One important issue for the simulation of flexible multibody systems is the quality controlled reduction in the flexible bodies degrees of freedom. In this work, the procedure is based on knowledge about the error induced by model reduction. For modal reduction, no error bound is available. For Gramian matrix based reduction methods, analytical error bounds can be developed. However, due to numerical reasons, the dominant eigenvectors of the Gramian matrix have to be approximated. Within this paper, two different methods are presented for this purpose. For moment matching methods, the development of a priori error bounds is still an active field of research. In this paper, an error estimator based on a new second order adaptive global Arnoldi algorithm is introduced and further assists the user in the reduction process. We evaluate and compare those methods by reducing the flexible degrees of freedom of a rack used for active vibration damping of a scanning tunneling microscope.
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e-mail: fehr@itm.uni-stuttgart.de
e-mail: eberhard@itm.uni-stuttgart.de
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July 2010
Research Papers
Error-Controlled Model Reduction in Flexible Multibody Dynamics
Jörg Fehr,
Jörg Fehr
Institute of Engineering and Computational Mechanics,
e-mail: fehr@itm.uni-stuttgart.de
University of Stuttgart
, Pfaffenwaldring 9, 70569 Stuttgart, Germany
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Peter Eberhard
Peter Eberhard
Institute of Engineering and Computational Mechanics,
e-mail: eberhard@itm.uni-stuttgart.de
University of Stuttgart
, Pfaffenwaldring 9, 70569 Stuttgart, Germany
Search for other works by this author on:
Jörg Fehr
Institute of Engineering and Computational Mechanics,
University of Stuttgart
, Pfaffenwaldring 9, 70569 Stuttgart, Germanye-mail: fehr@itm.uni-stuttgart.de
Peter Eberhard
Institute of Engineering and Computational Mechanics,
University of Stuttgart
, Pfaffenwaldring 9, 70569 Stuttgart, Germanye-mail: eberhard@itm.uni-stuttgart.de
J. Comput. Nonlinear Dynam. Jul 2010, 5(3): 031005 (8 pages)
Published Online: May 14, 2010
Article history
Received:
January 15, 2009
Revised:
May 12, 2009
Online:
May 14, 2010
Published:
May 14, 2010
Citation
Fehr, J., and Eberhard, P. (May 14, 2010). "Error-Controlled Model Reduction in Flexible Multibody Dynamics." ASME. J. Comput. Nonlinear Dynam. July 2010; 5(3): 031005. https://doi.org/10.1115/1.4001372
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