Port-Hamiltonian Macroscopic Modelling based on the Homogenisation Method: case of an acoustic pipe with a porous wall
Authors
Alexis Thibault, Thomas Hélie, Henri Boutin, Juliette Chabassier
Abstract
This paper addresses linear propagation in an acoustic pipe with a porous wall, a common scenario in wooden wind instruments. First, a scale separation technique is proposed for dissipative propagation within the wall: the material is modelled as a periodic assembly of identical microscopic cells, forming a network of channels filled with air. It is shown that the resulting PDE admits a port-Hamiltonian formulation, of which the state, flow, effort, Hamiltonian, and Differential connection operator are structured using powers of the scale parameter. The resulting macroscopic description, derived from the governing equations at the two lowest orders, manifests as a constrained port-Hamiltonian system involving a Lagrange multiplier. As an example, using an academic cell geometry, we determine the effective wavenumber and dissipation coefficient of a straight tube with a porous wall.
Keywords
Modelling; Homogenisation method; Port-Hamiltonian systems; Distributed parameter systems; Acoustics
Citation
- Journal: IFAC-PapersOnLine
- Year: 2024
- Volume: 58
- Issue: 6
- Pages: 244–249
- Publisher: Elsevier BV
- DOI: 10.1016/j.ifacol.2024.08.288
- Note: 8th IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control LHMNC 2024- Besançon, France, June 10 – 12, 2024
BibTeX
@article{Thibault_2024,
title={{Port-Hamiltonian Macroscopic Modelling based on the Homogenisation Method: case of an acoustic pipe with a porous wall}},
volume={58},
ISSN={2405-8963},
DOI={10.1016/j.ifacol.2024.08.288},
number={6},
journal={IFAC-PapersOnLine},
publisher={Elsevier BV},
author={Thibault, Alexis and Hélie, Thomas and Boutin, Henri and Chabassier, Juliette},
year={2024},
pages={244--249}
}
References
- Allard, J. F. & Atalla, N. Propagation of Sound in Porous Media. (2009) doi:10.1002/9780470747339 – 10.1002/9780470747339
- ALOUGES, F. Introduction to Periodic Homogenization. Interdisciplinary Information Sciences vol. 22 147–186 (2016) – 10.4036/iis.2016.a.01
- Bensoussan, (2011)
- Biot, M. A. Theory of Propagation of Elastic Waves in a Fluid-Saturated Porous Solid. I. Low-Frequency Range. The Journal of the Acoustical Society of America vol. 28 168–178 (1956) – 10.1121/1.1908239
- Biot, M. A. Theory of Propagation of Elastic Waves in a Fluid-Saturated Porous Solid. II. Higher Frequency Range. The Journal of the Acoustical Society of America vol. 28 179–191 (1956) – 10.1121/1.1908241
- Boutin, H., Le Conte, S., Vaiedelich, S., Fabre, B. & Le Carrou, J.-L. Acoustic dissipation in wooden pipes of different species used in wind instrument making: An experimental study. The Journal of the Acoustical Society of America vol. 141 2840–2848 (2017) – 10.1121/1.4981119
- Bruneau, (2013)
- Butterfield, (1972)
- Mora, L. A., Le Gorrec, Y., Matignon, D., Ramirez, H. & Yuz, J. I. On port-Hamiltonian formulations of 3-dimensional compressible Newtonian fluids. Physics of Fluids vol. 33 (2021) – 10.1063/5.0067784
- Regev, (2016)
- van der Schaft, A. & Jeltsema, D. Port-Hamiltonian Systems Theory: An Introductory Overview. Foundations and Trends® in Systems and Control vol. 1 173–378 (2014) – 10.1561/2600000002