Základní pojmy
Definice
Vibration(alsoknownasoscillation)referstoaprocessofstatechange.Thatis,thereciprocatingmotionoftheobject.
Inhighschoolphysics,thereareonlyfoursimplestmotionsthatcanbestudiedquantitatively(theformulamethod,drawingmethod,andlistmethodcanbeusedtogivedefinitevalues):uniformlyvariablelinearmotion,uniformlycircularmotion,Projectilemotionandsimpleharmonicmotion.
Complicatedsportscanbequalitativelystudiedbyrelyingonthesefoursports.
Ifyouinsistonquantitativelystudyingcomplexmotions,youwillalsorelyonthesefourtypesofmotionsforapproximateresearch.
Z těchto čtyř nejjednodušších pohybů jsou rovnoměrně proměnlivý lineární pohyb a pohyb projektilu "nenávratně pryč" pohyby a vztah mezi stavem pohybu (poloha, rychlost) a časostopologickým stavem (odpovídající jedna k jedné) a neopakovatelným.
Pojem
Vibrationisoneofthemostcommonphenomenainnature.Fromtheuniversetothesmallsubatomicparticles,thereisnovibration.Variousformsofphysicalphenomena,includingsound,light,heat,etc.,containvibration.Peoplecannotlivewithoutvibration:thebeatingoftheheart,thevibrationoftheeardrumandthevocalcordsareallindispensablefunctionsofthehumanbody;humanvisionisstimulatedbylight,andlightisessentiallyanelectromagneticvibration;youcannotlivewithoutsoundAndmusic,andsoundproduction,transmissionandreceptionareinseparablefromvibration.Inthefieldofengineeringtechnology,vibrationphenomenaarealsoeverywhere.Forexample,thevibrationofbridgesandbuildingsundergustsorearthquakes,thevibrationofaircraftandshipsinnavigation,thevibrationofmachinetoolsandtoolsduringprocessing,thevibrationofvariouspowermachinery,theself-excitedvibrationinthecontrolsystem,etc..
Inmanycases,vibrationisconsideredanegativefactor.Forexample,vibrationcanaffectthefunctionsofprecisioninstrumentsandequipment,reduceprocessingaccuracyandsmoothness,andaggravatefatigueandwearofcomponents,therebyshorteningtheservicelifeofmachinesandstructures.Vibrationmayalsocauselargedeformationanddamagetothestructure.Somebridgeshavebeencausedbyvibration.Andcollapse;theflutterofaircraftwingsandthebuffetingofwheelsoftencauseaccidents;thevibrationofvehicles,shipsandcabinswilldegradetheloadingconditions;strongvibrationandnoisewillcauseseriouspublichazards.
However,vibrationalsohasitspositiveside.Forexample,vibrationisthebasisofcommunications,radio,television,radarandothertasks.Sincethe1950s,manyproductionequipmentandprocessesusingvibrationhaveappearedoneafteranother.Forexample,vibrationtransmission,vibrationscreening,vibrationgrinding,vibrationpolishing,vibrationpiledriving,vibrationeliminationofinternalstressandsoon.Theyhavegreatlyimprovedworkingconditionsandincreasedlaborproductivitybytenorahundredtimes.Itcanbeexpectedthatwiththecontinuousprogressofproductionpracticeandscientificresearch,theuseofvibrationwillincreasedaybyday.
Althoughvibrationphenomenaindifferentfieldshavetheirowncharacteristics,theyoftenhavesimilarmathematicaldescriptions.Itisonthebasisofthiscommonalitythatitispossibletoestablishaunifiedtheorytodealwithvariousvibrationproblems.Vibrationissuchabasicsubject.Itusesmathematics,physics,experimentsandcalculationtechniquestoexplorethemechanismofvariousvibrationphenomenaandclarifythebasiclawsofvibrationinordertoovercomethenegativefactorsofvibrationandmakeuseofitspositivefactorstobereasonable.Providetheoreticalbasisforsolvingvariousvibrationproblemsencounteredinpractice.
Klasifikace vibrací
Accordingtowhetheritcanbedescribedbyadefinitetimefunctionrelationship,vibrationisdividedintotwocategories,namelydeterministicvibrationandrandomvibration(non-deterministicvibration).Deterministicvibrationcanbedescribedbyacertainmathematicalrelationship,andforaspecifiedmoment,acorrespondingfunctionvaluecanbedetermined.Randomvibrationhasrandomcharacteristics,andtheresultsofeachobservationaredifferent.Itcannotbedescribedbyprecisemathematicalrelationsandcannotpredicttheprecisevalueatanymomentinthefuture.Instead,itcanonlybedescribedbyprobabilityandstatistics.Forexample:Anearthquakeisakindofrandomvibration.
