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Subharmonic resonance vibration system parameters of the new theory of the results of : degenerate bifurcation solution

ionofaNonlinear_9rs Co -I. . { . r. 32Il95, p. 809-t02 [9] Golubitsky, M. , 5chaeffer, D. G. , SingnlaritlesandGroa! OsinBiFCO-tionTheory, Vo1.1, Spfingef-Veflg,[link widoczny dla zalogowanych], 1985. [10] Golubitsky, M. , LangftDrd, W. F. 1ClassificationandUnfoldlagsofDegenerateHopfBifurcations,[link widoczny dla zalogowanych],,. Df,,. Eg. , 41 (3), 1981Ip375ll3Lau, S. L. , Cheung, Y. K. ,[link widoczny dla zalogowanych], Wu, S. Y. 1ariableParameterIncrementationMethodforDynamicInstabilityofLinearandNonlinearElasticSystems,,. p. Mech. , Vo1.49, 1982Ipp. 849-853SomeNewResultsabouttheSubharmonieResonanceofNonlinearparametricallyExcitedSystems. DegenerateBifurcationChertyushuZhanKaijunLang / ord. . F (TianjinUniversity,) (UniversityofGuelph, Canada) AbstrtctThesubharmoniedegenerateblfqrcatlonanditsmechaaieSbehaviottrofaclassofparametricallyexcitedsystemswithZ2-symmetryarestudiedfirsttimeinc ~ etai [byuseofLiapaoov-scl ~ midtMatho ~ andsiagularitytheory. t-terethedegeneratecKseisthatal0ineqaation (10). Thisca. ewecanmaotinengineeringvibrationsystems. TheeffectlvemethodforcalculatingcoefficientsofthebifarcationequationbyLiapuaov-Schmidtmethodisgiven. ByuseofthesingularitytheoryweprovedthattheCodimenslonofthedegeneratesystemisthree. Thedegeneratesystempresentssomeverycomplicatedandinterestingdynamicalphmena,[link widoczny dla zalogowanych], asshowninFig. 2. usually, weccrnsiderthatthereisaperiodicsolutionInnonlinearpa, rametricallyexcitedsystemaoatywhene> O. Butweprovedthatthereisaperiodicsolutionhene <d. NamerlcateatcatloashowsthattheresultoftheoreticalanalysisisaceUrateenough. keywordsInon-linearvibration, parametricvibration, degeneratebifurcation, singularitytheory, transitionvariety

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