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

The displacement response of an elastic perfectly plastic oscillator under a zero mean, stationary, broad band random load is known not to reach stationarity: asymptotically, its mean is zero but its variance linearly increases with time. Thus, as time passes the oscillator gradually drifts away from its initial position. A method is presented for estimating the time asymptotic behavior of this drifting. Developed within the context of stochastic averaging, the method is based on a generalized van der Pol transformation that differs from its classical counterpart by an extra term that is meant to capture the drifting. The introduction of this term makes it possible to successfully address the drifting by using a linearization technique, even when the excitation power spectrum vanishes at zero frequency. The results obtained with the method are in good agreement with Monte Carlo simulation estimates.

When using a classical SHPB (Split Hopkinson Pressure Bar) set-up, the useful measuring time is limited by the need of separating the waves propagating in opposite directions. A new method for separating and rebuilding waves in finite bars was developed, with no time limit, from $\text{N}$ strain measurements and $\text{P}$ particle velocity measurements $\text{(N+P⩾2)}$. It takes account of the wave dispersion in elastic and viscoelastic bars. The method is illustrated with the loading of a free bar where the measured displacement is 30 times longer than the displacement that would be obtained with the classical method.

We study thermal phenomena which occur during compressive loading tests on some damaged or not concrete. Two calorific effects are shown through an experimental study using infrared thermography. The first, intrinsically reversible, is due to the thermoelastic coupling. The second is due to damage concrete state.

A homogeneous and isotropic turbulence is suddenly subjected to a rigid body rotation, whose influence on the turbulent vorticity field is studied. It is shown that only the odd statistical moments are influenced by the rotation at the first order in time. This effect is shown in particular for triple correlations and should be more important for a small Rossby number.

Natural convection of air inside a rectangular cavity, differentially heated under large temperature gradients, is considered. The low Mach approximation equations are those obtained by Paolucci allowing for filtering of sound waves. Transition to unsteadiness is studied with numerical simulation, with a finite volume code based on a fractional time step method derived from projection methods used for incompressible flows. When the fluid physical properties are prescribed constants, transition to unsteadiness follows the classical scheme of a Hopf bifurcation. The transition is quite different when viscosity obeys Sutherland's law while the Prandtl number is kept constant. There is evidence of hysteresis, therefore the transition seems to be subcritical. In the vicinity of the transition, on the large amplitude branch, an intermittent solution is observed, with periodic bursts separating quasi-steady states.

We consider the $\text{N}$-body ($\text{N=p·n}$) problem (where the bodies are submitted to their mutual attractions derived from a potential of the type $\text{V(r)=Cte/r}{}^{\mathrm{2\alpha }}$ where $\text{0⩽α<∞}$). We prove the existence of relative equilibrium configurations (denoted C.E.R.) when the ponctual bodies are at the vertices of $\text{p}$ regular polygons centered around a given mass $\text{M}$, the masses being equal on the vertices of each polygon. In the Newtonian case ($\text{α=1/2}$) we enrich the last result for values of n lower or equal than $\text{472}$.

We consider the propagation of singularities for a differential system which constitutes a simplified model of thin shells with developable middle surface (parabolic case). Extensions of the solutions out of the domain allow us to consider either boundary or internal singularities. The properties of propagation of singularities and their relation with the structure of the boundary layers are given. We remove a mistake in [2], Section 6.1, concerning the analyticity of solutions (in fact they are in the Gevrey class of order 3).

It is proposed to represent the dynamics of a moving contact line by an Onsager like mobility relation between the contact angle and the speed of the moving line, including an Arrhenius factor small enough in many physical situations to be the limiting factor for the motion. The liquid-vapor interface is then in quasiequilibrium, which allows one to analyse a dynamical wetting transition. This approach predicts well the formation of angular points on the rear edge of droplets sliding on a tilted plane.

The onset of Soret-driven convection in an infinite cell filled with a porous medium saturated by a binary fluid is studied. The impermeable horizontal walls are maintained at different and uniform temperatures. For a cell heated from below, the motionless solution loses its stability via a stationary bifurcation when the separation ratio $\text{ψ}$ is higher than a Lewis and normalized porosity dependent value $\text{ψ}{}_0$; for $\text{ψ<ψ}{}_0$, it loses its stability via a Hopf bifurcation. For a cell heated from above, the motionless solution is infinitely linearly stable if $\text{ψ>0}$, while a stationary bifurcation occurs if $\text{ψ<0}$. These results are widely corroborated by direct numerical simulations.

The present note describes work related to anisotropy of acoustical properties of felt materials being compressed with a rate $\text{n}$ varying from 1 to 4. Following a recent note [1], it is shown that such compression induces some anisotropy, which is small but still significant, clearly visible on the elliptical shape of the tortuosity spatial distribution, and also on the Brewster angle shifts, which are predictible. Some fine experimental studies of the reflection coefficient versus the angle of incidence have been performed and discussed.