Deterministicvibrationisdividedintoperiodicvibrationandnon-periodicvibration.Periodicvibrationincludessimpleharmonicperiodicvibrationandcomplexperiodicvibration.Simpleharmonicperiodicvibrationcontainsonlyonevibrationfrequency.Thecomplexperiodicvibrationcontainsmultiplevibrationfrequencies,andtheratioofanytwovibrationfrequenciesisarationalnumber.Non-periodicvibrationincludesquasi-periodicvibrationandtransientvibration.Quasi-periodicvibrationhasnoperiodicity,andtheratioofatleastonevibrationfrequencytotheothervibrationfrequencyamongthemultiplevibrationfrequenciescontainedisirrational.Transientvibrationsarevibrationsthatcanbedescribedbyvariousimpulsefunctionsordecayfunctions.
Konstantní kruhový pohyb a jednoduchý harmonický pohyb
Z dlouhodobého hlediska (neboli "makropohledu") je periodické, Opakovaně. V určitém časovém období (nebo "mikroskopicky") je topologické a neopakovatelné. Proto jsou poslední dvě cvičení mnohem složitější než první dvě cvičení.
Jednoduché harmonické vibrace
Definice
Jednoduché harmonické vibracecanberegardedasauniformcircularmotionthatdecomposesintwodirectionsorthogonal(thatis,perpendiculartoeachother)(thatis,Projection),themovementinanyonedirectionissimpleharmonicvibration.Itcanbeseenthatsimpleharmonicmotionismuchmorecomplicatedthanuniformcircularmotion.
Theprojectilemotioncanbedecomposedinto:anorthogonallinearmotionwithauniformspeedandanotherlinearmotionwithauniformspeed.Therefore,theprojectilemotionismuchmorecomplicatedthanalinearmotionwithauniformspeed.
Intheprocessoforthogonaldecompositionofuniformcircularmotion,theoriginalcentripetalforcewithconstantmagnitudebecomesarestoringforcewhosemagnitudeanddirectionchangeperiodically.Jednoduché harmonické vibraceiscomplexenough.Therefore,thevibrationisquantitativelystudieduptothesimpleharmonicvibration.
However,themicroscopicconditionsofvibrationthatweusuallyencounteraremuchmorecomplicatedthansimpleharmonicvibrations.Therefore,thetransitionfromstudyingsimpleharmonicvibrationtostudyingvibration,thermalvibration,etc.requiresinsight,imagination,abstractthinking,andlogicalreasoning.
Funkce
Thecharacteristicsofsimpleharmonicvibrationare:1.Thereisanequilibriumposition(theonlypositionwherethevibratorshouldbestationaryafterthemechanicalenergyisexhausted).2.Thereisarestoringforcewhosesizeanddirectionarechangedperiodically.3.Singlefrequencyandconstantamplitude.
Thevibratorisanabstractionofthevibratingobject:Ignoretheshapeandsizeoftheobject,andusethemasspointtoreplacetheobjectforresearch.Thismasspointthatreplacesthevibratingobjectiscalledavibrator.
Thepositionofthevibratoratacertainmomentisrepresentedbydisplacementx.Thedisplacementxisthedistanceanddirectionofthe"positionofthevibratoratacertainmoment"obtainedbytakingtheequilibriumpositionasthereference(basepoint-datumpoint).
Whenwestudyuniformlyvariablelinearmotionandprojectilemotion,thereferencepointisselectedatthestartingpointofthemotion.Whenwestudyuniformcircularmotionandsimpleharmonicvibration,thereferencepointisselectedatthecenterofthecircleorattheequilibriumposition(fixedpoint).
Thereferenceobjectshouldoriginallybeapointthatremainsstationary(orassumedtobestationary)duringtheresearchprocess.Ourphysicalthinkingisto"studyfromadefinitequantityandaconstantquantity."
