Publications on SSM-Theory

Publications on SSM-Theory

Contents

2024

SSMTool 2.5 allows for extracting forced response surfaces.

Non-intrusive computation of SSMs

2023

SSMTool2.3, SSM theory is applied in for the analysis of dynamical systems with algebraic constraints.

SSM Theory is expanded to mixed-mode manifolds and expansions are developed for so called fractional spectral submanifolds. Results are mainly presented for the data driven setting but theoretical developments are valid for the analytical approach for computing SSMs as well.

SSMTool2.4, SSMs are used for the anlysis of systems subject to parametric excitation. An automated algorithm for the computation of the non-autonomous SSMs is developed and employed to obtain stability diagrams and FRCs directly from the reduced dynamics for such systems.

2022

SSMTool2.2, Systems with internal resonances which result in invariant tori are analysed in the following publications:

2021

SSMs are used for predicting an appropriate modal basis for creating projective ROMs. The curvature of the SSMs, which is and indicator for the strength of nonlinear couplings, is advocate to make a suitable modal selection.

SSMTool 2.1, SSMs are now computed directly on physical coordinates, no modal transformation is required. This allows for the treatment of large scale dynamical systems (200k DOFs). Exact ROMs on the SSM are automatically computed and the capabilities of the toolbox are showcased with several peer reviewed examples.

2020

Improvements to the algorithmic implementation allow the treatment of larger dynamical systems with up to 10k DOFs. First exhibition of parallel computation for the FRC extraction over the desired frequency ranges.

2019

Analytic expressions for the extraction of forced response curves in 2D SSMs that allow for the direct extraction of isolated regions of forced response. Integration of these expressions with SSMTool.

2018

SSMTool: an automated toolbox for the computation of autonomous SSMs on the modal space, the extraction of backbone curves and leading order approximations to forced response curves.

SSMs are applied in combination with an initial slow-fast decomposition for the analysis of a finite element van Karman beam. An initial slow manifold is computed, further reduction to an SSM is consequently performed to obtain an exact reduced order model for the transverse dynamics of the beam.

Development of analytical expressions for the analysis of FRCs and backbone curves in forced damped systems using SSM computations in modal coordinates.

2017

SSMs are computed for the extraction of backbone curves directly from the reduced order model provided by the autonomous reduced dynamics:

Fundamentals

The foundations of SSM-Theory for autonomous and non-autonomous dynamical systems is established in

Data driven SSM Computation

SSMs can also be learned from trajectory data, rather than from analytical models. An open software toolbox for SSM computations from data is provided under SSMLearn.

The first publication which showcased how the behaviour of dynamical systems can be predicted from ROMs that are obtained from SSMs that have been learned from trajectory data is

Further publications on data-driven SSMs are