Authors

Thomas Hélie, Denis Matignon

Abstract

This paper introduces linear and nonlinear damping models, which preserve the eigenspaces of conservative linear mechanical problems. After some recalls on the finite dimensional case and on Caughey’s linear dampings, an extension to a nonlinear class is introduced. These results are recast in the port-Hamiltonian framework and generalized to infinite dimensional systems. They are applied to an Euler-Bernoulli beam, excited by a distributed force. Simulations yield sounds of xylophone, glockenspiel (etc) and some interpolations for nonlinear dampings.

Keywords

energy storage; port-Hamiltonian systems; eigenfunctions; damping; nonlinear model; partial differential equations; sound synthesis

Citation

  • Journal: IFAC-PapersOnLine
  • Year: 2015
  • Volume: 48
  • Issue: 13
  • Pages: 200–205
  • Publisher: Elsevier BV
  • DOI: 10.1016/j.ifacol.2015.10.239
  • Note: 5th IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control LHMNC 2015- Lyon, France, 4–7 July 2015

BibTeX

@article{H_lie_2015,
  title={{Nonlinear damping models for linear conservative mechanical systems with preserved eigenspaces: a port-Hamiltonian formulation}},
  volume={48},
  ISSN={2405-8963},
  DOI={10.1016/j.ifacol.2015.10.239},
  number={13},
  journal={IFAC-PapersOnLine},
  publisher={Elsevier BV},
  author={Hélie, Thomas and Matignon, Denis},
  year={2015},
  pages={200--205}
}

Download the bib file

References