166 citations · 729 across the 17 of their papers we have counts for
18 papers
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…
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…
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 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…
Model reduction for constrained mechanical systems via spectral submanifolds
Mingwu Li, Shobhit Jain, George Haller
Dynamical systems are often subject to algebraic constraints in conjunction to their governing ordinary differential equations. In particular, multibody systems are commonly subjec…
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…
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…
Model Order Reduction for Temperature-Dependent Nonlinear Mechanical Systems: A Multiple Scales Approach
Shobhit Jain, Paolo Tiso
The thermal dynamics in thermo-mechanical systems exhibits a much slower time scale compared to the structural dynamics. In this work, we use the method of multiple scales to reduc…
Fast Computation of Steady-State Response for Nonlinear Vibrations of High-Degree-of-Freedom Systems
Shobhit Jain, Thomas Breunung, George Haller
We discuss an integral equation approach that enables fast computation of the response of nonlinear multi-degree-of-freedom mechanical systems under periodic and quasi-periodic ext…
Hyper-reduction over nonlinear manifolds for large nonlinear mechanical systems
Shobhit Jain, Paolo Tiso
Common trends in model order reduction of large nonlinear finite-element-discretized systems involve the introduction of a linear mapping into a reduced set of unknowns, followed b…
Exact Nonlinear Model Reduction for a von Karman beam: Slow-Fast Decomposition and Spectral Submanifolds
Shobhit Jain, Paolo Tiso, George Haller
We apply two recently formulated mathematical techniques, Slow-Fast Decomposition (SFD) and Spectral Submanifold (SSM) reduction, to a von Karman beam with geometric nonlinearities…
Generalization of Quadratic Manifolds for Reduced Order Modeling of Nonlinear Structural Dynamics
J. B. Rutzmoser, D. J. Rixen, P. Tiso +1
In this paper, a generalization of a quadratic manifold approach for the reduction of geometrically nonlinear structural dynamics problems is presented. This generalization is cons…
A Quadratic Manifold for Model Order Reduction of Nonlinear Structural Dynamics
Shobhit Jain, Paolo Tiso, Daniel J. Rixen +1
This paper describes the use of a quadratic manifold for the model order reduction of structural dynamics problems featuring geometric nonlinearities. The manifold is tangent to a…