Authors

Andrea Brugnoli, Daniel Alazard, Valérie Pommier-Budinger, Denis Matignon

Abstract

The port-Hamiltonian framework allows for a structured representation and interconnection of distributed parameter systems described by Partial Differential Equations (PDE) from different realms. Here, the Mindlin-Reissner model of a thick plate is presented in a tensorial formulation. Taking into account collocated boundary control and observation gives rise to an infinite-dimensional port-Hamiltonian system (pHs). The Partitioned Finite Element Method (PFEM), already presented in our previous work, allows obtaining a structure-preserving finite-dimensional port-Hamiltonian system, and accounting for boundary control in a straightforward manner. In order to illustrate the flexibility of PFEM, both types of boundary controls can be dealt with: either through forces and momenta, or through kinematic variables. The discrete model is easily implementable by using the FEniCS platform. Computation of eigenfrequencies and vibration modes, together with time-domain simulation results demonstrate the consistency of the proposed approach.

Keywords

Port-Hamiltonian systems (pHs); Geometric Discretization; Mindlin-Reissner Plate; Partitioned Finite Element Method (PFEM); Symplectic Integration

Citation

  • Journal: IFAC-PapersOnLine
  • Year: 2019
  • Volume: 52
  • Issue: 2
  • Pages: 88–95
  • Publisher: Elsevier BV
  • DOI: 10.1016/j.ifacol.2019.08.016
  • Note: 3rd IFAC Workshop on Control of Systems Governed by Partial Differential Equations CPDE 2019- Oaxaca, Mexico, 20–24 May 2019

BibTeX

@article{Brugnoli_2019,
  title={{Partitioned Finite Element Method for the Mindlin Plate as a Port-Hamiltonian system}},
  volume={52},
  ISSN={2405-8963},
  DOI={10.1016/j.ifacol.2019.08.016},
  number={2},
  journal={IFAC-PapersOnLine},
  publisher={Elsevier BV},
  author={Brugnoli, Andrea and Alazard, Daniel and Pommier-Budinger, Valérie and Matignon, Denis},
  year={2019},
  pages={88--95}
}

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References