Thereisanessentialdifferencebetweenthedeterminedquantityandtheconstantquantity.Whenstudyingthelinearmotionwithuniformspeedandtheprojectilemotion,thereferencepointisselectedatthestartingpointofthemotion.Thisisacertainamount,butnotnecessarilyaconstantamount.Especiallywhenweconductasegmentedstudy,theendofeachstageisthestartingpointofthenextstage.Wechoosethestartingpointofthemovementasthereferencepoint,whichcansimplifytheresearchprocess.Thisissubjecttotheprincipleof"simplifyingcomplexity"inphysicsresearch.Therefore,wedonothesitatetochoosedifferentreferencepointsatdifferentresearchstages.
Inthestudyofuniformcircularmotionandsimpleharmonicmotion,duetotheperiodicityonthemacroscopicandthetopologyonthemicroscopic,theproblemisverycomplicated,soitisimpossibletochoosethestartingpointofthemotionanduseitasthereferencepointforresearch.Tochooseadefiniteandunchangingcenterorbalancepositionanduseitasareferencepointforresearchisalsosubjecttotheprincipleof"simplifyingcomplexity"inphysicsresearch.
Inasimpleharmonicvibration,theamplitudeAisthemaximumvalueofthedisplacementx,whichisaconstantquantity.
Theshortesttimerequiredforthevibratortoreturnfromacertainstate(positionandvelocity)tothatstateiscalledaperiodT.Thevibrationofthevibratorinaperiodiscalledatotalvibration.The"number"oftotalvibrationofthevibratorinonesecondiscalledfrequencyf.
TheperiodTisthetimeofonefullvibration,andthefrequencyfisthenumberoffullvibrationsinonesecond,soTf=1(equivalenceformula1ofthefourequations)
Thefrequencyω(pronounced[oumiga])isthecentralanglecorrespondingtoonesecond.Thecentralanglecorrespondingtoafullvibrationis2π(thatis,360degrees).Thisborrowedtheconceptofuniformcircularmotion.Inauniformcircularmotion,ωiscalledtheangularvelocity.Whenauniformcircularmotionisorthogonallydecomposedintoasimpleharmonicmotion,theangularvelocityisconvertedintoacircularfrequency.(Somepeoplecallthecircularfrequencytheangularfrequency)
Je zřejmé, že ω=2πf(ekvivalenční vzorec 3ze čtyř rovnic),(úhel odpovídající celkovému počtu vibrací za sekundu)
ωT=2π(ekvivalenční vzorec 2ze čtyř rovnic)(úhel odpovídající každé plné vibraci)
Nakonec definujte počet plných vibrací za minutu jako "rychlost rotacen". Je zřejmé, že n=60f(čtyřiEkvivalentní vzorec4)
Ze čtyř množství T, f, ω, n, jedna je známa a ostatní tři jsou známé, se tedy tyto čtyři vzájemně transformovatelné vzorce nazývají „čtyři ekvivalentní“.
Aslongastheobjectreciprocatesperiodically,itisvibration.Forexample,whenplayingaball,itsv-tdiagramcorrespondstothesawtoothwaveinelectricalengineering,soitisalsovibration.Somepeoplesay:"Theballhasnoequilibriumposition,ortheequilibriumpositionisnotatthecenterofsymmetryofmotion,soitcannotbeconsideredasvibration."Thosewhosaythat,certainlydidnotlearnelectricalengineeringwell.
ThereisabranchofmathematicscalledFourierintegral,whichcandecomposeanyvibrationintoseveralsimpleharmonicvibrations.Thefrequencyofthesesimpleharmonicvibrationsisanintegermultipleoftheoriginalvibration,andthemainfrequency(fundamentaltone)oftheoriginalvibrationistheminimumfrequencyofthesesimpleharmonicvibrations.
Jiná oktáva (nadtón),amplituda je menší než základní tón.Proto to představuje koncept "zabarvení" neharmonické vibrace.
TheprocessbywhichthehumaneardistinguishesthesoundingbodyistheprocessofusingFourierintegralspontaneously,automatically,andinstinctively,whichisveryclever.
Becausethefrequencyofthesoundisdeterminedbythesoundsource,nomatterhowthesoundwavepropagatestoourears,westillaccuratelyidentifythecharacteristicsofthestartingsoundbody.
