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math.DS2021
Nonlinear analysis of forced mechanical systems with internal resonance using spectral submanifolds, Part I: Periodic response and forced response curve
Mingwu Li, Shobhit Jain, George Haller
We show how spectral submanifold theory can be used to construct reduced-order models for harmonically excited mechanical systems with internal resonances. Efficient calculations o…
cs.CE2021
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,…