高維非線性系統(tǒng)全局分岔與混沌若干問(wèn)題的研究.pdf

1、南京航空航天大學(xué)博士學(xué)位論文高維非線性系統(tǒng)全局分岔與混沌若干問(wèn)題的研究姓名：俞衛(wèi)琴申請(qǐng)學(xué)位級(jí)別：博士專業(yè)：一般力學(xué)與力學(xué)基礎(chǔ)指導(dǎo)教師：陳芳啟201004高維非線性系統(tǒng)全局分岔與混沌若干問(wèn)題的研究IIABSTRACTTherearevariousnonlinearfactsintherealengineeringsystems.Thecertaintyfthesolutionsoflinearsystemsisnotsatisfiedft

2、hatofnonlinearsystemssotherearemecomplexitiesinnonlinearsystems.Thestudyofbifurcationschaosofnonlinearsystemsarecuttingedgetopics.Theinvestigationsofmodebifurcationsinteractionsplayanimptantpartinthisarea.Thepresentdisse

3、rtationisdevotedtotheglobalbifurcationschaosofsomenonlinearfourdimensionalmechanicalsystems.Thepaperismainlydividedintosixchapters.Inthefirsttersomeimptantconceptspropertiesmethodstheiesofbifurcationchaosareintroducedwhi

4、charequotedherefearlierreferencesuntiltheyareappliedinlaterchapters.Inthesecondtertheglobalbifurcationsinmodeinteractionsofasimplysupptedrectangularmetallicplatesubjectedtoatransverseharmonicexcitationareinvestigatedwith

5、thecaseofthe1:1internalresonance.Firstlyfthe“nonresonant”caseMelnikovmethodhasbeenusedtostudythechaoticbehavis.Secondlyfthe“resonant”casetheKovacicWigginsglobalperturbationmethodenergyphasemethodareutilizedtoanalyzethegl

6、obalbifurcationsftherectangularmetallicplate.TheexistenceofSilnikovtypesinglepulsemultipulsehomoclinicbitsisobtainedwhichimplythatchaoticmotionsmayoccurfthisclassofrectangularmetallicplates.Thisisquitedifferentfromtheear

7、liercasebasedonMelnikovmethod.Finallynumericalresultsarepresentedsomenewdynamicalphenomenaareobtained.Inthethirdchaptertheglobalbifurcationschaoticdynamicsofanaxiallymovingviscoelasticbeamareinvestigatedwiththecaseof1:2i

8、nternalresonance.Onthebasisofthemodulationequationsderivedbythemethodofmultiplescalesthetheyofnmalfmisutilizedtofindtheexplicitfmulasofnmalfmassociatedwithadoublezeroeigenvaluesapairofpureimaginaryeigenvalues.TheKovacicW

9、igginsperturbationmethodenergyphasemethodareemployedtoanalyzetheglobalbifurcationsftheaxiallymovingviscoelasticbeam.TheresultsobtainedhereindicatethatthereexisttheSilnikovtypesinglepulsemultipulsebitshomoclinictocertaini

10、nvariantsetsfthe“resonant”caseleadingtochaosinthesystem.Theresultsgivetheexplanationfthejumpingbehavisobservedinthisclassofaxiallymovingviscoelasticbeams.Inthefourthchaptertheexistenceofhomoclinicbitsheteroclinicbitsfash