Vibrace v širokém smyslu
Inabroadsense,vibrationreferstotheprocessinwhichtheparametersdescribingthestateofthesystem(suchasdisplacementandvoltage)alternateupanddownitsreferencevalue.Inanarrowsense,itreferstomechanicalvibration,thatis,vibrationinamechanicalsystem.Electromagneticvibrationistraditionallycalledoscillation.Themechanicalsystemcanmaintainvibrationandmusthaveelasticityandinertia.Duetoelasticity,whenthesystemdeviatesfromitsequilibriumposition,itwillgeneraterestoringforce,promptingthesystemtoreturntoitsoriginalposition;duetoinertia,thesystemaccumulateskineticenergyintheprocessofreturningtotheequilibriumposition,sothatthesystemmovesacrosstheequilibriumpositiontotheotherside.Itispreciselybecauseofthemutualinfluenceofelasticityandinertiathatthesystemvibrates.Accordingtothedegreeoffreedomofsystemmovement,therearesingle-degree-of-freedomsystemvibration(suchasthevibrationofapendulum)andmulti-degree-of-freedomsystemvibration.Thefinitemulti-degree-of-freedomsystemcorrespondstothediscretesystem,anditsvibrationisdescribedbyordinarydifferentialequations;theinfinitemulti-degree-of-freedomsystemcorrespondstothecontinuoussystem(suchasrods,beams,plates,shells,etc.),anditsvibrationisdescribedbypartialdifferentialequations.Asystemthatdoesnotexplicitlycontaintimeintheequationiscalledanautonomoussystem;asystemthatexplicitlycontainstimeiscalledanon-autonomoussystem.Accordingtotheforceofthesystem,therearefreevibration,attenuatedvibrationandforcedvibration.Accordingtothepropertiesofelasticforceanddampingforce,therearelinearvibrationandnonlinearvibration.Vibrationcanbedividedintodeterministicvibrationandrandomvibration.Thelatterhasnodeterministiclaw,suchasbumpsinthecourseofavehicle.Vibrationisacommonphenomenoninnatureandengineering.Thenegativeaspectsofvibrationare:itaffectsthefunctionsofinstrumentsandequipment,reducestheworkingaccuracyofmechanicalequipment,increasescomponentwear,andevencausesstructuralfatiguedamage;thepositiveaspectsofvibrationare:therearemanyequipmentandprocessesthatrequirevibration(suchasvibrationtransmission,vibrationgrinding),Vibratingpiles,etc.).Thebasictaskofvibrationanalysisistodiscussthesystem'sexcitation(i.e.input,referstotheexternaldisturbanceofthesystem,alsoknownasinterference),response(i.e.output,referstothereactionofthesystemafterbeingexcited)andthedynamiccharacteristicsofthesystem(orphysicalparameters).Relationshipbetween.Afterthe1960s,majoradvancesincomputersandvibrationtestingtechnologyopenedupbroadprospectsforthecomprehensiveutilizationofanalysis,experiment,andcalculationmethodstosolvevibrationproblems.
Mechanické vibrace
Definice
Mechanické vibraceisthereciprocatingmotionofanobject(orpartofanobject)neartheequilibriumposition(thepositionwhentheobjectisstationary).Therearedifferentclassificationmethodsformechanicalvibration.Accordingtothecauseofthevibration,itcanbedividedintofreevibration,forcedvibrationandself-excitedvibration;accordingtothelawofvibration,itcanbedividedintosimpleharmonicvibration,non-harmonicperiodicvibrationandrandomvibration;accordingtothecharacteristicsofthestructuralparametersofthevibrationsystem,itcanbedividedintolinearvibrationAndnonlinearvibration;accordingtothecharacteristicsofvibrationdisplacement,itcanbedividedintotorsionalvibrationandlinearvibration.
Freevibration:Thevibrationofthemechanicalsystemaftertheexcitationorconstraintisremoved.Thevibrationismaintainedonlybyitselasticrestoringforce,andwhenthereisdamping,thevibrationwillgraduallyattenuate.Thefrequencyoffreevibrationisonlydeterminedbythephysicalpropertiesofthesystemitself,whichiscalledthenaturalfrequencyofthesystem.
