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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…
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…
Data-Assisted Non-Intrusive Model Reduction for Forced Nonlinear Finite Elements Models
Mattia Cenedese, Jacopo Marconi, George Haller +1
Spectral submanifolds (SSMs) have emerged as accurate and predictive model reduction tools for dynamical systems defined either by equations or data sets. While finite-elements (FE…
Fast computation and characterization of forced response surfaces via spectral submanifolds and parameter continuation
Mingwu Li, Shobhit Jain, George Haller
For mechanical systems subject to periodic excitation, forced response curves (FRCs) depict the relationship between the amplitude of the periodic response and the forcing frequenc…
Nonautonomous Spectral Submanifolds for Model Reduction of Nonlinear Mechanical Systems under Parametric Resonance
Thomas Thurnher, George Haller, Shobhit Jain
We use the recent theory of Spectral Submanifolds (SSM) for model reduction of nonlinear mechanical systems subject to parametric excitations. Specifically, we develop expressions…
Using Spectral Submanifolds for Optimal Mode Selection in Model Reduction
Gergely Buza, Shobhit Jain, George Haller
Model reduction of large nonlinear systems often involves the projection of the governing equations onto linear subspaces spanned by carefully-selected modes. The criteria to selec…