具有對稱約束兩自由度碰振系統(tǒng)的研究.pdf

1、廣西大學碩士學位論文具有對稱約束兩自由度碰振系統(tǒng)的研究姓名：譚潔燕申請學位級別：碩士專業(yè)：應用數(shù)學指導教師：李群宏20100501RESEARCH0NATW0一DEGREE一0F—FREEDOMVIBRO—IMPACTSYSTEMWITHSYMMETRIOALRlGIDSTOPSABSTRACTAtwodegree—offreedomimpactvibratingsystemhavingsymmetricallyrigidstopsan

2、dsubjectedtoperiodicexcitationsisinvestigatedinthisdissertationThemethodforcalculatingthespectrumofLyapunovexponentsandasymmetricalperiodicgrazingmotionwhichgrazeswitIlbothconstrainsarestudiedanalyticallyThemainrespectso

3、ftheresearchinvolve：1IntroducelocalmapsbetweendifferentstagesofmotioninthewholeimpactprocessThePoincardmapofthissystemisconstructedbyusingthelocalmapmethodandthentheformulaofJacobianmarxisobtainedWiththeGramSchmidtorthog

4、onalizationandnormalizationmethod，wepresentamethodforcalculatingthespectrumofLyapunovexponentsofthisimpactvibratingsystemThenthephaseportraitsofperiodicandchaoticattractorsforthissystemaregivenaswellasthecorrespondingcon

5、vergencediagramsofthespectrumofLyapunovexponentsthroughthenumericalsimulationsTofurtherverifythevalidityofourcomputingmethod，thebifurcationdiagramofthelargestLyapunovexponentvaryingwiththevariationofthebifurcationparamet

6、erCOisgiven2Usingthemethodofdiscontinuitybypassmapping，wederivethelocalPoincardmappingofthedoublegrazingtrajectoryintheneighborhoodofthefight—handsidegrazingpointAndthelocalPoincardmappingisexpressedasafoursectionpiecewi

7、sefunctionTobeginwithtwogroupsofparameterconditionsinwhichtheoriginalsystemundergoesdoublegrazingmotionareobtainedbynumericalsimulationFurthermore，takingtheclearanceb嬲thebifurcationparameterandfixingtheotherparameters，we

8、studythegrazingbifurcationwiththehelpofthelocalPoincardmappingobtainedbeforeTwodifferenttypesoftransitionnamelyfromperiodlmotionthroughgrazingbifurcationtoanotherperiod1motionandfromthechaoticbandthroughgrazingbifurcatio