Rigorous model reduction for a damped-forced nonlinear beam model: an infinite-dimensional analysis

DOI10.1007/s00332-018-9443-4zbMath1402.35279arXiv1705.06133OpenAlexW3098996774MaRDI QIDQ722016

Florian Kogelbauer, György Haller

Publication date: 20 July 2018

Published in: Journal of Nonlinear Science (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1705.06133

zbMATH Keywords

invariant manifoldsmodel reductionnonlinear vibrationsbeam equationsspectral submanifolds

Mathematics Subject Classification ID

Rods (beams, columns, shafts, arches, rings, etc.) (74K10) Nonlinear elasticity (74B20) Vibrations in dynamical problems in solid mechanics (74H45) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Normal forms, center manifold theory, bifurcation theory for infinite-dimensional dissipative dynamical systems (37L10) Inertial manifolds and other invariant attracting sets of infinite-dimensional dissipative dynamical systems (37L25) PDEs in connection with mechanics of deformable solids (35Q74)

Related Items (8)

Invariant spectral foliations with applications to model order reduction and synthesis ⋮ Validated numerical approximation of stable manifolds for parabolic partial differential equations ⋮ Capturing the edge of chaos as a spectral submanifold in pipe flows ⋮ 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 ⋮ Quasi-periodic travelling waves for beam equations with damping on 3-dimensional rectangular tori ⋮ Finite element approximation of invariant manifolds by the parameterization method

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