結(jié)構(gòu)動(dòng)力學(xué)第III篇-碩士知識(shí)資料P17知識(shí)資料石巖

PartIIIDistributed--ParameterSystems第III篇分布參數(shù)體系Chapter17Partialdifferentialequationsofmotion34567891011121314151617181920212223242526（1）國(guó)內(nèi)教材(點(diǎn)擊閱讀)劉晶波、杜修力--結(jié)構(gòu)動(dòng)力學(xué)俞載道--結(jié)構(gòu)動(dòng)力學(xué)基礎(chǔ)于建華--高等結(jié)構(gòu)動(dòng)力學(xué)邱吉寶--計(jì)算結(jié)構(gòu)動(dòng)力學(xué)李明昭--橋梁結(jié)構(gòu)動(dòng)力分析

胡宗武--工程振動(dòng)分析基礎(chǔ)胡兆同--結(jié)構(gòu)振動(dòng)與穩(wěn)定胡少偉--結(jié)構(gòu)振動(dòng)理論及其應(yīng)用包世華--結(jié)構(gòu)動(dòng)力學(xué)彭俊生--結(jié)構(gòu)動(dòng)力學(xué)、抗震計(jì)算與SAP2000應(yīng)用盛宏玉--結(jié)構(gòu)動(dòng)力學(xué)輔導(dǎo)與習(xí)題精解盛宏玉--結(jié)構(gòu)動(dòng)力學(xué)

