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Membranes élastiques et capillaires : instabilités, singularités et auto-adaptation

Abstract : This thesis is devoted to the experimental, numerical and analytical study of some examples of elastic or liquid sheets. Large deformations of elastic plates generally lead to the focusing of energy around nearly singular zones, either lines (ridges) or points (cones). These singularities are well understood only when they are isolated. We consider two model situations showing multiple ridges and cones. Simulations of the full equations and asymptotic expansions using the singularities elastic energy and geometrical arguments are in quantitative agreement with the experiments. At short times, thin viscous liquid sheets behave like elastic plates. We use the analogy between viscous liquid flows and elastic solid deformations to find a new type of conical singularity on a viscous sheet. At long times, liquid sheets evolve toward shapes with a minimum of capillary energy, \textit{i.e.} minimal surfaces. We determine the minimal surfaces bounded by a double helix and we study their stability using their vibration spectra. When a minimal solid surface is forced into vibration, its response is small unless the excitation frequency is near one of its eigenfrequencies. At equilibrium, a soap film has the shape of a minimal surface. In contrast, we found that when the liquid film is forced, its vibration amplitude has only a weak dependence on the excitation frequency, because the thickness distribution of the film adapts to the forcing. We examine an analogous mechanical system, a bead threaded on a string, and we show that a vibrating system with an additional degree of freedom acquire a self-adaptative behavior : it responds to any forcing frequency.
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Contributor : Arezki Boudaoud <>
Submitted on : Saturday, March 15, 2003 - 1:50:05 PM
Last modification on : Thursday, October 29, 2020 - 3:01:51 PM
Long-term archiving on: : Tuesday, September 11, 2012 - 8:05:34 PM


  • HAL Id : tel-00002559, version 1


Arezki Boudaoud. Membranes élastiques et capillaires : instabilités, singularités et auto-adaptation. Autre. Université Pierre et Marie Curie - Paris VI, 2001. Français. ⟨tel-00002559⟩



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