The predictor-corrector Galerkin method (PCGM) is employed to obtain a lower order system for a two-span rotor-bearing system. First of all, a 32-DOF nonlinear dynamic model is established for the system. Then, the predictor-corrector algorithm based on the Galerkin method is employed to deal with the problem of order reduction for such a complicated system. The first six modes are chosen to be the master subsystem and the following six modes are taken to be the slave subsystem. Finally, the dynamical responses are numerically worked out for the master and slave subsystems using the PCGM, and the results obtained are used to compare with those obtained by using the SGM. It is shown that the PCGM provides a considerable increase in accuracy for a little computational cost in comparison with the SGM in which the first six modes are reserved.
Order Reduction Jump Phenomenon Component Mode Synthesis Order Reduction Method Reduce Order System
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, log in to check access.
This research was supported by National Natural Science Foundation of China (10772056, 10632040) and the Natural Science Foundation of Hei-Long-Jiang Province, China (ZJG0704).
Ding J, Krodkiewski JM (1993) Inclusion of static indetermination in the mathematical model for non-linear dynamic analyses of multi-bearing rotor systems. J Sound Vib 164(2):267–280MATHCrossRefGoogle Scholar
Krodkiewski JM, Ding J, Zhang N (1994) Identification of unbalance change using a non-linear mathematical model for multi-bearing rotor systems. J Sound Vib 169(5):685–698CrossRefGoogle Scholar
Ding J (1997) Computation of multi-plane imbalance for a multi-bearing rotor system. J Sound Vib 205(3):364–371CrossRefGoogle Scholar
Hu W, Miah H, Feng NS, et al (2000) A rig for testing lateral misalignment effects in a flexible rotor supported on three or more hydrodynamic journal bearings. Tribol Int 33:197–204CrossRefGoogle Scholar
Ding Q, Leung AYT (2005) Numerical and experimental investigations on flexible multi-bearing rotor dynamics. J Vib Acoust 127:408–415CrossRefGoogle Scholar
Garcia-Archilla B, Novo J, Titi ES (1998) Postprocessing the Galerkin method: a novel approach, to approximate inertial manifolds. SIAM J Numer Anal 35:941–972MathSciNetMATHCrossRefGoogle Scholar
Sansour C, Wriggers P, Sansour J (2003) A finite element post-processed Galerkin method for dimensional reduction in the non-linear dynamics of solids: applications to shells. Comput Mech 32:104–114MATHCrossRefGoogle Scholar
Garcia-Archilla B, Novo J, Titi ES (1999) An approximate inertial manifolds approach to postprocessing the Galerkin method for the Navier–Stokes equations. Math Comput 68:893–911MathSciNetMATHCrossRefGoogle Scholar