Une application de diagramme de Newton a la recherche des solutions periodiques d'un oscillateur quasiharmonique et l'etude de la stabilite de ces solutions

Periodic solutions of autonomous quasiharmonic systems are studied in the resonant case if the branching equation has multiple roots. In order to find all the real solutions of this equation, we use Newton's diagram. This problem may have no real periodic solution. This depends upon the configuration of the descending section of Newton's diagram and upon the roots of the appropriate defining equations. The stability of these periodic solutions is also considered. Sufficient conditions of the solutions depend upon the defining equation.     

Methode de centrage-estimation de l'erreur et comportement des trajectoires dans l'espace des phases

We establish certain estimates of the error of the averaging method for differential equations in Banach spaces in the [0, ∞[ interval of the variable t. If there is an equilibrium point common to the exact and averaged equations, we study, under certain stability hypotheses, the behavior of the solutions of the exact equation according to the type of the equilibrium point for the averaged equation (node, focus, …).     

Les contraintes normales et les spectres de relaxation dans les systèmes polymères

Résumé Ce mémoire considère les relations entre les contraintes normales qui naissent au cours des déformations de cisaillement des systèmes polymères fluides (effetWeissenberg) et leurs spectres de relaxation. Les auteurs montrent que la croissance des contraintes tangentielles et leur relaxation évoluent plus rapidement que celles des contraintes normales. Une formule qui a été établie de déterminer le spectre de relaxation en fonction des variations des contraintes normales en régime transitoire de de déformation. Il a été démontré que le coefficient des contraintes normales dans le domaine linéaire est identique à la déformabilité (compliance) d'équilibre. Cette conclusion est confirmée par plusieurs résultats expérimentaux. Il découle de là l'applicabilité de la formule deLodge qui donne une relation entre les contraintes et les déformations élastiques dans le domaine linéaire de comportement méchanique des systèmes visco-élastiques. Les auteurs examinent les relations entre les contraintes et la vitesse de cisaillement et entre le module dynamique et la fréquence aussi bien dans les domaines linéaire et non linéaire.     

Détection de fissures dans les poutres d'acier : une nouvelle approche par balayage de mesures de vibrations

In the last few years, the techniques of detection and identification of damage in structures benefited from important research efforts. Several methods of non-destructive damage detection, such as techniques based on modal analysis, were developed in addition to the traditional methods. The difficulties encountered by these techniques are their low performance, considering the industrial requirements to detect cracks as early as possible.     

Effects of conductivity jumps in the envelope of a kinematic dynamo flowInfluence des discontinuités de conductivité dans l'enveloppe de l'écoulement d'une dynamo cinématique

This Note reports on numerical simulations of the kinematic dynamo action in a test flow modeling the Von Kármán Sodium (VKS) experiment performed at CEA-Cadarache. We show that the conductivity of the vessel greatly influences the critical magnetic Reynolds number. These effects are dramatically amplified as the ratio of the conductivity of the vessel to that of the sodium increases from 1 to 5. To cite this article: R. Laguerre et al., C. R. Mecanique 334 (2006).     

Investigation of mechanical properties of water-based friction modifier for railway applicationsRecherches des propriétés mécaniques du modificateur frottement dans une forme de l'émulsion d'eau applique dans les chemins de fer

This Note outlines the investigation of the water-based friction modifier used in railway technology. This investigation involves measurements made using a novel measuring stand, a new modelling of the modifier and the identification of its parameters using measured results. The proposed model of the modifier is composed of a dry friction slider, a dash-pot and a spring. The investigation contributes to a deeper understanding of the modifier's performance. To cite this article: J. Piotrowski, C. R. Mecanique 332 (2004).     

On the thermal anisotropy affecting transfers in a multilayer porous mediumSur l'effet de l'anisotropie thermique sur les transferts dans un milieu poreux multicouches

An analytical model for studying double-diffusive natural convection within a multilayer anisotropic porous medium is developed and validated with respect to a direct numerical silmulation. The studied domain is composed of two horizontal porous layers where the lower one is thermally anisotropic and is submitted to a uniform horizontal heat flux and a vertical mass flux. The assumption of parallel flow is validated and the effect of anisotropy on dynamic transitions is investigated. To cite this article: R. Bennacer et al., C. R. Mecanique 332 (2004).     

Loi d'évolution de l'endommagement pour la prise en compte de l'adoucissement dans les milieux élastomères chargésDamage evolution law for the study of stress-softening in reinforced rubber-like materials

An experimental study on oligo-cyclic fatigue of rubber-like materials submitted to tension test in large deformation, to constant amplitude of loadings, brings to the fore that the stress during the loading, at a given cycle, is always smaller than during the previous cycle. These tests highlight that this phenomenom, called stress-softening, depends on the maximal stretch and on the number of cycles to which the materials has been submitted. A model, taking into account these two parameters is proposed and experimental validations are proposed. To cite this article: M. Brieu et al., C. R. Mecanique 332 (2004).     

Thermodynamics modelling of plasticity and damage of argilliteModélisation thermodynamique de la plasticité et de l'endommagement d'une argilite.

The study of the physical and mechanical characteristics of argillites allows us to retain the state variables useful for the thermodynamic modelling of their behaviour. We built a thermodynamic potential which reproduces the nonlinear behaviour. Plasticity-damage coupling is taken into account by using an effective stress coming from strain equivalence principle. To cite this article: N. Conil et al., C. R. Mecanique 332 (2004).     

