Boundary Limitation of Wavenumbers in Taylor-Vortex Flow

We report experimental results for a boundary-mediated wavenumber-adjustment mechanism and for a boundary-limited wavenumber-band of Taylor-vortex flow (TVF). The system consists of fluid contained between two concentric cylinders with the inner one rotating at an angular frequency $\Omega$. As observed previously, the Eckhaus instability (a bulk instability) is observed and limits the stable wavenumber band when the system is terminated axially by two rigid, non-rotating plates. The band width is then of order $\epsilon^{1/2}$ at small $\epsilon$ ($\epsilon \equiv \Omega/\Omega_c - 1$) and agrees well with calculations based on the equations of motion over a wide $\epsilon$-range. When the cylinder axis is vertical and the upper liquid surface is free (i.e. an air-liquid interface), vortices can be generated or expelled at the free surface because there the phase of the structure is only weakly pinned. The band of wavenumbers over which Taylor-vortex flow exists is then more narrow than the stable band limited by the Eckhaus instability. At small $\epsilon$ the boundary-mediated band-width is linear in $\epsilon$. These results are qualitatively consistent with theoretical predictions, but to our knowledge a quantitative calculation for TVF with a free surface does not exist.Comment: 8 pages incl. 9 eps figures bitmap version of Fig

On the asymptotic reduction of a bifurcation equation for edge-buckling instabilities

Weakly clamped uniformly stretched thin elastic plates can experience edge buckling when subjected to a transverse pressure. This situation is revisited here for a circular plate, under the assumption of finite rotations and negligible bending stiffness in the pre-buckling range. The eigenproblem describing this instability is formulated in terms of two singularly perturbed fourth-order differential equations involving the non-dimensional bending stiffness ε>0. By using an extension of the asymptotic reduction technique proposed by Coman and Haughton (Acta Mech 55:179–200, 2006), these equations are formally reduced to a simple second-order ordinary differential equation in the limit ε→0+. It is further shown that the predictions of this reduced problem are in excellent agreement with the direct numerical simulations of the original bifurcation equations

The Asymptotical Numerical Method (ANM) for solving nonlinear multiscale problems

Séminaire invité, Technische Universiteit, Eindhoven, The Netherlands (3 mars 2010

Sur le flambage plastique de l'éprouvette cruciforme

International audienc

Nouvelles approches basées sur la réduction de modèle pour le calcul multi-échelles des matériaux hyperélastiques en grandes déformations

National audienc

About finite element modeling of film/substrate systems

International audienceVarious models in the literature can predict the instabilities in film/substrate systems, however only a few of them are based on full standard techniques of computational mechanics. For instance, the use of Fourier spectral method permits fairly low cost computations, but imposes periodic boundary conditions. In this talk we revisit the numerical modeling of film/substrate systems by the finite element method, which allows accounting for various geometries, material properties and boundary conditions. Generally, the substrate is taken to be thick, which prescribes 2D/3D elements, while thin shell elements are more suitable for the film, however 2D/3D elements are necessary in the case of short instability wavelength. The simulation of many wrinkles by finite elements leads to large-scale problems and therefore to High Performance Computing. In this present communication we will revisit this question, furthermore, specific responses due to boundary conditions can be observed by full finite element computations and some examples will be presented

Sull’interazione fra instabilità locale e frattura nella crisi di lastre elastiche sottili fessurate

SOMMARIO. Si valutano gli effetti della instabilità locale delle regioni adiacenti ai bordi delle fessure, sul raggiungimento della condizione limite di crisi per distacco in lastre elastiche sottili soggette a trazione monoassiale. Con riferimento al caso di una lastra quadrata fessurata centralmente, lo studio della biforcazione dell’equilibrio viene affrontato attraverso il Metodo Asintotico Numerico. Per tale via, si può istituire un confronto sulla pericolosità di stati tensionali corrispondenti sul ramo fondamentale e su quello biforcato, e dedurre delle stime precise del valore dell’ampiezza iniziale della fessura al di là del quale l’instabilità locale precede ed innesca la propagazione della lesione. ABSTRACT. In this paper, the effects of buckling upon the rupture of thin elastic sheets subjected to a uniform traction are evaluated. Referring to the case of a square central cracked panel, the buckling analysis is performed via the Asymptotic Numerical Method. This method makes easy to perform a comparison between corresponding stress states belonging to the fundamental branch and to the bifurcated one, and to have an assessment of the initial crack length for which buckling precedes the unstable propagation phase of the crack

Modal approach to evaluate passive and active damping of sandwich viscoelastic and piezoelectric beams

In this paper, a modal approach is developed to estimate damping properties (i.e. loss factor and frequency per vibration mode) of sandwich beams with viscoelastic and/or piezoelectric layers. This method uses the classical laminate beam theory and a linear approximation of the electric potential through the thickness. Two control laws are considered. So, it appears that the piezoelectric material can yield an efficient solution to damp vibration modes