On two-scale homogenized equations of one-dimensional nonlinear thermoviscoelasticity with rapidly oscillating nonsmooth data

We study the initial-boundary value problem for a system of quasilinear equations of one-dimensional nonlinear thermoviscoelasticity with rapidly oscillating nonsmooth coefficients and initial data. We rigorously justify the passage to the corresponding limit initial-boundary value problem for a system of two-scale homogenized integro-differential equations, including the existence theorem for the limit problem. The results are global with respect to the time interval and the data.     

Asymptotic modeling of assemblies of thin linearly elastic plates

We derive various models of assemblies of thin linearly elastic plates by abutting or superposition through an asymptotic analysis taking into account small parameters associated with the size and the stiffness of the adhesive. They correspond to the linkage of two Kirchhoff–Love plates by a mechanical constraint which strongly depends on the magnitudes of the previous parameters. To cite this article: C. Licht, C. R. Mecanique 335 (2007).     

Asymptotic modeling of linearly piezoelectric slender rods

The piezoelectric thin plate modeling already derived by the authors is extended to rod-like structures. Two models corresponding to sensor or actuator behavior are obtained. The conditions of existence of non-local terms in the limit models are discussed. To cite this article: T. Weller, C. Licht, C. R. Mecanique 336 (2008).     

Modèles discrets de structures tissées : Analyse de stabilité et de drapéDiscrete models of woven structures: stability and draping analysis

A discrete model of a woven fabric structure is established, whereby nodes endowed with a mass and a rotational rigidity are connected by rigid bars to form a two-dimensional truss. The set of four bars that delineate a quadrilateral area is further endowed with a torsion deformation mode. The kinematics of the truss reproduces the large rotations and displacements encountered for real tissues. The equilibrium shape of such a structure is obtained as the minimum of its total potential energy versus the whole set of kinematic translational and rotational variables, accounting for eventual kinematic constraints due to contact with a rigid surface by the Lagrange multipliers method. A stability analysis is conducted, and the potentiality of the model is illustrated by fabric draping simulations. To cite this article: B. Ben Boubaker et al., C. R. Mecanique 330 (2002) 871–877.     

Extension of the non-uniform warping theory to an orthotropic composite beam

This Note proposes an extension to composite section of the non-uniform (out-of-plane) warping beam theory recently established for homogeneous and isotropic beam by R. El Fatmi (C. R. Mecanique 335 (2007) 467–474). For the present work, which constitutes a first step of this extension, the cross-section is assumed to be symmetric and made by orthotropic materials; however, Poisson's effects (called here in-plane warping) are also taken into account. Closed form results are given for the structural behavior of the composite beam and for the expressions of the 3D stresses; these ones, easy to compare with 3D Saint Venant stresses, make clear the additional contribution of the new internal forces induced by the non-uniformity of the (in and out) warpings. As first numerical applications, results on torsion and shear-bending of a cantilever sandwich beam are presented.     

Resolution of linear viscoelastic equations in the frequency domain using real Helmholtz boundary integral equations

Boundary integral equations are well suitable for the analysis of seismic waves propagation in unbounded domains. Formulations in elastodynamics are well developed. In contrast, for the dynamic analysis of viscoelastic media, there are very seldom formulations by boundary integral equations. In this Note, we propose a new and simple formulation of time harmonic viscoelasticity with the Zener model, which reduces to classical elastodynamics if a compatibility condition is satisfied by boundary conditions. Intermediate variables which satisfy the classical elastodynamic equations are introduced. It makes it possible to utilize existing numerical tools of time harmonic elastodynamics. To cite this article: S. Chaillat, H.D. Bui, C. R. Mecanique 335 (2007).     

Asymptotics of eigenfrequencies of an elastic body with a heavy and hard peak-shaped inclusion

A heavy and hard peak-shaped inclusion in an elastic body provokes to concentration of eigenvalues in the low-frequency range of the spectrum and localization of the corresponding eigenmodes near the peak tip. To cite this article: S.A. Nazarov, C. R. Mecanique 335 (2007).     

Vérification expérimentale de la relation de réciprocité d'Onsager pour l'électro-osmose et l'électro-filtration dans une argile naturelleExperimental verification of the Onsager's reciprocal relations for electro-osmosis and electro-filtration phenomena on a saturated clay

This Note is devoted to the experimental verification of the Onsager's reciprocal relations in the particular case of electro-osmosis and electro-filtration. A special set up has been designed to carry out the measurements of both the electro-osmotic permeability and the streaming potential. This has been performed by using a natural material i.e., saturated kaolinite. To cite this article: K. Beddiar et al., C. R. Mecanique 330 (2002) 893–898.     