（第二版）王光遠(yuǎn)--應(yīng)用分析動(dòng)力學(xué)（2）Clough教材資料(點(diǎn)擊閱讀)克拉夫--結(jié)構(gòu)動(dòng)力學(xué)(81版)結(jié)構(gòu)動(dòng)力學(xué)（第2版）中文版克拉夫--DynamicsofStructure（英文原版）結(jié)構(gòu)動(dòng)力學(xué)習(xí)題詳解(Clough版)（3）Chopra教材資料(點(diǎn)擊閱讀)Chopra--結(jié)構(gòu)動(dòng)力學(xué)_理論及其在地震工程中的應(yīng)用（第2版）(中文版)Chopra--DynamicsofStructures(4thEdition，英文原版)Chopra--(入門(mén))結(jié)構(gòu)動(dòng)力學(xué)入門(mén)Chopra--(入門(mén))DynamicsofStructures：APrimerChopra哈工大結(jié)構(gòu)動(dòng)力學(xué)講義結(jié)構(gòu)動(dòng)力學(xué)學(xué)習(xí)資料下載鏈接：/post/109.html272024/2/25蘭州理工大學(xué)土木工程學(xué)院韓建平3017--1INTRODUCTIONThediscrete--coordinatesystemsdescribedinPartTwoprovideaconvenientandpracticalapproachtothedynamicresponseanalysisofarbitrarystructures.However,thesolutionsobtainedcanonlyapproximatetheiractualdynamicbehaviorbecausethemotionsarerepresentedbyalimitednumberofdisplacementcoordinates.Theprecisionoftheresultscanbemadeasrefinedasdesiredbyincreasingthenumberofdegreesoffreedomconsideredintheanalyses.Inprinciple,however,aninfinitenumberofcoordinateswouldberequiredtoconvergetotheexactresultsforanyrealstructurehavingdistributedproperties;hencethisapproachtoobtaininganexactsolutionismanifestlyimpossible.Theformalmathematicalprocedureforconsideringthebehaviorofaninfinitenumberofconnectedpointsisbymeansofdifferentialequationsinwhichthepositioncoordinatesaretakenasindependentvariables.Inasmuchastimeisalsoanindependentvariableinadynamicresponseproblem,theformulationoftheequationsofmotioninthiswayleadstopartialdifferentialequations.Differentclassesofcontinuoussystemscanbeidentifiedinaccordancewiththenumberofindependentvariablesrequiredtodescribethedistributionoftheirphysicalproperties.Forexam-ple,thewave--propagationformulasusedinseismologyandgeophysicsarederivedfromtheequationsofmotionexpressedforgeneralthree--dimensionalsolids.Simi-larly,instudyingthedynamicbehaviorofthin-plateorthin--shellstructures,specialequationsofmotionmustbederivedforthesetwo--dimensionalsystems.Inthepresentdiscussion,however,attentionwillbelimitedtoone--dimensionalstructures,thatis,beam--androd--typesystemswhichmayhavevariablemass,damping,andstiffnesspropertiesalongtheirelasticaxes.Thepartialdifferentialequationsofthesesystemsinvolveonlytwoindependentvariables:timeanddistancealongtheelasticaxisofeachcomponentmember.Itispossibletoderivetheequationsofmotionforrathercomplexone--dimensionalstructures,includingassemblagesofmanymembersinthree-dimensionalspace.Moreover,theaxesoftheindividualmembersmightbearbitrarilycurvedinthree--dimensionalspace,andthephysicalpropertiesmightvaryasacomplicatedfunctionofpositionalongtheaxis.However,thesolutionsoftheequationsofmotionforsuchcomplexsystemsgenerallycanbeobtainedonlybynumericalmeans,andinmostcasesadiscrete--coordinateformulationispreferabletoacontinuous--coordinateformulation.Forthisreason,thepresenttreatmentwillbelimitedtosimplesystemsinvolvingmembershavingstraightelasticaxesandassemblagesofsuchmembers.Informulatingtheequationsofmotion,generalvariationsofthephysicalpropertiesalongeachaxiswillbepermitted,althoughinsubsequentsolutionsoftheseequations,thepropertiesofeachmemberwillbeassumedtobeconstant.Becauseoftheseseverelimitationsofthecaseswhichmaybeconsidered,thispresentationisintendedmainlytodemonstratethegeneralconceptsofthepartial--differential--equationformulationratherthantoprovideatoolforsignificantpracticalapplicationtocomplexsystems.Closedformsolutionsthroughthisformulationcan,however,beveryusefulwhentreatingsimpleuniformsystems.Chapter17PartialDifferentialEquationsofMotion17--2BeamFlexure:ElementaryCaseFIGURE17-1Basicbeamsubjectedtodynamicloading:(a)beampropertiesandcoordinates;(b)resultantforcesactingondifferentialelement.Afterdroppingthetwosecond--ordermomenttermsinvolvingtheinertiaandappliedloadings,onegetsThisisthepartialdifferentialequationofmotionfortheelementarycaseofbeamflexure.Thesolutionofthisequationmust,ofcourse,satisfytheprescribedboundaryconditionsatx=0andx=L.17--3BeamFlexure:IncludingAxial--ForceEffectsFIGURE17-2Beamwithstaticaxialloadinganddynamiclateralloading:(a)beamdeflectedduetoloadings;(b)resultantforcesactingondifferentialelement.17--4BeamFlexure:IncludingViscousDampingIntheprecedingformulationsofthepartialdifferentialequationsofmotionforbeam--typemembers,nodampingwasincluded.Nowdistributedviscousdampingoftwotypeswillbeincluded:(1)anexternaldampingforceperunitlengthasrepresentedbyc(x)inFig.8--3and(2)internalresistanceopposingthestrainvelocityasrepresentedbythesecondpartsofEqs.(8--8)and(8--9).17--6AXIALDEFORMATIONS:UNDAMPEDTheprecedingdiscussionsinSections17--2through17--5havebeenconcernedwithbeamflexure,inwhichcasethedynamicdisplacementsareinthedirectiontransversetotheelasticaxis.Whilethisbendingmechanismisthemostcommontypeofbehaviorencounteredinthedynamicanalysisofone--dimensionalmembers,someimportantcasesinvolveonlyaxialdisplacements,e.g.,apilesubjectedtohammerblowsduringthedrivingprocess.Theequationsofmotiongoverningsuchbehaviorcanbederivedbyaproceduresimilartothatusedindevelopingtheequationsofmotionforflexure.However,derivationissimplerfortheaxial--deformationcase,sinceequilibriumneedbeconsideredonlyinonedirectionratherthantwo.Inthisformulation,dampingisneglectedbecauseitusuallyhaslittleeffectonthebehaviorinaxialdeformation.FIGURE17-4Barsubjectedtodynamicaxialdeformations:(a)barpropertiesandcoordinates;(b)forcesactingondifferentialelement.Chapter18Analysisofundampedfreevibration18-1BEAMFLEXURE:ELEMENTARYCASEFollowingthesamegeneralapproachemployedwithdiscrete-parametersys-tems,thefirststepinthedynamic--responseanalysisofadistributed--parametersystemistoevaluateitsundampedmodeshapesandfrequencies.Becauseofthemathematicalcomplicationsoftreatingsystemshavingvariableproperties,thefollowingdiscussionwillbelimitedtobeamshavinguniformpropertiesalongtheirlengthsandtoframesassembledfromsuchmembers.Thisisnotaseriouslimitation,however,becauseitismoreefficienttotreatanyvariable--propertysystemsusingdiscrete-parametermodeling.（17-7）（18-1）（18-2）（18-3）First,letusconsidertheelementarycasepresentedinSection17--2withandsetequaltoconstantsand,respectively.AsshownbyEq.(17--7),thefree--vibrationequationofmotionforthissystemisExampleE18-1.SimpleBeamConsideringtheuniformsimplebeamshowninFig.E18-1a,itsfourknownboundaryconditionsareFIGUREE18-1Simplebeam-vibrationanalysis:(a)basicpropertiesofsimplebeam;(b)firstthreevibrationmodes.第五章無(wú)限自由度體系的振動(dòng)分析5.1運(yùn)動(dòng)方程的建立一.彎曲振動(dòng)方程微段平衡方程撓曲微分方程消去內(nèi)力,得加慣性力,得運(yùn)動(dòng)方程二.考慮軸力對(duì)彎曲的影響時(shí)的彎曲振動(dòng)方程三.考慮剪切變形與慣性力矩對(duì)彎曲的影響時(shí)的彎曲振動(dòng)方程1.考慮剪切變形時(shí)的幾何方程桿軸轉(zhuǎn)角截面轉(zhuǎn)角2.慣性力矩的計(jì)算單位長(zhǎng)度上的慣性力矩3.運(yùn)動(dòng)方程4.物理方程5.方程整理幾何方程：物理方程：運(yùn)動(dòng)方程：對(duì)于等截面桿：對(duì)于等截面細(xì)長(zhǎng)桿：四.考慮阻尼影響時(shí)的彎曲振動(dòng)方程外阻尼力內(nèi)阻尼力1.粘滯阻尼

