Constrained port-Hamiltonian modeling and structure-preserving discretization of the Rayleigh beam

Authors

Cristobal Ponce, Hector Ramirez, Yann Le Gorrec, Yongxin Wu

Abstract

This paper addresses the port-Hamiltonian modeling of the Rayleigh beam, which bridges the gap between the Euler-Bernoulli and Timoshenko beam theories. This balance makes the Rayleigh model particularly suitable for scenarios where Euler-Bernoulli assumptions are insufficient, but Timoshenko’s complexity is unnecessary, such as in cases of moderate oscillations. The originality of the approach lies in deriving the Rayleigh beam model from the displacement field of the Timoshenko beam and incorporating an algebraic constraint consistent with Rayleigh beam theory. The resulting model is formulated as an infinite-dimensional port-Hamiltonian differential-algebraic equation (PH-DAE). A structure-preserving spatial discretization strategy is developed using the mixed finite element method, ensuring the preservation of the PH-DAE structure in the finite-dimensional setting. Numerical simulations demonstrate the accuracy and effectiveness of the proposed model and discretization approach.

Keywords

Port-Hamiltonian Systems; Differential-Algebraic Equations; Modeling; Rayleigh beam; Structure-preserving discretization

Citation

• Journal: IFAC-PapersOnLine
• Year: 2025
• Volume: 59
• Issue: 8
• Pages: 108–113
• Publisher: Elsevier BV
• DOI: 10.1016/j.ifacol.2025.08.075
• Note: 5th IFAC Workshop on Control of Systems Governed by Partial Differential Equations - CPDE 2025- Beijing, China, June 18 - 20, 2025

BibTeX

@article{Ponce_2025,
  title={{Constrained port-Hamiltonian modeling and structure-preserving discretization of the Rayleigh beam}},
  volume={59},
  ISSN={2405-8963},
  DOI={10.1016/j.ifacol.2025.08.075},
  number={8},
  journal={IFAC-PapersOnLine},
  publisher={Elsevier BV},
  author={Ponce, Cristobal and Ramirez, Hector and Le Gorrec, Yann and Wu, Yongxin},
  year={2025},
  pages={108--113}
}

Download the bib file

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