Modeling of a Fluid-structure coupled system using port-Hamiltonian formulation
Authors
Flávio Luiz Cardoso-Ribeiro, Denis Matignon, Valérie Pommier-Budinger
Abstract
The interactions between fluid and structural dynamics are an important subject of study in several engineering applications. In airplanes, for example, these coupled vibrations can lead to structural fatigue, noise and even instability. At ISAE, we have an experimental device that consists of a cantilevered plate with a fluid tank near the free tip. This device is being used for model validation and active control studies. This work uses the port-Hamiltonian systems formulation for modeling this experimental device. Structural dynamics and fluid dynamics are independently modeled as infinite-dimensional systems. The plate is approximated as a beam. Shallow water equations are used for representing the fluid in the moving tank. The global system is coupled and spatial discretization of the infinite-dimensional systems using mixed finite-element method allows to obtain a finite-dimensional system that is still Hamiltonian.
Keywords
Port-Hamiltonian systems; fluid-structure interactions; mixed finite-element method
Citation
- Journal: IFAC-PapersOnLine
- Year: 2015
- Volume: 48
- Issue: 13
- Pages: 217–222
- Publisher: Elsevier BV
- DOI: 10.1016/j.ifacol.2015.10.242
- Note: 5th IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control LHMNC 2015- Lyon, France, 4–7 July 2015
BibTeX
@article{Cardoso_Ribeiro_2015,
title={{Modeling of a Fluid-structure coupled system using port-Hamiltonian formulation}},
volume={48},
ISSN={2405-8963},
DOI={10.1016/j.ifacol.2015.10.242},
number={13},
journal={IFAC-PapersOnLine},
publisher={Elsevier BV},
author={Cardoso-Ribeiro, Flávio Luiz and Matignon, Denis and Pommier-Budinger, Valérie},
year={2015},
pages={217--222}
}
References
- Bassi, An Algorithm to Discretize One-Dimensional Distributed Port Hamiltonian Systems. (2007)
- Cardoso-Ribeiro, Modeling of a coupled fluid-structure system excited by piezoelectric actuators. (2014)
- Duindam, (2009)
- Golo, Hamiltonian discretization of boundary control systems.. Auto-matica (2004)
- Hamroun, Approche hamiltonienne à ports pour la modélisation, la réduction et la commande des systémes non linéaires à paramétres distribués: application aux écoulements.. (2009)
- Hamroun, B., Dimofte, A., Lefèvre, L. & Mendes, E. Control by Interconnection and Energy-Shaping Methods of Port Hamiltonian Models. Application to the Shallow Water Equations. European Journal of Control vol. 16 545–563 (2010) – 10.3166/ejc.16.545-563
- Hodges, (2011)
- Jacob, (2012)
- Kunkel, P. & Mehrmann, V. Differential-Algebraic Equations. EMS Textbooks in Mathematics (2006) doi:10.4171/017 – 10.4171/017
- Matignon, D. & Hélie, T. A class of damping models preserving eigenspaces for linear conservative port-Hamiltonian systems. European Journal of Control vol. 19 486–494 (2013) – 10.1016/j.ejcon.2013.10.003
- Morris, Strong stabilization of piezoelectric beams with magnetic effects. (2013)
- Moulla, R., Lefévre, L. & Maschke, B. Pseudo-spectral methods for the spatial symplectic reduction of open systems of conservation laws. Journal of Computational Physics vol. 231 1272–1292 (2012) – 10.1016/j.jcp.2011.10.008
- Petit, N. & Rouchon, P. Dynamics and solutions to some control problems for water-tank systems. IEEE Transactions on Automatic Control vol. 47 594–609 (2002) – 10.1109/9.995037
- Van Der Schaft, A. J. & Maschke, B. M. On the Hamiltonian formulation of nonholonomic mechanical systems. Reports on Mathematical Physics vol. 34 225–233 (1994) – 10.1016/0034-4877(94)90038-8
- Voß, T. & Scherpen, J. M. A. Port-Hamiltonian Modeling of a Nonlinear Timoshenko Beam with Piezo Actuation. SIAM Journal on Control and Optimization vol. 52 493–519 (2014) – 10.1137/090774598
- Wu, Port Hamiltonian System in Descriptor Form for Balanced Reduction: Application to a Nanotweezer. (2014)