Asymptotics at infinity of solutions to the Neumann problem in a sieve-type layerComportement asymptotique à l'infini d'un problème de Neumann dans une couche perforée

The Neumann problem is considered in a domain $\text{Ω}$, which can differ from a periodic layer inside a compact set. We prove the Fredholm property of the corresponding operator in step-weighted Sobolev spaces and determine its kernel and cokernel. All these results are based on the obtained asymptotic representation of solutions at infinity. To cite this article: S.A. Nazarov, G. Thäter, C. R. Mecanique 331 (2003).     

Instabilité et particularités de l'évolution d'une nappe tourbillonnaireInstability and features of vortex sheet evolution

The instability and the features of vortex sheet evolution are studied. We consider the self-organization of localized vortices (in two-dimensional flows) into clusters-like and spiral-like structures and show that quasi-final states do not ‘forget’ conditions of their initial origin. We discuss the physical significance of the obtained results. To cite this article: V. Pavlov et al., C. R. Mecanique 330 (2002) 757–762.     

On the stability of a Bingham fluid flow in an annular channelSur la stabilité de l'écoulement d'un fluide de Bingham dans une conduite annulaire

Linear stability of a fully developed Bingham fluid flow between two coaxial cylinders subject to infinitesimal axisymetric perturbations is investigated. The analysis leads to two uncoupled Orr–Sommerfeld equations with appropriate boundary conditions. The numerical solution is obtained using fourth order finite difference scheme. The computations were performed for various plug flow dimensions and radii ratios. Within the range of the parameters considered in this paper, the Poiseuille flow of Bingham fluid is found to be linearly stable. To cite this article: N. Kabouya, C. Nouar, C. R. Mecanique 331 (2003).     

On a closure of mass conservation equation and stability analysis in the mathematical theory of vehicular traffic flowSur une fermeture des équations de conservation de la masse et l'analyse de la stabilité dans la théorie mathématique de la circulation véhiculaire

This Note deals with the development of mathematical methods for the closure of the mass conservation equation for macroscopic hydrodynamical models of traffic flow on roads. The closure is obtained by a phenomenological model, relating the local mean velocity to local density earlier in time. An evolution equation is obtained for the flux and a stability analysis is performed; this qualitatively describes some features of congested flow. To cite this article: V. Coscia, C. R. Mecanique 332 (2004).     

Evolution of the volumetric interfacial area in two-phase mixturesEvolution de l'aire interfaciale volumique dans les mélanges diphasiques

We investigate the time evolution of the density of interfaces in a two-phase mixture, with particular emphasis on the role of compressibility, dilatability and phase transitions. Two different and complementary routes are considered: a rather intuitive one based on exact results for dilute mixtures which are then interpolated to all concentrations, and a more systematic approach based on the statistical average of the exact transport equation for elementary pieces of interfaces. To cite this article: D. Lhuillier, C. R. Mecanique 332 (2004).     

Self adjoint extensions of differential operators in application to shape optimizationExtensions autoadjointes d'opérateurs différentiels et application à l'optimisation de forme

Two approaches are proposed for the modelling of problems with small geometrical defects. The first approach is based on the theory of self adjoint extensions of differential operators. In the second approach function spaces with separated asymptotics and point asymptotic conditions are introduced, and the variational formulation is established. For both approaches the accuracy estimates are derived. Finally, the spectral problems are considered and the error estimates for eigenvalues are given. To cite this article: S.A. Nazarov, J. Sokolowski, C. R. Mecanique 331 (2003).     

Singularités de la rhéologie de l'air humide saturé et diffusion moléculaire dans les milieux nuageuxSingularities in the rheology of saturated humid air,and molecular diffusion in cloods

Under realistic assumptions, we propose a thermodynamical formalism providing, for the moist-saturated air (cloudy air), a generalized Fick's law. This Fick's law leads to a double diffusive rheology with Dufour effect. The form taken by the energy equation is slightly different from the classical form used in convection problems. We compare the equations with those of the convection in moist unsaturated air (the Dufour effect and all double diffusive effects disappear in this case). As application we demonstrate some consequences of this diffusion in cloudy convection. To cite this article: P.A. Bois, C. R. Mecanique 330 (2002) 627–632.     

Simulation numérique directe de l'influence de la forme aval d'une plaque séparatrice sur une couche de mélangeDirect-numerical simulation of the splitting-plate downstream-shape influence upon a mixing layer

In this Note, we present direct numerical simulation results of a spatial mixing layer generated behind an upstream plate separating two boundary layers. The effect of the shape of the trailing edge of the plate is considered through comparisons between flows obtained from a bevelled or a blunt plate. In the former case, a spatial mixing layer consistent with previous experimental and numerical observations is obtained. In the latter case, the self-excited state that establishes in the near wake region dominates primary and secondary instability mechanisms while understating the importance of inflow perturbations. This behaviour is interpreted in terms of convective or absolute instability. The effects on turbulent statistics are also discussed. To cite this article: S. Laizet, E. Lamballais, C. R. Mecanique 334 (2006).     

Validation of averaged equations for thermal vibrational convection in near-critical fluidsValidation d'équations moyennées pour l'étude de la convection vibrationnelle dans les fluides supercritiques.

Within an averaging approach, the governing equations and effective boundary conditions describing both the average and pulsation motion of a near-critical fluid subjected to high-frequency vibrations are obtained. Vibrations induce the non-homogeneities in average temperature. Owing to these non-homogeneities, the average flows can be generated even in isothermal cavity under weightlessness. These flows are examined for 1D and 2D configurations. The direct numerical simulations fulfilled earlier confirm the averaged model, we obtain the same flow structures by essentially smaller requirements for computational time. To cite this article: A.Vorobev et al., C. R. Mecanique 332 (2004).