Nonlinear dynamic behaviors of a rotor dynamical system with finite hydrodynamic bearing supports were investigated. In order to increase the numerical accuracy and decrease computing costs, the isoparametric finite element method based on variational constraint approach is introduced because analytical bearing forces are not available. This method calculates the oil film forces and their Jacobians simultaneously while it can ensure that they have compatible accuracy. Nonlinear motion of the bearing-rotor system is caused by strong nonlinearity of oil film forces with respect to the displacements and velocities of the center of the rotor. A method consisting of a predictor-corrector mechanism and Newton-Raphson method is presented to calculate equilibrium position and critical speed corresponding to Hopf bifurcation point of the bearing-rotor system. Meanwhile the dynamic coefficients of bearing are obtained. The nonlinear unbalance periodic responses of the system are obtained by using Poincaré-Newton-Floquet method and a combination of predic- tor-corrector mechanism and Poincaré-Newton-Floquet method. The local stability and bifuration behaviors of periodic motions are analyzed by the Floquet theory. Chaotic motion of long term dynamic behaviors of the system is analyzed with power spectrum. The numerical results reveal such complex nonlinear behaviors as periodic, quasi-periodic, chaotic, jumped and coexistent solutions.
The nonlinear dynamic behaviors of flexible rotor system with hydrodynamicbearing supports are analyzed. The shaft is modeled by using the finite element method that takesthe effect of inertia and shear into consideration. According to the nonlinearity of thehydrodynamic journal bearing-flexible rotor system, a modified modal synthesis technique withfree-interface is represented to reduce degrees-of-freedom of model of the flexible rotor system.According to physical character of oil film, variational constrain approach is introduced tocontinuously revise the variational form of Reynolds equation at every step of dynamic integrationand iteration. Fluid lubrication problem with Reynolds boundary is solved by the isoparametricfinite element method without the increasing of computing efforts. Nonlinear oil film forces andtheir Jacobians are simultaneously calculated and their compatible accuracy is obtained. Theperiodic motions are obtained by using the Poincare -Newton-Floquet (PNF) method. A method,combining the predictor-corrector mechanism to the PNF method, is presented to calculate thebifurcation point of periodic motions to be subject to change of system parameters. The localstability and bifurcation behaviors of periodic motions are obtained by Floquet theory. The chaoticmotions of the bearing-rotor system are investigated by power spectrum. The numerical examples showthat the scheme of this study saves computing efforts but also is of good precision.