Comptes Rendus de l'Académie des Sciences - Series IIB - Mechanics-Physics-Astronomy最新文献

A model is developed to calculate the period and damping of a rigid pendulum's oscillations when submitted to friction. A theoretical investigation shows that the pendulum is a sensitive accurate tool for assessing friction phenomena of very low intensity. The process of measurement and analysis method is then used to identify a real pendulum.

The mechanics of paper is considered from the standpoint of fibre networks. It is shown that the classical model of paper, based on a network of infinitely long fibres capable of carrying only axial forces [1], having the geometry of a Poisson line field, does not possess generic rigidity. This pathological behaviour can be removed by the introduction of rigid fibre-fibre bonds (justified by the presence of hydrogen bonding between cellulose fibres) and fibre flexural stiffness.

Ne compute the energy flux from a fluid flowing to an elastic hollow cylindrical tube generated by unstable modes. The basic fluid velocity flow is the parabolic Hagen-Poiseuille flow. We show that the energy flux from the fluid flowing to the elastic wall is positive when the mode is unstable, negative when the mode is stable, and null when the mode is neutral. Moreover the energy flux from the fluid flowing to the elastic solid is generated by the component of the force perpendicular to the wall at the interface for high Reynolds numbers, and essentially by the streamwise component of the force at interface for low Reynolds numbers.

We examine in this paper the energy flux carried out by the most unstable non-axisymmetric mode from Hagen-Poiseuille flow to an elastic tube where the Poiseuille flow takes place. The energy flux, from the flowing fluid to the elastic tube and the rate of amplification of unstable modes are plotted against the depth of the elastic material H — 1 and against the Reynolds number Re. The power developed by each component of the force at the interface is plotted too against H and Re. In this way, the force component at the interface which provides energy transfer to the solid medium is identified, and the origin of the instability is better understood.

To evaluate the thickness of the layers of a Ti/TiAl₃/Al system, experiments based on surface resistance measurements have been performed. The thickness of each layer is deduced from a comparison among calculated and measured values of resistance. We present here a solution for the simulation of surface resistance and the results obtained with this method on Ti/TiAl₃/Al systems.

After more than 3 years of operations, the SOHO solar mission has brought a large body of new results, the full exploitation of which continues. SOHO has provided evidence of the role of magnetic reconnection at many different spatial scales (including scales smaller than any spatial resolution) in direct heating by the Joule effect, or in generating MHD waves or accelerating particles. Reconnection seems to occur very low in the atmosphere with a permanent reshuffling of magnetic fields resulting from flux emergence at the borders of the supergranulation network. SOHO has also demonstrated the multifluid nature of the solar wind in the low corona where ion (and proton) temperatures are higher than electron temperatures. This ion heating can be explained by resonance between MHD waves and ion (and proton) gyration around the field lines. Such conclusions (and others) will be tested over the next few years with new observations from SOHO.

We propose a method of solving the Navier-Stokes equations in incompressible flow. It is based on the projection of the velocity field, approached by a prediction step on a zero divergence field. The novelty of this method concerns how the projection is made, directly operating on all the components of the velocity field through a coupling. A highly implicit algorithm allows us to maintain all physical boundary conditions of the problem during the solution steps.

Rotating stall is a fundamental hydrodynamic instability which is encountered in most hydraulic and aeraulic turbomachinery. It appears to exist only with cascades that considerably slow down the fluid flow and occurs in the form of rotating structures in which the flow rate may be negative. The paper analyses this instability and its transitions in a simple two-dimensional configuration using a multi-domain numerical scheme and solver. The space-time variation of the flow rates occurring for an angle of attack increasing by steps shows first standing waves, then intermittent and permanent travelling waves of limited amplitude, corresponding to blade stall. At higher angles of attack, a high amplitude wave propagates a single structure (cell) with a negative flow rate, corresponding to stalling of the cascade.

We consider a multi-structure made of two shells of thickness 2ɛ, having a middle surface of class %plane1D;49E;³ glued together on a part of their boundaries. We suppose that at every point of their intersection, the middle surfaces have distinct tangent planes. We make an assumption on the junction and on the applied body force density, and we identify the limit, when ɛ → 0, of the scaled three-dimensional displacement field for the multi-structure, showing in particular that the limit displacement field does not depend on the transverse variable, is inextensional, and that the angle between the two shells remains the same during the deformation.

Simple mathematical models with two time constants are used to study the dynamics of pressure variation during permeability measurements on dual porosity saturated media. We think that these transient phase dynamic aspects, which Darcy's Law cannot explain, are a macroscopic image of flows in macro and micropores.