Complex Inner Product Averaging Method And Its Aplication To Rotor Systems

At present, there are still many special problems about nonlinear dynamics should be resolved to put ultra-supercritical steam turbine into operation. It is essential to develop the nonlinear dynamical theory in order to overcome the difficulty in the solving process of the large-scale rotor-bearing systems with parameters and huge-capacity. Therefore, an efficient approach of dimensionality reduction is desirable. In addition, the problem in establishing and developing the basic theory to analyze the dynamical behaviors of complex nonlinear systems is also a main topic in the study of nonlinear dynamics. In fact, the problem of dimension reduction for high-dimensional systems is a key issue, not only for rotor-bearing systems but also complex nonlinear dynamical systems in various engineering fields.Periodic solutions of nonlinear dynamic systems under external excitations were investigated by developing the complex inner product averaging method (CIPAM). The solving procedures of both nonresonant and resonant cases were proposed for multi-degree-of-freedom systems in detail. And the nonresonant case is distinguished from the resonant one.The rotor-bearing system is important for the large-scale steam turbine. It is necessary to analyze the dynamical characteristics of the system, especially for the nonlinear case. In the last two decades, numerical methods have been used to study the nonlinear dynamical characteristics, but it is difficult to obtain the analytical solutions of the problem. The approximate solution of the geometrically nonlinear rotor systems has been obtained using the CIPAM. And the stability of periodic motion is discussed.Due to the significant status of nonlinear oil-film force in rotor dynamics, stable solution for rotor systems with nonlinear oil-film forces is investigated. Considering the strong nonlinear patterns, oil-film force of short bearing is divided into linear and nonlinear parts employing the Taylor expansion principle. After getting the fist order resonant bifurcation equation, the singularity of bifurcation is analyzed by C-L method. And then lots of bifurcation models are obtained. The result can be used in the optimization of system parameters and fault diagnosis, and providing important theoretical guidance for nonlinear dynamical design.