Nonlinear dynamics of uniformly loadedElastica: Experimental and numerical evidence of motion around curled stable equilibrium configurations

Autor: Djebar Baroudi, Antonio Battista, Leonid A. Igumnov, Ivan Giorgio, Emilio Turco
Přispěvatelé: Aalto University, International Research Centre on Mathematics & Mechanics of Complex Systems (M&MoCS), Università degli Studi dell'Aquila (UNIVAQ), Laboratoire des Sciences de l'Ingénieur pour l'Environnement - UMR 7356 (LaSIE), Université de La Rochelle (ULR)-Centre National de la Recherche Scientifique (CNRS), University of Sassari, Department of Civil Engineering, Università La Sapienza, Università degli Studi dell'Aquila, Lobachevsky State University of Nizhni Novgorod, Aalto-yliopisto
Rok vydání: 2019
Předmět:
Zdroj: Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik
Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, Wiley-VCH Verlag, In press, ⟨10.1002/zamm.201800121⟩
ISSN: 1521-4001
0044-2267
Popis: ZAMM - Journal of Applied Mathematics and Mechanics It has been numerically observed and mathematically proven that for a clamped Euler’s Elastica, which is uniformly loaded, there exist, in large deformations, some ‘undocumented’ equilibrium configurations which resemble a curled pending wire. Even if Elastica is one of the most studied model in mathematical physics, we could not find in the literature any description of an equilibrium like the one whose existence was forecast theoretically in [36]. In this paper, we prove that this kind of equilibrium configurations can be actually observed experimentally when using ‘soft’ beams. We mean with soft beams: Elasticae whose ratio between the applied load intensity and the bending stiffness is large enough. Moreover, we prove experimentally that such equilibrium configurations are actually stable, by observing their oscillations around the considered nonstandard equilibrium configuration. To describe theoretically such oscillations we consider, instead of a ‘soft’ Elastica model, directly a Hencky-type discrete model, i.e. a ‘masses-springs’ finite dimensional Lagrangian model. In this way we formulate, avoiding the use of an intermediate continuum model, a model for which numerical simulations can be performed without the introduction of any further discretization. In this way, we can also predict quantitatively the motions of soft beams, in the regime of large displacements and deformations. Postponing to future investigations more careful quantitative measurements, we report here that it was possible to get a rather promising qualitative agreement between observed motions and predictive numerical simulations.
Databáze: OpenAIRE
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