Un élément fini de poutre fissurée application à la dynamique des arbres tournants

International audienceDans ce travail on présente une méthode originale de construction d'un élément fini de poutre affectée de fissurations. La souplesse additionnelle due à la présence des fissures est identifiée à partir de calculs éléments finis tridimensionnels tenant compte des conditions de contact unilatéral entre les lèvres. Cette souplesse est répartie sur toute la longueur de l'élément dont on se propose de construire la matrice de rigidité. La démarche permet un gain considérable en temps de calcul par rapport à la représentation nodale de la section fissurée lors de l'intégration temporelle de systèmes différentiels en dynamique des structures

Stability of hexagonal pattern in Rayleigh-Bénard convection for thermodependent shear-thinning fluids

International audienceStability of hexagonal patterns in Rayleigh–Bénard convection for shear-thinning fluids with temperature-dependent viscosity is studied in the framework of amplitude equations. The rheological behaviour of the fluid is described by the Carreau model and the relationship between the viscosity and the temperature is of exponential type. Ginzburg–Landau equations including non-variational quadratic spatial terms are derived explicitly from the basic hydrodynamic equations using a multiple scale expansion. The stability of hexagonal patterns towards spatially uniform disturbances (amplitude instabilities) and to long wavelength perturbations (phase instabilities) is analysed for different values of the shear-thinning degree α of the fluid and the ratio r of the viscosities between the top and bottom walls. It is shown that the amplitude stability domain shrinks with increasing shear-thinning effects and increases with increasing the viscosity ratio r . Concerning the phase stability domain which confines the range of stable wavenumbers, it is shown that it is closed for low values of r and becomes open and asymmetric for moderate values of r . With increasing shear-thinning effects, the phase stability domain becomes more decentred towards higher values of the wavenumber. Beyond the stability limits, two different modes go unstable: longitudinal and transverse modes. For the parameters considered here, the longitudinal mode is relevant only in a small region close to the onset. The nonlinear evolution of the transverse phase instability is investigated by numerical integration of amplitude equations. The hexagon–roll transition triggered by the transverse phase instability for sufficiently large reduced Rayleigh number ϵ is illustrated

Adoption of network technologies in the presence of converters

In many high-tech industries, the emergence of new digital technologies allows companies to develop converters to overcome technology incompatibility. In this paper, we analyze the effects of converter introduction on the adoption process of competing, incompatible technologies in the presence of network externalities. Converter introduction may accelerate, extend or reverse the technology lock-in process. We determine which conversion options are profitable for weak as well as for dominant incumbents, depending on the timing of converter introduction and the degrees of conversion. We find that the optimal strategy for weak incumbents is to introduce full one-way converters early. For dominant incumbents, the optimal conversion option is to provide two-way converters with partial compatibility for the users of the competing network at a later introduction time. We illustrate our analytical results with numerical examples.compatibility, consumer choice, converter, network externality, standards war, technology adoption,