3 papers
math.DS2026
Predicting Generalized Steady States in Aperiodically Forced Mechanical Systems
Roshan S. Kaundinya, Isabella Thiel, Bálint Kaszás +2
The existence of generalized steady states (GSSs) in nonlinear mechanical systems under moderate temporally aperiodic forcing has only been shown recently. Here we derive systemati…
math.NA2024
Data-free Non-intrusive Model Reduction for Nonlinear Finite Element Models via Spectral Submanifolds
Mingwu Li, Thomas Thurnher, Zhenwei Xu +1
The theory of spectral submanifolds (SSMs) has emerged as a powerful tool for constructing rigorous, low-dimensional reduced-order models (ROMs) of high-dimensional nonlinear mecha…
math.DS2024
Nonlinear Model Reduction to Random Spectral Submanifolds in Random Vibrations
Zhenwei Xu, Roshan S. Kaundinya, Shobhit Jain +1
Dynamical systems in engineering and physics are often subject to irregular excitations that are best modeled as random. Monte Carlo simulations are routinely performed on such ran…