Forcedvibration:Thevibrationofthemechanicalsystemcausedbycontinuousexternalexcitation.Simpleharmonicexcitationisthesimplestcontinuousexcitation.Forcedvibrationincludestransientvibrationandsteady-statevibration.Thetime-varyingvibrationthatoccurswithinaperiodoftimeatthebeginningofvibrationiscalledtransientvibration.Afterashortperiodoftime,thetransientvibrationdisappears.Thesystemcontinuouslyobtainsenergyfromtheoutsidetocompensatefortheenergydissipatedbythedamping,soitcanmakecontinuousconstantamplitudevibration.Thefrequencyofthisvibrationisthesameastheexcitationfrequency,whichiscalledsteady-statevibration.Forexample,avibrationexciterisinstalledinthemiddleofabeamfixedatbothends,andthecontinuousconstant-amplitudevibrationofthebeamaftertheexciterisactivatedforashorttimeisasteady-statevibration,andthefrequencyofthevibrationisthesameasthefrequencyoftheexciter.Whenthesystemissubjectedtoexternalforceorotherinput,itscorrespondingoutputiscalledresponse.Whenthefrequencyoftheexternalexcitationisclosetothenaturalfrequencyofthesystem,theamplitudeofthesystemwillincreasesharply.Resonanceoccurswhentheexcitationfrequencyisequaltotheresonancefrequencyofthesystem.Resonancemustbepreventedwhendesigningandusingmachinery.Forexample,inordertoensurethesafeoperationofrotatingmachinery,theworkingspeedoftheshaftshouldbeoutsideacertainrangeofitscriticalspeed.
Self-excitedvibration:Innonlinearvibration,thesystemisonlymaintainedbytheexcitationgeneratedbyitself.Inadditiontothevibrationcomponents,theself-excitedvibrationsystemalsohasnon-oscillatingenergysources,adjustmentlinksandfeedbacklinks.Therefore,itcanalsoproduceastableperiodicvibrationwhenthereisnoexternalexcitation,andthealternatingforcethatmaintainstheself-excitedvibrationisgeneratedbythemotionitselfandcontrolledbythefeedbackandadjustmentlinks.Assoonasthevibrationstops,thisalternatingforcealsodisappears.Theself-excitedvibrationhasnothingtodowiththeinitialconditions,anditsfrequencyisequaltoorclosetothenaturalfrequencyofthesystem.Forexample,theflutterofthewingsduringtheflightoftheaircraft,thecrawlingofthemachinetooltablewhenmovingatlowspeedontheslidingguiderail,theswingoftheclockpendulumandthevibrationofthestringsareallself-excitedvibrations.
Aplikace vibrací ve strojírenském průmyslu
Theapplicationofvibrationinmachineryisverycommon.Forexample,inthevibratingscreeningindustry,thebasicprincipleisbasedontheheavyhammerinstalledattheupperandlowerendsofthemotorshaft.(Unevenheavyhammer),whichconvertstherotatingmotionofthemotorintoahorizontal,vertical,andinclinedthree-dimensionalmotion,andthentransmitsthismotiontothescreensurface.Ifyouchangethephaseangleoftheupperandlowerweights,thedirectionoftraveloftherawmaterialscanbechanged.
Nebezpečí a ochrana proti vibracím lidského těla
1.Zdroje vibrací se počítají ve výrobě
(1)Nýtovací stroj,Pneumatické nástroje, jako jsou vrtačky a větrné lopaty;
(2) Elektrické nářadí, jako jsou elektrické vrtačky, elektrické pily, lesnické řetězové pily, brusky, leštičky, brusky, stroje na pěchování silnic atd.;
(3)dieselové komotivy, lodě, motocykly a jiná dopravní vozidla;
(4) Traktory, kombajny, mlátičky a jiné zemědělské stroje.
Za druhé, dopad vibrací na různé lidské systémy
(1)Změny elektroencefalogramu;změny podmíněné reflexní latence;sympatická hyperfunkce;nestabilita krevního tlaku,arytmie atd.;Sensorická funkce kůže je snížena,jako je dotek,teplo,bolest,zejména pocity vibrací,které se objevují nejdříve.
(2)Vibrationof40～300Hzcancausechangesinthemorphologyandtensionofperipheralcapillaries,manifestedasperipheralvasospasmandabnormalcerebralbloodflowdiagram;bradycardiaandsinusrhythmcanoccurintheheart.Qiandintra-room,indoor,atrioventricularconductionblock,etc.
(3) Snížená síla úchopu, abnormální elektromyogram, svalová fibrilace, svalová atrofie a bolest atd.
(4)Large-amplitudevibrationbelow40Hzcaneasilycausechangesinbonesandjoints.Bonetradeformation,osteoporosis,boneandjointdeformationandnecrosiscanbeseenonboneX-rayfilms.
(5)Thehearingchangescausedbyvibrationarecharacterizedbyhearinglossinthe125-250Hzfrequencyband,butintheearlystage,thehearinglossisstilldominatedbythehighfrequencyband,andthenthelowfrequencyhearinglossoccurs.Vibrationandnoisehaveacombinedeffect.
