MechE Colloquium: Exact Model Reduction and Forced Response in High-Degree-of-Freedom Nonlinear Mechanical Systems
Event details
| Date | 22.10.2019 |
| Hour | 12:15 › 13:15 |
| Speaker | Prof. George Haller, Chair in Nonlinear Dynamics, Institute for Mechanical Systems, ETH Zürich |
| Location | |
| Category | Conferences - Seminars |
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. As a consequence, 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, which 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.
Bio:
George Haller received his Ph.D. in Applied Mechanics at the California Institute of Technology in 1993. He then spent a year as postdoc at the Courant Institute of Mathematical Sciences at New York University, prior to joining the Division of Applied Mathematics at Brown University as Assistant Professor in 1994. In 2001, he left Brown University as Associate Professor to join the Department of Mechanical Engineering at the Massachusetts Institute of Technology, where he became Professor in 2005. While still a professor at MIT, he became the first director of Morgan Stanley's Mathematical Modeling Center in Budapest, which he headed for three years. He then joined the Department of Mechanical Engineering at McGill University in 2009, serving as Department Chair till 2011. Over the period 2014-2018, he headed the Institute for Mechanical Systems at ETH Zurich, where he currently holds the Chair in Nonlinear Dynamics.
Professor Haller has served on the editorial boards of the SIAM Journal for Mathematical Analysis, the Journal of Discrete and Continuous Dynamical Systems and the Zeitschrift für Angewandte Mathematik und Physik (ZAMP). He is currently Senior Editor at the Journal of Nonlinear Science and Associate Editor at the Journal of Applied Mechanics. His honors include a Manning Assistant Professorship at Brown University, an Alfred P. Sloan Research Fellowship in mathematics, an Albert Szent-Gyorgyi Fellowship, an ASME Thomas J.R. Hughes Young Investigator Award, an Honorary Doctorate from the Budapest University of Technology and Economics and a Faculty of Engineering Distinguished Professorship at McGill University. He is an elected external member of the Hungarian Academy of Sciences since 2019.
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. As a consequence, 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, which 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.
Bio:
George Haller received his Ph.D. in Applied Mechanics at the California Institute of Technology in 1993. He then spent a year as postdoc at the Courant Institute of Mathematical Sciences at New York University, prior to joining the Division of Applied Mathematics at Brown University as Assistant Professor in 1994. In 2001, he left Brown University as Associate Professor to join the Department of Mechanical Engineering at the Massachusetts Institute of Technology, where he became Professor in 2005. While still a professor at MIT, he became the first director of Morgan Stanley's Mathematical Modeling Center in Budapest, which he headed for three years. He then joined the Department of Mechanical Engineering at McGill University in 2009, serving as Department Chair till 2011. Over the period 2014-2018, he headed the Institute for Mechanical Systems at ETH Zurich, where he currently holds the Chair in Nonlinear Dynamics.
Professor Haller has served on the editorial boards of the SIAM Journal for Mathematical Analysis, the Journal of Discrete and Continuous Dynamical Systems and the Zeitschrift für Angewandte Mathematik und Physik (ZAMP). He is currently Senior Editor at the Journal of Nonlinear Science and Associate Editor at the Journal of Applied Mechanics. His honors include a Manning Assistant Professorship at Brown University, an Alfred P. Sloan Research Fellowship in mathematics, an Albert Szent-Gyorgyi Fellowship, an ASME Thomas J.R. Hughes Young Investigator Award, an Honorary Doctorate from the Budapest University of Technology and Economics and a Faculty of Engineering Distinguished Professorship at McGill University. He is an elected external member of the Hungarian Academy of Sciences since 2019.
Practical information
- General public
- Free