Nonlinear Dynamic Analysis Of An Elastic Rotor System With A Slant Crack

The crack is one of the commo n reasons why the rotor system is in troub le.App lying an equiva lent line-spring mode, the nonlinear dyna mic response of theelastic sha ft and rigid disk rotor system with a s lant crack is stud ied in thisdissertation considering geometric nonlinearity.Firstly, us ing an equiva lent line-spring model to s imulate the s lant crack of therotor and applying the theory o f fracture mecha nics, the flexib ility matr ix of theline-spring model a nd the equiva le nt fle xib ility matrix o f the s lant-cracked rotor arederived. Then based on the d imens ionless Lagra nge equatio ns, the non-lineardimens ionless differentia l equations of motion for the sla nt-cracked rotor areobtained.Further more, the nonlinear dyna mic response of the rotor system with a slantcrack is discussed systematica lly. In the first part, the linear dyna mic responses of therotor syste m with two free degrees are studied by the har monic ba lance theory. Theeffects o f the a ngle, the depth a nd the positio n of the s lant-cracked rotor on thenon-linear dyna mic responses of the rotor system are stud ied detailed ly.In the secondpart, the nonlinear dyna mic responses of the rotor syste m with one free degree arestudied by the multip le-scale method. The effects of the angle, the depth of the sla ntcrack, the damp ing of the rotor and the load on the non-linear dyna mic responses ofthe rotor system are studied detailedly.Third ly, the bifurcation a nd chaos of the rotor syste m with a s lant crack arediscussed cons idering the geo metric nonlinearity and the angle of the s lant crack. Thevibratio n bifurcation cur ves of the rotor system with a slant crack in the vertica l planeare shown under different damp ing parameters and rotationa l speed. The chaosphenome non is disc ussed by one set of the da mping parameter and the rotationa lspeed, by whic h the bifurcation and chaos of the rotor system with a s lant crack areinvestigated.Fina lly, the ana lysis o f the frequenc y reponse in the rotor system with a s lantcrack is perfor med by the finite ele ment method with some finite ele me nt softwares.Then the effects of the angle, the depth of the sla nt crack on the frequenc y reponseanalys is are discussed. The solutions are compared with the theory so lutio ns to checkthe validity.