4 papers
Using Spectral Submanifolds for Nonlinear Periodic Control
Florian Mahlknecht, John Irvin Alora, Shobhit Jain +4
Very high dimensional nonlinear systems arise in many engineering problems due to semi-discretization of the governing partial differential equations, e.g. through finite element m…
How to Compute Invariant Manifolds and their Reduced Dynamics in High-Dimensional Finite-Element Models
Shobhit Jain, George Haller
Invariant manifolds are important constructs for the quantitative and qualitative understanding of nonlinear phenomena in dynamical systems. In nonlinear damped mechanical systems,…
Integral Equations & Model Reduction For Fast Computation of Nonlinear Periodic Response
Gergely Buza, George Haller, Shobhit Jain
We propose a reformulation for the integral equations approach of Jain, Breunung \& Haller [Nonlinear Dyn. 97, 313--341 (2019)] to steady-state response computation for periodicall…
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…