(6)Long-termuseofvibrationtoolscancauselocalvibrationdiseases.Localvibrationdiseaseisadiseasemainlycausedbyperipheralcirculatorydisorders,anditcanalsoaffectthenervesandmotorfunctionsofthelimbs.Thesiteofthediseaseisusuallyattheendoftheupperextremity,andthetypicalmanifestationisparoxysmalwhiteningofthefingers(referredtoaswhitefingers).Inmycountry,localvibrationdiseasewasdesignatedasanoccupationaldiseasein1957.
(7)Thefactorsthataffectvibrationarevibrationfrequency,accelerationandamplitude.Thehumanbodyonlyproducesvibrationsensationto1～1000Hzvibration.Frequencyplaysanimportantroleinthepathogenesis.30～300Hzmainlycausesperipheralvasospasmandwhitefingers.Whenthefrequencyisthesame,thegreatertheacceleration,thegreaterthedamage.Vibrationswithlargeamplitudeandlowfrequencymainlyactonthevestibularorgansandcancauseinternalorganstoshift.Whenthefrequencyisconstant,thegreatertheamplitude,thegreatertheimpactonthebody.Coldisoneoftheimportantexternalconditionsfortheonsetofvibrationdisease.Coldcanreducebloodflowandchangebloodcirculation,leadingtoinsufficientlocalbloodsupplyandpromotingtheoccurrenceofvibrationdisease.Thelongertheexposuretovibration,thehighertheincidenceofvibrationdisease.Restatworkhasapositiveeffectonthepreventionofvibrationdiseases.Thesensitivityofapersontovibrationisrelatedtothepositionofthebody.Thehumanbodyissensitivetoverticalvibrationwhenstandingup;itissensitivetohorizontalvibrationwhenlyingdown.Somejobsrequireaforcedposture,evenifthechest,abdomenorlowerlimbsareclosetothevibratingobject,theharmofvibrationisevengreater.Whenthehardnessoftheprocessedpartsishigh,theworkerswillsuffermoredamage,andthevibrationwithhighimpactforcewilleasilycausethebonesandjointstodisease.
3.Ovládání nebezpečí vibrací
Reformtheprocess,fundamentallyeliminateandreducetheoperationofhand-heldpneumatictools,usinghydraulicpressure,welding,andbondingInsteadofriveting;improvepneumatictools,adopteffectivevibrationreductionmeasures,andreformthepositionoftoolexhaust;useautomaticandsemi-automaticcontroldevicestoreducedirectcontactwiththevibratingbody;thosewhoholdvibrationtoolsshouldweardouble-layerpadsandfingerlessGlovesorpaddedfoamplasticfingerlessgloves,andpayattentiontokeepwarmandcold;fornewworkers,apre-employmentphysicalexamination,patientswithvasospasm,acralvasculardisorders,andneuritis,areprohibitedfromperformingvibrationoperations;workersexposedtovibrationshouldberegularlyTheintervalbetweenphysicalexaminationsshouldbe2to3years;necessarytreatmentsshouldbegiventopatientswithvibrationdiseases,andthosewithrepeatedcomplaintsshouldberemovedfromthevibrationworkposition.
Theactualvibrationproblemisoftenintricateandcomplicated,anditmayincludeseveralaspectssuchasidentification,analysis,andsynthesisatthesametime.Usuallytheactualproblemisabstractedasamechanicalmodel,whichisessentiallyasystemidentificationproblem.Theprocessofsolvingthesystemmodelformulationisessentiallytheprocessofvibrationanalysis.Analysisisnottheendoftheproblem.Theresultsoftheanalysismustalsobeusedtoimprovethedesignortroubleshoot(actualorpotential).Thisistheproblemofvibrationsynthesisordesign.
Themethodtosolvethevibrationproblemisnothingmorethantheoreticalanalysisandexperimentalresearch,whicharecomplementarytoeachother.Inthetheoreticalanalysisofvibration,alargenumberofmathematicaltools,especiallytheincreasingdevelopmentofdigitalcomputers,providepowerfulmeanstosolvecomplexvibrationproblems.Sincethemid-1960s,therehavebeenmajorbreakthroughsandadvancesinvibrationtestingtechnology,whichinturnopenedupbroadprospectsforexperiments,analysisandresearchonvibrationproblems.Seelinearvibration,nonlinearvibration,randomvibration.