Numerical Solution of High-Dimensional Nonlinear Rotor-Bearing Dynamic System with Precise Integration

Guangtian Shi*
School of Mechatronic Engineering, Lanzhou Jiaotong University, Lanzhou 730070, P.R. China

© 2014 Guangtian Shi

open-access license: This is an open access article distributed under the terms of the Creative Commons Attribution 4.0 International Public License (CC-BY 4.0), a copy of which is available at: ( This license permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

* Address correspondence to this author at the School of Mechatronic Engineering, Lanzhou Jiaotong University, Lanzhou 730070, P.R. China; Tel:+86-931-4938013; Fax:+86-931-4938023; E-mail:


Through an example of rotor system which has multi-degree of freedom mounted on the nonlinear fluid film bearings, this paper analyzes the precise integration algorithm, a new numerical solution for high–dimensional nonlinear dynamics system. The precise integration method has advantages of long step, high precision and absolute stability for solving nonlinear dynamics equations. To make good use of the method, firstly, the precise integral iterative formula is given and then the mechanism of controlling high precision and efficiency is discussed. The evolution of precise integration method is an algorithm with explicit, simple form, self-start, and fast to solve nonlinear dynamics equations. High power of athwart of Hamiltonian matrix is not needed, so it is convenient in this case. The stability of period response of nonlinear rotor-bearing system is analyzed by employing the precise integration method. The bifurcation rules of the period response of the elastic rotor system with multi-degree of freedom are obtained and the chaos of the system is determined according to the fractal dimension of Poincare mapping of phase space at a certain speed.

Keywords: Chaos, High dimensional nonlinear system, Precise integration, Rotor-bearing system, Stability.