Computation of a Damping Matrix for Finite Element Model Updating

The characterization of damping is important in making accurate predictions of both the true response and the frequency response of any device or structure dominated by energy dissipation. The process of modeling damping matrices and experimental verification of those is challenging because damping can not be determined via static tests as can mass and stiffness. Furthermore, damping is more difficult to determine from dynamic measurements than natural frequency. However, damping is extremely important in formulating predictive models of structures. In addition, damping matrix identification may be useful in diagnostics or health monitoring of structures. The objective of this work is to find a robust, practical procedure to identify damping matrices. All aspects of the damping identification procedure are investigated. The procedures for damping identification presented herein are based on prior knowledge of the finite element or analytical mass matrices and measured eigendata. Alternately, a procedure is based on knowledge of the mass and stiffness matrices and the eigendata. With this in mind, an exploration into model reduction and updating is needed to make the problem more complete for practical applications. Additionally, high performance computing is used as a tool to deal with large problems. High Performance Fortran is exploited for this purpose. Finally, several examples, including one experimental example are used to illustrate the use of these new damping matrix identification algorithms and to explore their robustness. iii Acknowledgments First, I would like to express my thanks and gratitude to my two advisors, Dr. Daniel Inman and Dr. Calvin Ribbens. For the last four years, Dan Inman has supplied an endless amount of moral support and encouragement. Cal Ribbens has advised me for two years, always providing rational, realistic views and thoughts. My gratitude goes out to David Keyes and Manny Salas at ICASE for believing in me, my abilities, my integrity, and my future. My summers were made complete by the generosity and friendship offered by all the ICASE employees, especially my fellow graduate students, Kevin Roe and Dave Cronk. My friendships along the way have been invaluable. For this I thank all of the MSL gang (old and new) and the new CIMSS group. I owe a special thanks to all of my office-mates along the way: Park was generous enough to provide experimental data. Joel Grasmeyer deserves many thanks for sharing with me his powerful and addicting love of life and the outdoors. My parents have been …