 Self-ActionofaLow-FrequencyAcousticWaveandGenerationofthe SecondHarmonicinDryandWater-SaturatedRiverSand 222 8.4.1 ExperimentalSchemeandMethodofMeasurement 222 8.4.2 MeasurementResults 223 8.4.3 AnalyticalDescriptionofthePhenomenaofSelf-Actionand GenerationoftheSecondHarmonic 226 8.5 AmplitudeModulationofSoundbySoundinWater-SaturatedRiver Sand 228 References 231 9. NonlinearPhenomenainSeismicWaves 233 9.1 StaticDeformationoftheEarth’sSurfaceNeartheHarmonicSource ofSeismicVibrations 233 9.2 AmplitudeModulationofSoundbySoundinSandySoil 237 9.3 Self-ActionoftheSeismicWaveinSandySoil 237 9.4 Amplitude–PhaseModulationofaSeismo–AcousticWaveunder DiurnalTides 242 References 245 Index 249
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