The Dynamical Response Analysis Of The Nonlinear Rotor Systems

An approximate analytical approach using the idea of Newton iteration method is presented for seeking the approximate analytical solutions of the nonlinear dynamical equations. By this means, the iteration operator L which may have an undetermined parameter can be either linear or nonlinear. Furthermore, it has a unique technique which can be called as filtering function. This technique has also unified, simplified and developed the variational iteration method, the homotopy perturbation method, the parameterized perturbation method and the linear perturbation method. Using some nonlinear dynamical equations as examples, a convictive result has been achieved. Synchronously, a nonlinear model of the rotor system with pedestal looseness has been proosed and the dynamical response has been achieved by the generalized modified Newton iteration method.The energy adjust numerical algorithm for the nonlinear dynamic equation with multi-degree of freedom has been proposed. Firstly, by the Taylor's expanded formula and Duhamel's integration, an integral iteration formula which has an undetermined parameter has been achieved. Secondly, through some mathematic approach, the original dynamical equation has been converted to an energy adjusting equation which can determine the undetermined parameter. Finally, substituting the parameter into the integral iteration formula, an accurate numerical value has been achieved. All examples show that the method can eliminate the algorithm damping and has better stability than the Runge-Kutta method under bigger integral step.Rotors mounted on fluid film bearings of turbines carry one or more disks. The total number of unknowns to be determined for their computational model may range up to several hundreds. The author focuses on numerical analyzing for nonlinear dynamics system with multi-d.o.f. Firstly, two numerical methods to solve nonlinear dynamic response have been proposed and have been successfully used in the analysis of an example with 112 d.o.f, of 200 MW rotor subjected on unsteady and nonlinear oil-film force in which the disk unbalanceand gravity effects have been taken into account. Secondly, in order to examine the efficiency and reliability of the methods, the examples have also been used to study the nonlinear dynamical phenomena, such as periodic doubling, quasi-periodic, and chaotic motion etc. The computational results have shown that the numerical stability of the method plays a very significant role. Finally, a method which can eliminate the ill-condition and singularity of the stiff matrix through an equivalence transformation has been proposed. By changing the original dynamic system to general nonlinear system by Hamilton's criterion, a very satisfied numerical solution has been achieved. It must be pointed out that Runge-Kutta method is out of control for the 200 MW rotor systems. All numerical result could be a reference for the design of the high speed rotor system with a flexible bearing.The bifurcation and chaos behavior of the nonlinear rotor systems with multi-degree-of-freedom which have both nonlinear oil-film force and impact-rubbi force has been calculated. Firstly, the variation range of the clearance and rotating speed according to the bifurcation and chaos motion has been achieved. Secondly, the damping effect has been proved by using the constitutive relations and temperature effecting. Thirdly, the influence to the dynamical behavior of the systems has been obtained through the energy dissipation character of the SMA. Finally, a strategy of controlling the dynamical behavior of the rotor systems by the damping effect of the shape memory alloy's intelligence curve has been proposed.