Power preserving model reduction of 2D vibro-acoustic system: A port Hamiltonian approach

Authors

Yongxin Wu, Boussad Hamroun, Yann Le Gorrec, Bernhard Maschke

Abstract

In this paper we consider a geometric discretization so called mixed elements finite method to 2D vibro-acoustic system modeling by the port Hamiltonian approach. By using this method, the Hamiltonian structure and passivity of the system are preserved. At last, numerical simulations is given to illustrate the effectiveness of proposed discretization scheme.

Keywords

Mixed elements finite method; Spatial discretization; Port Hamiltonian system; 2D vibro-acoustic system

Citation

• Journal: IFAC-PapersOnLine
• Year: 2015
• Volume: 48
• Issue: 13
• Pages: 206–211
• Publisher: Elsevier BV
• DOI: 10.1016/j.ifacol.2015.10.240
• Note: 5th IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control LHMNC 2015- Lyon, France, 4–7 July 2015

BibTeX

@article{Wu_2015,
  title={{Power preserving model reduction of 2D vibro-acoustic system: A port Hamiltonian approach}},
  volume={48},
  ISSN={2405-8963},
  DOI={10.1016/j.ifacol.2015.10.240},
  number={13},
  journal={IFAC-PapersOnLine},
  publisher={Elsevier BV},
  author={Wu, Yongxin and Hamroun, Boussad and Gorrec, Yann Le and Maschke, Bernhard},
  year={2015},
  pages={206--211}
}

Download the bib file

References

• David, P., Collet, M. & Cote, J.-M. Experimental implementation of acoustic impedance control by a 2D network of distributed smart cells. Smart Materials and Structures vol. 19 035028 (2010) – 10.1088/0964-1726/19/3/035028
• Duindam, (2009)
• Durand, J.-F., Soize, C. & Gagliardini, L. Structural-acoustic modeling of automotive vehicles in presence of uncertainties and experimental identification and validation. The Journal of the Acoustical Society of America vol. 124 1513–1525 (2008) – 10.1121/1.2953316
• Gardonio, P. Review of Active Techniques for Aerospace Vibro-Acoustic Control. Journal of Aircraft vol. 39 206–214 (2002) – 10.2514/2.2934
• Golo, G., Talasila, V., van der Schaft, A. & Maschke, B. Hamiltonian discretization of boundary control systems. Automatica vol. 40 757–771 (2004) – 10.1016/j.automatica.2003.12.017
• 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
• Seslija, M., van der Schaft, A. & Scherpen, J. M. A. Discrete exterior geometry approach to structure-preserving discretization of distributed-parameter port-Hamiltonian systems. Journal of Geometry and Physics vol. 62 1509–1531 (2012) – 10.1016/j.geomphys.2012.02.006
• van der Schaft, A. J. & Maschke, B. M. Hamiltonian formulation of distributed-parameter systems with boundary energy flow. Journal of Geometry and Physics vol. 42 166–194 (2002) – 10.1016/s0393-0440(01)00083-3