具有對(duì)稱約束兩自由度碰振系統(tǒng)的研究.pdf

1、廣西大學(xué)碩士學(xué)位論文具有對(duì)稱約束兩自由度碰振系統(tǒng)的研究姓名：譚潔燕申請(qǐng)學(xué)位級(jí)別：碩士專業(yè)：應(yīng)用數(shù)學(xué)指導(dǎo)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