3 papers
math.DS2019
Exact Model Reduction and Fast Forced Response Calculation in High-Dimensional Nonlinear Mechanical Systems
Sten Ponsioen, George Haller
We show how spectral submanifold (SSM) theory can be used to extract forced-response curves, including isolas, without any numerical simulation in high-degree-of-freedom, periodica…
math.DS2018
Analytic Prediction of Isolated Forced Response Curves from Spectral Submanifolds
Sten Ponsioen, Tiemo Pedergnana, George Haller
We show how spectral submanifold theory can be used to provide analytic predictions for the response of periodically forced multi-degree-of-freedom mechanical systems. These predic…
math.DS2016
Exact Model Reduction by a Slow-Fast Decomposition of Nonlinear Mechanical Systems
George Haller, Sten Ponsioen
We derive conditions under which a general nonlinear mechanical system can be exactly reduced to a lower-dimensional model that involves only the most flexible degrees of freedom.…