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Cracked rotor system stability analysis and numerical bifurcation

373 Conclusion From the above simulation results the following conclusions: (1) the response for the bifurcation problem of a cracked rotor, using Newmark integration method, combined with numerical Floquet multiplier matrix, can more accurately determine the response to the occurrence and type of bifurcation . (2) Xff in the cracked rotor system,[link widoczny dla zalogowanych], a common way for the bifurcation period doubling bifurcation; Hopf points and, its performance for the sport into the quasi-periodic solutions of periodic solutions; saddle bifurcation of a node,[link widoczny dla zalogowanych], its performance for the movement from one cycle Solutions to jump to another periodic solution. (3) a node bifurcation in the saddle, there is the same response in the period jump between the track of the situation. 1234 Reference Li Xiaofeng, Xuping Yong, SHI Tie-lin. The crack with the whirl of the rotor fault feature. Applied Mathematics and Mechanics, 2002; 23 (6) :643-652 YANG Ji Dong, Xu Peimin,[link widoczny dla zalogowanych], ROTOR. Hands crack bifurcation, chaotic behavior. Solid Mechanics, 2002; 23 (1) :115-119 Ya-Peng Pu, Chen Jin, Jian Zou. Vibration of a cracked rotor with flexible supporting quasi-periodic features. Vibration Engineering, 2002; 15 (3) :359-362Jun0S, EunHJ. Modelingandvibrationanalysisofasimplerotorwithabreathingcrack. JournalofSoundandVibration, 1992; 155 (2) :273-29OAnalysisonStabilityandBifurcationofCrackedJeffcottRotorQinWeiyangRenXingminYangYongfeng (DepartmentofEngineeringMechanics, NorthwesternPolytechnicalUniversity.Xian, 710072.China) Abstract: Thestabilityandbifurcationoftheresponsesofcrackedrotorarestudied. Forthecrackinshaft. thecosineswitchfunctionisappliedtOdescribetheopeningandclosingofthecrackinrotation, andthecrossstiffnessoriginatedfromcrackisconsidered. Themotionequationsarederived. Tosolvedifferentialmotionequations, Newmark-Bmethodisapplied. AmethodofcomputingFloquetMatrixbydisturbingresponseispresented. BasedontheFloquettheory, theFloquetMultiplierwascomputedbynumericalmethodtOanalyzebifurcations. Fromsimulationresults, thejumpfromoneperiodictOanotherperiodicmotioncorrespondstOSaddle-nodebifurcation, andtheevolutionfromperiodtOquasi-periodcorrespondstOHopfbifurcation. Thereexistsperioddoublingbifurcation. Keywords: nonlinearvibration; rotor; cracks; Floquetmultiplier; bifurcation first author: Qinwei Yang, male,[link widoczny dla zalogowanych], associate professor of Health in April 1967. Phone: (029) 88492895; E-mail: weiyangq @ sina. com, mengg @ nwpu. edu. cn

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