Theory of Propagation of Elastic Waves in a Fluid-Saturated Porous Solid. I. Low-Frequency Range

Theory of Propagation of Elastic Waves in a Fluid-Saturated Porous Solid. I. Low-Frequency Range

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1、THEJOURNALOFTHEACOUSTICALSOCIETYOFAMERICAVOLUME28.NUMBER2MARCH.1956TheoryofPropagationofElasticV?ravesinaFluid-SaturatedPorousSolid.I.Low-FrequencyRangeM.A.B?OT*ShellDevelopmentCompany,RCAB1dlding,NewYork,NewYork(ReceivedSeptember1,1955)Atheoryisdevelopedforthepropagationofstresswavesin

2、aporouselasticsolidcontainingacompressibleviscousfluid.Theemphasisofthepresenttreatmentisonmaterialswherefluidandsolidareofcomparabledensitiesasforinstanceinthecaseofwater-saturatedrock.ThepaperdenotedhereasPartIisrestrictedtothelowerfrequencyrangewheretheassumptionofPoiseuilleflowisval

3、id.TheextensiontothehigherfrequencieswillbetreatedinPartII.Itisfoundthatthematerialmaybedescribedbyfournondimen-sionalparametersandacharacteristicfrequency.Therearetwodilatationalwavesandonerotationalwave.Thephysicalinterpretationoftheresultisclarifiedbytreatingfirstthecasewherethefluid

4、isfrictionless.Thecaseofamaterialcontainingaviscousfluidisthendevelopedanddiscussednumerically.Phasevelocitydispersioncurvesandattenuationcoefficientsforthethreetypesofwavesareplottedasafunctionofthefrequencyforvariouscombinationsofthecharacteristicparameters.1.INTRODUCTIONThisisobtaine

5、difa"dynamiccompatibility"relationisverifiedbetweentheelasticanddynamicconstants.ThisURofelasticpurposewavesistoinestablishasystematheorycomposedofpropagationofaporousisacasewheredissipationduetofluidfrictionwillelasticsolidsaturatedbyaviscousfluid.Itisassumeddisappear.InSec.6thedynamic

6、relationsarederivedthatthefluidiscompressibleandmayflowrelativetowiththeadditionoffluidviscosityandSec.7derivesthesolidcausingfrictiontoarise.PartIwhichisthepropertiesofthepropagationofthewaveswhenpresentedhereassumesthattherelativemotionofthedissipationispresent.Itisfoundthatthephaseve

7、locityfluidintheporesisofthePoiseuilletype.AsalreadyofrotationalwavesincreasesslightlywiththefrequencypointedoutbyKirchhoffthisisvalidonlybelowafwhiletheabsorptioncoefficientisproportionaltothecertainfrequencywhichwedenotebyf?,andwhichsquareofthefrequency.Allplotsarepresentedno

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