Extended three-dimensional digital image correlation (X3D-DIC)

A correlation algorithm is proposed to measure full three-dimensional displacement fields in a three-dimensional domain. The chosen kinematic basis for this measurement is based on continuous finite-element shape functions. It is furthermore proposed to account for the presence of strong discontinuities, similarly to extended finite element schemes, with a suited enrichment of the kinematics with discontinuities supported by a (crack) surface. An optimization of the surface geometry is proposed based on correlation residuals. The procedure is applied to analyze one loading cycle of a fatigue-cracked nodular graphite cast iron sample by using computed tomography pictures. Subvoxel crack openings are revealed and measured. To cite this article: J. Réthoré et al., C. R. Mecanique 336 (2008).     

Physical and perceptual estimation of differences between loudspeakers

Differentiating the restitution of timbre by several loudspeakers may result from standard measurements, or from listening tests. This work proposes a protocol keeping a close relationship between the objective and perceptual evaluations: the stimuli are musical excerpts, and the measuring environment is a standard listening room. The protocol involves recordings made at a listener position, and objective dissimilarities are computed using an auditory model simulating masking effects. The resulting data correlate very well with listening tests using the same recordings, and show similar dependencies on the major parameters identified from the dissimilarity matrices. To cite this article: M. Lavandier et al., C. R. Mecanique 334 (2006).     

Solutions exactes de fissure d'interface sous contact frottant avec un milieu indéformableExact solutions of the interface crack between elastic and rigid bodies under contact with friction

One considers an interface crack between an elastic half-plane and a rigid half-plane, in the presence of Coulomb's friction. There exists two singular solutions at the semi-infinite crack tip, which correspond physically to the push-in and the pull-out of a rigid fiber in an elastic matrix. The exact solutions show that only the mode II is present and there is no oscillatory behavior of the stress and the displacement near the crack tip, but an oscillatory behavior is observed at the transition point with the stress free zone. There exists four types of singular solutions for finite crack in bounded medium, but only one in an infinite medium. To cite this article: H.D. Bui, A. Oueslati, C. R. Mecanique 332 (2004).     

Chaos synchronization on the N-torus and cryptography

A class of chaotic dynamical systems on the N-dimensional torus is proposed for masking some information in secure communications. The information is then recovered thanks to a chaos synchronization process. To cite this article: L. Rosier et al., C. R. Mecanique 332 (2004).

Résumé

Nous proposons une classe de systèmes chaotiques sur le tore N-dimensionnel pour masquer une information à transmettre dans une communication sécurisée. Cette information est ensuite reconstruite à l'aide d'un mécanisme de synchronisation du chaos. Pour citer cet article : L. Rosier et al., C. R. Mecanique 332 (2004).     

Injection coupling with high amplitude transverse modes: Experimentation and simulation

High frequency combustion instabilities have technical importance in the design of liquid rocket engines. These phenomena involve a strong coupling between transverse acoustic modes and combustion. They are currently being investigated by combining experimentation and numerical simulations. On the experimental level, the coupling is examined in a model scale system featuring a multiple injector combustor (MIC) comprising five coaxial injectors fed with liquid oxygen and gaseous methane. This system is equipped with a novel VHAM actuator (Very High Amplitude Modulator) which comprises two nozzles and a rotating toothed wheel blocking the nozzles in an alternate fashion. This device was designed to obtain the highest possible levels of transverse oscillation in the MIC. After a brief review of the VHAM, this article reports cold flow experiments using this modulator. Velocity maps obtained under resonant conditions using the VHAM are examined at different instants during a cycle of oscillation. Experimental data are compared with numerical pressure and velocity fields obtained from an acoustic solver. The good agreement observed in the nozzle vicinity indicates that numerical simulations can be used to analyze the complex flow field generated by the VHAM. To cite this article: Y. Mery et al., C. R. Mecanique 337 (2009).     

On the slow gravity-driven migration of arbitrary clusters of small solid particles

A new approach is advocated to compute at a low cpu time cost the rigid-body motions of settling solid particles when inertial effects are negligible. In addition to the relevant boundary-integral equations, the numerical implementation and a few convincing benchmark tests we address two configurations of equivalent spheres and spheroids, i.e. that exhibit when isolated the same settling velocity. To cite this article: A. Sellier, C. R. Mecanique 332 (2004).

Résumé

On propose une approche originale pour déterminer le mouvement d'une assemblée de particules solides et de formes arbitraires soumise à l'action de la pesanteur dans l'approximation de Stokes. Outre les intégrales de frontière et la méthode numérique associées on présente quelques comparaisons et examine le cas de deux configurations de sphères et ellipsoides de révolution équivalents, c'est-à-dire dotés lorsqu'ils sont seuls de la même vitesse de sédimentation. Pour citer cet article : A. Sellier, C. R. Mecanique 332 (2004).     

A DES method applied to a Backward Facing Step reactive flow

Hybrid Reynolds Averaged Navier Stokes–Large Eddy Simulation is a trend which is becoming of common use in aerodynamics but has seldom been employed to simulate reactive flows. Such methods, like the Delayed Detached Eddy Simulation (DDES) presented in this article, have been created to treat near wall flows with a RANS approach while switching to LES in the separated flow region. It is indeed an affordable solution to simulate complex and unsteady compressible flows and to have access to accurate skin friction and wall thermal fluxes. In order to validate this technique in combustion, we chose a simple and well documented Backward Facing Step combustor. To account for turbulent combustion a Dynamic Thickened Flame was used. The results obtained on this case show a good agreement with the experimental database and are of the same quality as LES in the separated region for both inert and reactive flows. To cite this article: B. Sainte-Rose et al., C. R. Mecanique 337 (2009).     

