Journal
VIBRATION
Volume 4, Issue 1, Pages 175-204Publisher
MDPI
DOI: 10.3390/vibration4010014
Keywords
reduced-order model; direct normal form; geometric nonlinearity; modal derivatives; implicit condensation and expansion
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Funding
- China Scholarship Council [201806230253]
- Rolls-Royce plc [EP/R004951/1]
- EPSRC [EP/R004951/1]
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This contribution presents numerical comparisons of model-order reduction methods for geometrically nonlinear structures in the finite element framework. Three different methods are compared: ICE, MD, and DNF, highlighting their differences and common points. Simple analytical examples and beam cases demonstrate how these methods handle different nonlinearities and structural responses effectively.
The aim of this contribution is to present numerical comparisons of model-order reduction methods for geometrically nonlinear structures in the general framework of finite element (FE) procedures. Three different methods are compared: the implicit condensation and expansion (ICE), the quadratic manifold computed from modal derivatives (MD), and the direct normal form (DNF) procedure, the latter expressing the reduced dynamics in an invariant-based span of the phase space. The methods are first presented in order to underline their common points and differences, highlighting in particular that ICE and MD use reduction subspaces that are not invariant. A simple analytical example is then used in order to analyze how the different treatments of quadratic nonlinearities by the three methods can affect the predictions. Finally, three beam examples are used to emphasize the ability of the methods to handle curvature (on a curved beam), 1:1 internal resonance (on a clamped-clamped beam with two polarizations), and inertia nonlinearity (on a cantilever beam).
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