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.DS2019
Explicit Third-Order Model Reduction Formulas for General Nonlinear Mechanical Systems
Zsolt Veraszto, Sten Ponsioen, George Haller
For general nonlinear mechanical systems, we derive closed-form, reduced-order models up to cubic order based on rigorous invariant manifold results. For conservative systems, the…
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…