acousticsworkshop1ia.docx

acousticsworkshop1ia.docx

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acousticsworkshop1ia

Note:

ThisworkshopprovidesinstructionsintermsoftheABAQUSGUIinterface.IfyouwishtousetheABAQUSKeywordsinterfaceinstead,pleaseseethe“Keywords”versionoftheseinstructions.

PleasecompleteeithertheKeywordsorInteractiveversionofthisworkshop.

Goals

Whenyoucompletethisworkshop,youwillbeableto:

Determinethenaturalfrequenciesofanacousticdomain.

Determinethesteady-statedynamicresponseofanacousticsystem.

Defineaclassicalacousticplane-waveabsorbingboundary.

Defineacousticexcitationloads.

Viewrealandimaginarycomponentsofacousticpressure.

Createpathplotsofacousticoutputdata.

ABAQUS

Introduction

Asimpleacousticmodelofasectionofairductwillbeusedtointroducesomeofthebasicanalysistechniquesthatcanbeappliedtoanacousticmesh.Inthisworkshopyouwilladdimportantmodelingdetailstocompletethesuppliedmodeldatabasewhichalreadycontainsbasicmodelingdatasuchasgeometry,mesh,andmaterialdefinitions,fortheairductsectionshowninFigureW1–1.Themodelforthisworkshoprepresentsonlytheairinsidetheduct.Theacousticnaturalboundaryconditionofinfiniteimpedanceatameshboundaryimpliesrigidductwalls.Youwillperformnaturalfrequencyextractionanalyseswithdifferentsetsofacousticboundaryconditionsassignedtotheendsoftheduct.Youwillthenperformaseriesofsteady-statedynamicresponseanalysesonthemodelusingdifferentexcitationmethods.Thesteady-statedynamicanalyseswillalsoincludethedefinitionofacousticplane-waveabsorbingboundaryimpedanceatoneendoftheducttoinvestigatepostprocessingoftravelingwavesforfrequency-domainsolutions.

FigureW1–1Modelofasimpleairductsection.

Preliminaries

1.Entertheworkingdirectoryforthisworkshop:

../acoustics/interactive/workshop1

2.Runthescriptws_acoustic_duct.pyusingthefollowingcommand:

abaquscaestartup=ws_acoustic_duct.py

TheabovecommandcreatesanABAQUS/CAEdatabasenamedduct.caeinthecurrentdirectory.Thegeometry,materialandmeshdefinitionsfortheairductsectionmodelshowninFigureW1–1areincludedinthedatabase.Theairductsectionis4.25mlongandhasarectangularcross-sectionthatis0.2mby0.125m.Theacousticmediumisairwithadensityof1.225kg/m3andasoundspeedof340m/s.Thus,theeffectivebulkmodulusis141610Pa.Themodelisdesignedtoprovidereasonablequantitativeresultsforanalysesupto400Hzandutilizesfirst-orderacousticelementsthatare0.085mlong.Thismeshrefinementcorrespondsto10elements（nodaldivisions）peracousticwavelengthataresponsefrequencyof400Hz.Thelargestcross-sectionaldimensionoftheductissignificantlylessthanone-halfthe400Hzacousticwavelength;therefore,theductcross-sectioncanbemodeledwithasingleelement.Thesegeometric,material,andmeshpropertiesshouldnotbemodifiedforthisworkshop.However,aftercompletionofthisworkshopyoumaywanttoconsidermodifyingthemeshtoperformadditionalconvergenceandaccuracystudies.

Note:

Ingeneral,second-orderacousticelementsaremoreaccuratethanfirst-orderacousticelementsforthesamemeshnodaldensity.However,first-orderelementscanprovidenearlyasgoodanapproximationtoasinusoidalacousticpressurewaveascansecond-orderelementsaslongasthenodaldistributionsaresimilar.Therefore,whenperformingacousticanalysesinwhichdeterminingthepressurefieldisofprimaryinterest,first-orderelementsareoftenusedbecausetheycanbeeasiertoworkwith.Themainadvantageofsecond-orderacousticelementsisthattheyprovideforapiecewiselinearapproximationofthepressuregradients（and,thus,theparticlevelocities）,whilethefirst-orderelementsproduceapiecewiseconstantapproximation.Therefore,formesheswithsimilarnodaldensities,thesecond-orderelementswillprovidesignificantlybetterquantitativeresultsforitemssuchasacousticintensity（power）thatrequireaccurateestimatesofpressuregradientsandparticlevelocities.Usingfirst-orderacousticelementstodetermineapressurefieldisanalogoustousingfirst-orderstress-displacementelementstodeterminestiffness,whileusingsecond-orderacousticelementstodetermineacousticintensityisanalogoustousingsecond-orderstress-displacementelementstodetermineastress/strainconcentration.

Case1:

Naturalfrequencyextraction（rigid-rigidends）

ThefirstanalysisforWorkshop1involvesextractingthenaturalfrequenciesoftheairductsectionshowninFigureW1–1forthecasewherebothendsoftheductutilizethenaturalboundaryconditionassociatedwithanacousticmesh.Therefore,forthiscasenoboundaryconditionsorloadingoptionsareappliedtotheacousticpressuredegreeoffreedom.Thenaturalboundaryconditionassociatedwiththesurfaceofanacousticmeshcorrespondstoinfiniteboundaryimpedance.Themeshboundarycanthereforebeenvisionedasaninfinitelyrigidsurface.

