Details
| Original language | English |
|---|---|
| Pages (from-to) | 357-372 |
| Number of pages | 16 |
| Journal | Thin-walled structures |
| Volume | 140 |
| Early online date | 3 Apr 2019 |
| Publication status | Published - Jul 2019 |
Abstract
We present a framework to identify the main kinematic features that arise when considering the nonlinear dynamics of beam structures that takes advantage of the mathematical structure provided by the configuration space. This relies on: i) a finite-element formulation for geometrically exact beams; ii) a multibody formalism to deal with boundary conditions and to render complex structures; iii) a robust integration scheme; and, iv) a principal geodesic analysis to directly identify the main kinematic features. Our framework contributes to improve the understanding of the very complex nonlinear dynamics, and at the same time, provides some hints regarding the further model order reduction, but in a fully nonlinear setting. The proposed ideas are tested and their capabilities are illustrated with four examples: a swinging rod under gravity, a free oscillating clamped-free straight beam with pre-stress, a triple pendulum under gravity and a complete wind turbine.
Keywords
- Beam structures, Finite-element method, Nonlinear dynamics, Principal geodesic analysis, Robust integration
ASJC Scopus subject areas
- Engineering(all)
- Civil and Structural Engineering
- Engineering(all)
- Building and Construction
- Engineering(all)
- Mechanical Engineering
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In: Thin-walled structures, Vol. 140, 07.2019, p. 357-372.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Understanding the nonlinear dynamics of beam structures
T2 - A principal geodesic analysis approach
AU - Gebhardt, Cristian Guillermo
AU - Steinbach, Marc Christian
AU - Rolfes, Raimund
N1 - Funding information: We gratefully acknowledge the financial support of the Lower Saxony Ministry of Science and Culture (research project ventus efficiens, FKZ ZN3024 ) and of the German Federal Ministry for Economic Affairs and Energy (research project Deutsche Forschungsplattform für Windenergie, FKZ 0325936E ) that enabled this work. We gratefully acknowledge the financial support of the Lower Saxony Ministry of Science and Culture (research project ventus efficiens, FKZ ZN3024) and of the German Federal Ministry for Economic Affairs and Energy (research project Deutsche Forschungsplattform für Windenergie, FKZ 0325936E) that enabled this work. We also thank the reviewers for their valuable comments.
PY - 2019/7
Y1 - 2019/7
N2 - We present a framework to identify the main kinematic features that arise when considering the nonlinear dynamics of beam structures that takes advantage of the mathematical structure provided by the configuration space. This relies on: i) a finite-element formulation for geometrically exact beams; ii) a multibody formalism to deal with boundary conditions and to render complex structures; iii) a robust integration scheme; and, iv) a principal geodesic analysis to directly identify the main kinematic features. Our framework contributes to improve the understanding of the very complex nonlinear dynamics, and at the same time, provides some hints regarding the further model order reduction, but in a fully nonlinear setting. The proposed ideas are tested and their capabilities are illustrated with four examples: a swinging rod under gravity, a free oscillating clamped-free straight beam with pre-stress, a triple pendulum under gravity and a complete wind turbine.
AB - We present a framework to identify the main kinematic features that arise when considering the nonlinear dynamics of beam structures that takes advantage of the mathematical structure provided by the configuration space. This relies on: i) a finite-element formulation for geometrically exact beams; ii) a multibody formalism to deal with boundary conditions and to render complex structures; iii) a robust integration scheme; and, iv) a principal geodesic analysis to directly identify the main kinematic features. Our framework contributes to improve the understanding of the very complex nonlinear dynamics, and at the same time, provides some hints regarding the further model order reduction, but in a fully nonlinear setting. The proposed ideas are tested and their capabilities are illustrated with four examples: a swinging rod under gravity, a free oscillating clamped-free straight beam with pre-stress, a triple pendulum under gravity and a complete wind turbine.
KW - Beam structures
KW - Finite-element method
KW - Nonlinear dynamics
KW - Principal geodesic analysis
KW - Robust integration
UR - http://www.scopus.com/inward/record.url?scp=85063743163&partnerID=8YFLogxK
U2 - 10.1016/j.tws.2019.03.009
DO - 10.1016/j.tws.2019.03.009
M3 - Article
AN - SCOPUS:85063743163
VL - 140
SP - 357
EP - 372
JO - Thin-walled structures
JF - Thin-walled structures
SN - 0263-8231
ER -