Exact Model Reduction and Forced Response in High-Degree-of-Freedom Nonlinear Mechanical Systems: E201 Ocean Engineering Seminar Series, Spring 2019
Seminar | April 19 | 2:30-4 p.m. | 3110 Etcheverry Hall
Professor George Haller, Professor of Nonlinear Dynamics at ETH Zurich
Abstract: Despite major advances in computational power, mapping out the forced response of large, nonlinear mechanical systems for different forcing frequencies has remained a major challenge. One reason is the small damping in most engineered systems, which leads to exceedingly slow-decaying transients in direct numerical integration. Another reason is that computing periodic response is not a naturally parallelizable procedure: involving more processors tends to increase the computation time. For this reason, forced response is typically computed after ad hoc reduction procedures are applied to the original mechanical system. In this talk, we describe a recent tool from dynamical systems, spectral submanifold theory, that enables a mathematically exact reduction of nonlinear oscillatory systems to low-dimensional invariant manifolds. With the help of this reduction, previously unimaginable computational speeds can be achieved in computing nonlinear forced response. The approach also enables the detection of detached branches (isolas) of the response curves that remain undetected by classical numerical continuation, yet are critically important for structural health monitoring. We discuss these results on various problems, including analytic, numerical and experimental construction of spectral submanifolds and forced response curves.
Biography: Professor George Haller received his Ph.D. in Applied Mechanics at the California Institute of Technology in 1993. He then spent a year as a postdoc at the Courant Institute of Mathematical Sciences at New York University, prior to joining the Division of Applied Mathematics at Brown University, in Providence, Rhode Island, as an Assistant Professor in 1994.
In 2001, Prof. Haller left Brown University as an Associate Professor to join the Department of Mechanical Engineering at the Massachusetts Institute of Technology, where he became a Professor in 2005. While still a professor at MIT, he became the first director of Morgan Stanleys Mathematical Modeling Center in Budapest, which he headed for three years till 2009. Prior to joining ETH in 2012, he worked at the Department of Mechanical Engineering at McGill University as Faculty of Engineering Distinguished Professor, serving as Department Chair till 2011.
Professor Haller is the recipient of a James Manning Assistant Professorship (1996), an Alfred P. Sloan Fellowship in Applied Mathematics (1997), an Albert Szent-Györgyi Fellowship (2003), an ASME Special Achievement award in Applied Mechanics (2005), and an Honorary Doctorate from the Budapest University of Technology and Economics (2008). He has served on the editorials boards of the SIAM Journal for Mathematical Analysis, the Journal of Nonlinear Science, the Journal of Discrete and Continuous Dynamical Systems, and the Zeitschrift für Angewandte Mathematik und Physik (ZAMP).