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International Journal of Rotating Machinery
Volume 2009, Article ID 313526, 8 pages
Research Article

A Modal-Based Substructure Method Applied to Nonlinear Rotordynamic Systems

Institute of Technical Mechanics, University of Linz, Altenbergerstr. 69, 4040 Linz, Austria

Received 25 February 2009; Accepted 1 September 2009

Academic Editor: Eric Maslen

Copyright © 2009 Helmut J. Holl. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The discretisation of rotordynamic systems usually results in a high number of coordinates, so the computation of the solution of the equations of motion is very time consuming. An efficient semianalytic time-integration method combined with a substructure technique is given, which accounts for nonsymmetric matrices and local nonlinearities. The partitioning of the equation of motion into two substructures is performed. Symmetric and linear background systems are defined for each substructure. The excitation of the substructure comes from the given excitation force, the nonlinear restoring force, the induced force due to the gyroscopic and circulatory effects of the substructure under consideration and the coupling force of the substructures. The high effort for the analysis with complex numbers, which is necessary for nonsymmetric systems, is omitted. The solution is computed by means of an integral formulation. A suitable approximation for the unknown coordinates, which are involved in the coupling forces, has to be introduced and the integration results in Green's functions of the considered substructures. Modal analysis is performed for each linear and symmetric background system of the substructure. Modal reduction can be easily incorporated and the solution is calculated iteratively. The numerical behaviour of the algorithm is discussed and compared to other approximate methods of nonlinear structural dynamics for a benchmark problem and a representative example.