多裂纹结构的非线性动力分析

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1、ABSTRACTItiSwellknownthatacrackinthestructureinducesadropinitsnaturalfrequenciesandaffectsitsmodeshapes．ThispaperiSatheoreticalinvestigationofthegeometricallynon．1inearfreevibrationsofmulti—crackedstructurecontaininganopencrackunderlargevibrationamplitudesandasemi—analyt

2、icalsolutionaboutthebeamofnon-·linearvibrationsiSestablished．UsingthecombinedmodefunctionsoflinemodeltoexpressthemodefunctionsbasedontheRayleighmethod．Thefirstmodeexplicitexpressionofnon．1inearvibrationsiSestablished．Besides．bynumericalsimulationmethodvariouscracklocatio

3、nandcrackdepth．aswellasassigneddifferentfirstnon．1inearfunctioncontributionmaketheeffectonmaximumdisplacementsofthecrackstructure．Anexplicitsolutionissimpleandreadytouseforengineeringapplications．(11)TheestablishmentofacrackmodeliScombinedoflinearelasticfracturemechanics

4、．bywhichiSintroducedtherotationalflexibilitycoefjficient．TheestabIlishmentofcrackedbeamfunctionsareconsideredcrackasaflexiblehingewithoutmasswhichsatisfytheboundaryconditionsandcontinuityconditions，aswellascompatibilityconditions．Theapproachusesasemi．analyticalmodelbased

5、ontheextensionoftheRayleighmethodtonon—linearvibrationsbychoiceoftheadmissiblecrackbeamfunctions．(2)Theuseofsemi—analyticalmethodofasingle-crackedbeamwithdifferentboundarythenumericalanalysis，thesingle—crackedbeamdimensionlessnaturalfrequenciesandthecrackedbeamfunctions．

6、Usingthesolvedcrackedbeamfunctions．itiSobtainedbyanalysisofnon-lineargeometricparameters．Anexplicitsolutionofthefirstnon—linearisestablishedbyneglectingminoritemsforthesingle—crackedbeam．(3)Byanalysingtheclamped—clampedbeamwithdifferentcracklocationanddepth，itiSobtainedt

7、hedifferentchangesofnon—dimensionalnaturalfrequenciesofcrackedbeamforvarious10cationanddepthandthetrendstocrackbeamfunctions．II(4)Theuseofsemi—analyticalmethodwithtwocrackclamped—clampedbeamgeometricnon—lineardynamicanalysis．Keywordscrackbeam，geometricallynon—linear，natu

8、ralfrequency，non—linearvibrationofshape目录摘要⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯．IABSTRACT⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯II第一章绪论⋯⋯⋯⋯⋯⋯