Nonlinear model identification and spectral submanifolds for multi-degree-of-freedom mechanical vibrations

DOI10.1098/rspa.2016.0759zbMath1402.70021arXiv1610.02252OpenAlexW3105889694WikidataQ54855148 ScholiaQ54855148MaRDI QIDQ4557903

David Ehrhardt, Robert Szalai, György Haller

Publication date: 27 November 2018

Published in: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1610.02252

zbMATH Keywords

invariant manifoldsnonlinear vibrationsnonlinear normal modesmodel identification

Mathematics Subject Classification ID

Symmetries and conservation laws, reverse symmetries, invariant manifolds and their bifurcations, reduction for problems in Hamiltonian and Lagrangian mechanics (70H33)

Related Items (12)

Explicit backbone curves from spectral submanifolds of forced-damped nonlinear mechanical systems ⋮ Invariant spectral foliations with applications to model order reduction and synthesis ⋮ Validated numerical approximation of stable manifolds for parabolic partial differential equations ⋮ Reduced Order Characterization of Nonlinear Oscillations Using an Adaptive Phase-Amplitude Coordinate Framework ⋮ Data-driven reduced order models using invariant foliations, manifolds and autoencoders ⋮ How do conservative backbone curves perturb into forced responses? A Melnikov function analysis ⋮ Stability of forced–damped response in mechanical systems from a Melnikov analysis ⋮ Rigorous model reduction for a damped-forced nonlinear beam model: an infinite-dimensional analysis ⋮ Global Persistence of Lyapunov Subcenter Manifolds as Spectral Submanifolds under Dissipative Perturbations ⋮ Parameterization Method for Unstable Manifolds of Standing Waves on the Line ⋮ Analytic prediction of isolated forced response curves from spectral submanifolds ⋮ Fast computation of steady-state response for high-degree-of-freedom nonlinear systems

Uses Software

• GitHub

Cites Work

• Unnamed Item
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• The parameterization method for invariant manifolds. From rigorous results to effective computations
• Delay embeddings for forced systems. I: Deterministic forcing
• Nonlinear normal modes and spectral submanifolds: existence, uniqueness and use in model reduction
• On the Liapunov subcenter manifold
• Nonlinear System Identification
• NON-LINEAR FREE VIBRATION IDENTIFICATION VIA THE HILBERT TRANSFORM
• The use of normal forms for analysing nonlinear mechanical vibrations
• Normal Modes of Vibration for Non-Linear Continuous Systems
• The parameterization method for invariant manifolds I: Manifolds associated to non-resonant subspaces
• Nonlinear modal analysis of structural systems using multi-mode invariant manifolds

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