3.InanABAQUS/CAEsession,openthedatabasenamedduct.cae,whichwascreatedbyrunningthesetupscript.

4.Createanaturalfrequencyextractionsteptoobtainupto25naturalfrequenciesintherangefrom5Hzto400 Hzwithashiftpointcorrespondingto100Hz.Detailedinstructionsareprovidedbelow.UseofthedefaultLanczoseigensolverisrecommended.Theextractionofnaturalfrequenciesforanacousticmeshinrealworldproblemswilllikelyinvolverelativelylargemodels,forwhichtheLanczoseigensolverismoreefficientthanthesubspaceiterationeigensolver.Inaddition,theLanczoseigensolverallowsyoutoselectaprecisefrequencyrangefortheeigenvalueextraction.

a.IntheModelTree,double-clicktheStepscontainer.

b.IntheCreateStepdialogbox,choosetheLinearperturbationproceduretypeandselectFrequencyfromthelistofavailableprocedureoptions.Acceptthedefaultstepname,Step-1.

c.ClickContinue.

d.IntheEditstepdialogbox,specify25astherequestednumberofeigenvalues.Enter10000asthefrequencyshiftinsquaredcyclespertime.Specify5and400astheminimumandmaximumfrequenciesofinterest,respectively.Enteranappropriatestepdescription.AccepttheLanczoseigensolverandotherdefaultstepsettings.

e.ClickOK.

5.IntheModelTree,clickmousebutton3（MB3）onthejobnamedduct-1andselectSubmitinthemenuthatappearstosubmitthejobforanalysis.

6.Aftertheanalysiscompletes,useatexteditortoreviewtheprintedoutputfileduct-1.dat.ComparethenaturalfrequencieslistedintheEigenvalueOutputtabletotheexactclassicalvaluesforthisproblem.Theclassicalsolutionisforafundamentalmodeof40Hzwithanintervalof40Hzbetweensuccessivemodes.

7.IntheModelTree,clickMB3onthejobnamedduct-1andselectResultsinthemenuthatappears.ABAQUS/CAEloadstheVisualizationmoduleandopensthefileduct-1.odb.

8.ViewtheacousticmodeshapesbycreatingcontourplotsofthepressurevariablePOR（PlotContours）.

9.DefineapathalongthelengthoftheductsectionandcreateaplotofPORalongthispathusingtheprocedurebelow.

a.Fromthemainmenubar,selectToolsPathCreate.

b.IntheCreatePathdialogbox,acceptthedefaultpathname（Path-1）andtype（Nodelist）.ClickContinue.

c.IntheEditNodeListPathdialogbox,clickAddBefore.

d.Intheviewport,selectthestartandendpointsforthepath,asshowninFigureW1–2.ClickDoneinthepromptarea.

e.ThetableintheEditNodeListPathdialogboxnowcontainstheselectednodelabels.ClickOKtocompletethepathdefinition.

f.Fromthemainmenubar,selectToolsXYDataCreate.

g.IntheCreateXYDatadialogbox,choosePathandclickContinue.

h.IntheXYDatafromPathdialogbox,toggleonIncludeintersectionstoobtainX–Ydataatlocationswherethepathintersectsthemodelaswellasatthepointsthatmakeupthepath.

i.IntheYValuesportionoftheXYDatafromPathdialogbox,clickStep/Frame.IntheStep/Framedialogboxthatappears,choosethemodeofinterestandclickOK.

j.IntheCreateXYDatadialogbox,clickPlottogeneratethepathplot.

FigureW1–2containsexamplesofbothacontourandapathplotforthefifthmode.

FigureW1–2Fifthacousticmodeshapeofthe

airductsectionwithrigid-rigidends.

CASE2:

Naturalfrequencyextraction（rigid-freeends）

Asstatedearlier,thenaturalboundaryconditionassociatedwiththesurfaceofanacousticmeshcorrespondstoinfiniteboundaryimpedance.Thisimpliesthattheacousticparticlevelocitynormaltotheboundarysurfaceiszero.Theboundarysurfacecan,therefore,bethoughtofasrigid.Thenaturalboundaryconditionischaracterizedbyazeropressuregradient,asillustratedintheCase1analysisbythepathplotshowninFigureW1–2.Assigningavaluetotheacousticpressuredegreeoffreedomataboundingsurfacerepresentsakinematicboundaryconditionandcorrespondstozeroboundaryimpedance.Thistypeofboundaryconditionallowsacousticparticlestomovefreelyacrosstheboundingsurface.Theacousticparticlevelocityattheboundingsurface,characterizedbythepressuregradient,isthenunknowninamanneranalogoustoareactionforceinstructuralmechanics.Forthisanalysiscaseyouwilldeterminethenaturalfrequenciesoftheairductsectioninwhichoneendhasinfiniteboundaryimpedance（rigid）andtheotherhaszeroboundaryimpedance（free）.

1.Copythemodelduct-1toamodelnamedduct-2.

a.IntheModelTree,clickMB3onthemodelnamedduct-1andselectCopyModelinthemenuthatappears.

b.Enterduct-2asthenameofthenewmodel.

Allinstructionsthatfollowapplytothemodelnamedduc