Authors

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

Abstract

This article introduces a novel systematic methodology for modeling a class of multidimensional linear mechanical systems that directly allows to obtain their infinite-dimensional port-Hamiltonian representation. While the approach is tailored to systems governed by specific kinematic assumptions, it encompasses a wide range of models found in current literature, including ℓ-dimensional elasticity models (where ℓ = 1, 2, 3), vibrating strings, torsion in circular bars, classical beam and plate models, among others. The methodology involves formulating the displacement field using primary generalized coordinates via a linear algebraic relation. The non-zero components of the strain tensor are then calculated and expressed using secondary generalized coordinates, enabling the characterization of the skew-adjoint differential operator associated with the port-Hamiltonian representation. By applying Hamilton’s principle and employing a specially developed integration by parts formula for the considered class of differential operators, the port-Hamiltonian model is directly obtained, along with the definition of boundary inputs and outputs. To illustrate the methodology, the plate modeling process based on Reddy’s third-order shear deformation theory is presented as an example. To the best of our knowledge, this is the first time that a port-Hamiltonian representation of this system is presented in the literature.

Keywords

Infinite-dimensional systems; Port-Hamiltonian systems; Modeling; Hamilton’s principle

Citation

  • Journal: Applied Mathematical Modelling
  • Year: 2024
  • Volume: 134
  • Issue:
  • Pages: 434–451
  • Publisher: Elsevier BV
  • DOI: 10.1016/j.apm.2024.05.040

BibTeX

@article{Ponce_2024,
  title={{A systematic methodology for port-Hamiltonian modeling of multidimensional flexible linear mechanical systems}},
  volume={134},
  ISSN={0307-904X},
  DOI={10.1016/j.apm.2024.05.040},
  journal={Applied Mathematical Modelling},
  publisher={Elsevier BV},
  author={Ponce, Cristobal and Wu, Yongxin and Le Gorrec, Yann and Ramirez, Hector},
  year={2024},
  pages={434--451}
}

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References