2.滯變阻尼不計(jì)阻尼時(shí)計(jì)阻尼時(shí)習(xí)題：1.求剪切桿的運(yùn)動(dòng)方程。

2.求拉壓桿的運(yùn)動(dòng)方程。一.運(yùn)動(dòng)方程及其解邊界條件xyxyxy幾何邊界條件力邊界條件混合邊界條件初始條件已知函數(shù)5.2自由振動(dòng)分析設(shè)方程的特解為代入方程，得方程(1)的通解為運(yùn)動(dòng)方程的特解為運(yùn)動(dòng)方程的通解由特解的線性組合確定設(shè)方程(2)的特解為代入方程(2)，得方程(2)的通解為或二.振型與頻率振型方程xy頻率方程振型18--4BEAMFLEXURE:ORTHOGONALITYOFVIBRATIONMODESHAPESThevibrationmodeshapesderivedforbeamswithdistributedpropertieshaveorthogonalityrelationshipsequivalenttothosedefinedpreviouslyforthediscrete-parametersystems,whichcanbedemonstratedinessentiallythesame—byapplicationofBetti'slaw.ConsiderthebeamshowninFig.18--1.Forthisdiscussion,thebeammayhavearbitrarilyvaryingstiffnessandmassalongitslength,anditcouldhavearbitrarysupportconditions,althoughonlysimplesupportsareshown.Twodifferentvibrationmodes,mandn,areshownforthebeam.Ineachmode,thedisplacedshapeandtheinertialforcesproducingthedisplacementsareindicated.Betti'slawappliedtothesetwodeflectionpatternsmeansthattheworkdonebytheinertialforcesofmodenactingonthedeflectionofmodemisequaltotheworkoftheforcesofmodemactingonthedisplacementofmoden;thatis,（18-31）（18-34）Thefirsttwotermsinthisequationrepresenttheworkdonebytheboundaryverticalsectionforcesofmodenactingontheenddisplacementsofmodemandtheworkdonebytheendmomentsofmodenonthecorrespondingrotationsofmodem.Forthestandardclamped--,hinged--,orfree--endconditions,thesetermswillvanish.However,theycontributetotheorthogonalityrelationshipifthebeamhaselasticsupportsorifithasalumpedmassatitsend;thereforetheymustberetainedintheexpressionwhenconsideringsuchcases.（18-35）（18-40）三.振型的正交性振型可看作是慣性力幅值作為靜荷載所引起的靜力位移曲線。由虛功互等定理振型對(duì)質(zhì)量的正交性表達(dá)式物理意義為i振型上的慣性力在j振型上作的虛功為零。由變形體虛功定理振型對(duì)剛度的正交性表達(dá)式當(dāng)體系中有質(zhì)量塊、彈簧等時(shí)的情況Clough:振型對(duì)剛度的正交性表達(dá)式5.3受迫振動(dòng)一.振型分解法設(shè)方程的解為運(yùn)動(dòng)方程為代入方程,得設(shè)注意到方程兩端乘以并積分----振型j的廣義質(zhì)量----振型j的廣義荷載方程兩端乘以并積分----振型j的廣義質(zhì)量----振型j的廣義荷載令----j振型阻尼比內(nèi)力計(jì)算若外力是集中力或集中力偶例：試求圖示梁跨中點(diǎn)穩(wěn)態(tài)振幅。已知：解：例：試求圖示梁跨中點(diǎn)穩(wěn)態(tài)振幅。已知：解：例：試求圖示梁跨中點(diǎn)穩(wěn)態(tài)振幅。解：二.初速度、初位移引起的振動(dòng)設(shè)初位移、初速度已知，求位移反應(yīng)。設(shè)方程的解為由和確定例：桿件落到支座時(shí)的速度為v0，不反彈，不計(jì)阻尼，求位移。解：例：桿件落到支座時(shí)的速度為v0，不反彈，不計(jì)阻尼，求位移。解：練習(xí)題：振型分解法求圖示體系桿端轉(zhuǎn)角的穩(wěn)態(tài)幅值，不計(jì)阻尼。三.簡(jiǎn)諧荷載作用下的直接解法運(yùn)動(dòng)方程為設(shè)特解為若梁是等截面梁，且q(x)為常數(shù)令例：試求圖示梁跨中點(diǎn)穩(wěn)態(tài)振幅，不計(jì)阻尼。已知：解：例：試求圖示梁跨中點(diǎn)穩(wěn)態(tài)振幅，不計(jì)阻尼。已知：解：例：試求圖示梁跨中點(diǎn)穩(wěn)態(tài)振幅，