Edge singularities and structure of the 3-D Williams expansion

The elastic solution in a vicinity of a re-entrant wedge can be described by a Williams like expansion in terms of powers of the distance to a point on the edge. This expansion has a particular structure due to the invariance of the problem by translation parallel to the edge. We show here that some terms, so-called primary solutions, derive directly from solutions to the 2-D corner problem posed in the orthogonal cross section of the domain. The others, baptized shadow functions, derive of the primary solutions by integration along the axis parallel to the edge. This 3-D Williams expansion is shown to be equivalent to the edge expansion proposed by Costabel et al. [M. Costabel, M. Dauge, Z. Yosibash, A quasidual function method for extracting edge stress intensity functions, SIAM J. Math. Anal. 35 (5) (2004) 1177–1202]. To cite this article: T. Apel et al., C. R. Mecanique 336 (2008).     

Computing Green's function of elasticity in a half-plane with impedance boundary condition

This Note presents an effective and accurate method for numerical calculation of the Green's function G associated with the time harmonic elasticity system in a half-plane, where an impedance boundary condition is considered. The need to compute this function arises when studying wave propagation in underground mining and seismological engineering. To theoretically obtain this Green's function, we have drawn our inspiration from the paper by Durán et al. (2005), where the Green's function for the Helmholtz equation has been computed. The method consists in applying a partial Fourier transform, which allows an explicit calculation of the so-called spectral Green's function. In order to compute its inverse Fourier transform, we separate as a sum of two terms. The first is associated with the whole plane, whereas the second takes into account the half-plane and the boundary conditions. The first term corresponds to the Green's function of the well known time-harmonic elasticity system in (cf. J. Dompierre, Thesis). The second term is separated as a sum of three terms, where two of them contain singularities in the spectral variable (pseudo-poles and poles) and the other is regular and decreasing at infinity. The inverse Fourier transform of the singular terms are analytically computed, whereas the regular one is numerically obtained via an FFT algorithm. We present a numerical result. Moreover, we show that, under some conditions, a fourth additional slowness appears and which could produce a new surface wave. To cite this article: M. Durán et al., C. R. Mecanique 334 (2006).     

Effect of multiperforated plates on the acoustic modes in combustors

The analytical model derived by Howe assessing the acoustic effect of perforated plates has been implemented in a 3D Helmholtz solver. This solver allows one to compute the acoustic modes of industrial chambers taking into account the multiperforated plates present for the cooling of the walls. An academic test case consisting of two coaxial cylinders, with the inner one being perforated is used to validate the implementation in the general purpose AVSP code. This case is also used to show the effects of the presence of the plates. In particular, the sensitivity of the acoustic damping to the bias flow speed will be studied. A maximum absorption speed is shown, and the behaviour towards an infinite speed will be illustrated by the academic case. Computations are also conducted in the case of an industrial helicopter chamber. The value of the maximum absorption speed is discussed to explain why the modes are in fact not much absorbed by the perforated plates, and that the frequencies are the same as for walls. To cite this article: E. Gullaud et al., C. R. Mecanique 337 (2009).     

Impact of a bead on a rotating wall

We study experimentally the impact of a plastic bead on a rotating wall made of steel (velocity Ω; radial position x₀). The results show that the restitution coefficient is directly function of the impact velocity x₀Ω and is invariant by changing frame reference. The influence of the height of release of the particle on its angular velocity after impact is also studied. We observe an increase of the angular velocity with height followed by a saturation. We propose an interpretation for this evolution considering that the particle may roll without sliding during all the impact. This physical feature is not always taken into account in existing models of impact between rigid bodies. To cite this article: F. Rioual et al., C. R. Mecanique 336 (2008).     

Variance of the virtual displacement

We show that the affine structure of the 3-dimensional space is deeply enmeshed with the static laws expression. The relevance of tensorial rules for calculus in mechanics is thus enhanced. The virtual work principle is stated precisely but a little twist is given to the usual statements: the tensorial nature of the so-called virtual displacement vector is asserted to be covariant. To cite this article: C. Vallée et al., C. R. Mecanique 332 (2004).

Résumé

Nous montrons que la structure affine de l'espace tridimensionnel est fortement imbriquée avec l'expression des lois de la statique. La pertinence de l'application des règles du calcul tensoriel à la mécanique est ainsi renforcée. Le principe des travaux virtuels est établi précisément avec une seule entorse aux exposés classiques : la nature tensorielle de l'habituel vecteur déplacement virtuel est affirmée covariante. Pour citer cet article : C. Vallée et al., C. R. Mecanique 332 (2004).