Port-Hamiltonian modeling of multidimensional flexible mechanical structures defined by linear elastic relations $\star$ Article Swipe

MAKE IMPACT

Cristobal Ponce , Yongxin Wu , Yann Le Gorrec , Héctor Ramírez · YOU? · · 2023 · Open Access · · DOI: https://doi.org/10.48550/arxiv.2311.03796

This article presents a systematic methodology for modeling a class of flexible multidimensional mechanical structures defined by linear elastic relations that directly allows to obtain their infinite-dimensional port-Hamiltonian representation. The approach is restricted to systems based on a certain class of kinematic assumptions. However this class encompasses a wide range of models currently available in the literature, such as ${\ell}$-dimensional elasticity models (with ${\ell}$ = 1,2,3), vibrating strings, torsion in circular bars, classical beam and plate models, among others. The methodology is based on Hamilton's principle for a continuum medium which allows defining the energy variables of the port-Hamiltonian system, and also on a generalization of the integration by parts theorem, which allows characterizing the skew-adjoint differential operator and boundary inputs and boundary outputs variables. To illustrate this method, 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 an infinite-dimensional port-Hamiltonian representation of this system is presented in the literature.

Type

preprint

Language

en

Landing Page

https://doi.org/10.48550/arxiv.2311.03796

OA Status

green

Related Works

10

OpenAlex ID

https://openalex.org/W4388514609

Raw OpenAlex JSON

OpenAlex ID

https://openalex.org/W4388514609

Canonical identifier for this work in OpenAlex

DOI

https://doi.org/10.48550/arxiv.2311.03796

Digital Object Identifier

Title

Port-Hamiltonian modeling of multidimensional flexible mechanical structures defined by linear elastic relations $\star$

Work title

Type

preprint

OpenAlex work type

Language

en

Primary language

Publication year

2023

Year of publication

Publication date

2023-11-07

Full publication date if available

Authors

Cristobal Ponce, Yongxin Wu, Yann Le Gorrec, Héctor Ramírez

List of authors in order

Landing page

https://doi.org/10.48550/arxiv.2311.03796

Publisher landing page

Open access

Yes

Whether a free full text is available

OA status

green

Open access status per OpenAlex

OA URL

https://doi.org/10.48550/arxiv.2311.03796

Direct OA link when available

Concepts

Hamiltonian (control theory), Torsion (gastropod), Kinematics, Mathematics, Hamiltonian system, Boundary value problem, Differential operator, Mathematical analysis, Classical mechanics, Mathematical optimization, Physics, Surgery, Medicine

Top concepts (fields/topics) attached by OpenAlex

Cited by

0

Total citation count in OpenAlex

Related works (count)

10

Other works algorithmically related by OpenAlex

Full payload