The Karoo triple junction questioned : evidence from Jurassic and Proterozoc 40Ar/39Ar ages and geochemistry of the giant Okavango dyke swarm (Botswana).

The lower Jurassic Karoo-Ferrar magmatism represents one of the most important Phanerozoic continental flood basalt (CFB) provinces. The Karoo CFB province is dominated by tholeiitic traps and apparently radiating giant dyke swarms covering altogether ca. 3 106 km2. This study focuses on the giant N110j-trending Okavango dyke swarm (ODS) stretching over 1500 km across Botswana. This dyke swarm represents the main (failed) arm of the so-called Karoo triple junction that is generally considered as a key marker of the impingement of the Karoo starting mantle plume head. ODS dolerites yield six new plagioclase 40Ar/39Ar plateau (and miniplateau) ages ranging from 178.7F0.7 and 180.9F1.3 Ma. The distribution of the ages along a narrow Gaussian curve suggests a short period of magmatic activity centered around 179 Ma, i.e., f5 Ma younger than the emplacement age of Karoo mafic magmas in the southern part of the Karoo CFB province (f184). This age difference indicates that Karoo magmatism does not represent a short-lived event as is generally the case for most CFB but lasted at least 5Ma over the whole province. In addition, small clusters of plagioclase separated from 28 other dykes and measured by "speedy" step-heating experiments (with mostly two to three steps), gave either "Karoo" or Proterozoic ages.Integrated ages of the Proterozoic rocks range from 851 6 to 1672 7 Ma, and one plateau age (959.1 4.6 Ma) and one possibly geologically significant weighted mean age (982.7 4.0 Ma) were obtained. Proterozoic and Karoo mafic rocks are petrographically similar, but Proterozoic dykes display clear geochemical differences (e.g., TiO 22.1%). Geochemical data combined with available Ar/Ar dates allow the identification of the two groups within a total set of 77 dykes investigated: f10% of the bulk ODS dykes are Proterozoic. Thus, the Jurassic Karoo ODS dykes were emplaced along reactivated Proterozoic structures and there is no pristine Jurassic Nuanetsi triple junction as commonly proposed. This throws into doubt the validity of the "active plume head" Karoo CFB rift models as being responsible for the observed "triple junction" dyke geometr

Uncertainty quantification for post-buckling analysis of cylindrical shells with experimental comparisons

International audienceThe present work concerns the experimental identification of an uncertain nonlinear computational model in the context of the post-buckling analysis of a cylindrical shell. Theproposed methodology is adapted to the analysis of large static deformations of geometrically nonlinear structural systems in the presence of both system parameters uncertainties and model uncertainties. The available experimental data is made up of the nonlinear static deflection of a cylindrical shell. The deterministic nonlinear computational model is constructed using the finite element method and the corresponding nonlinear response is used as a reference deterministic solution for which a reduced-order basis is deduced using the POD analysis. The mean reduced-order nonlinear computational model is then explicitly constructed. The nonparametric probabilistic methodology for constructing the uncertain nonlinear reduced-order computational model is used. Finally, the experimental identification of the uncertain nonlinear computational model is carried out in order to validate the proposed methodology

Effects of structural uncertainties on the nonlinear elastic post-buckling behavior of a cylindrical shell. Stochastic computational modeling and comparison with experiments

International audienceA methodology for analyzing the response of geometrically nonlinear structural systems in presence of both system parameters uncertainties and model uncertainties is presented in the context of the robust identification of uncertain nonlinear computational models using experiments. This methodology requires the knowledge of a reference calculation issued from the mean model in order to obtain the POD-basis used for the construction of the mean reduced nonlinear computational model. This explicit construction is carried out in the context of three-dimensional solid finite elements. This allows the uncertain nonlinear computational model to be constructed in any general case with the nonparametric probabilistic approach. A numerical example is then carried out in order to show the efficiency of the method

Robust Analysis of Design in Vibration of Turbomachines

International audienceIn the context of turbomachinery design, a small variation in the blade characteristics due to manufacturing tolerances can affect the structural symmetry creating mistuning which increases the forced response. However, it is possible to detune the mistuned system in order to reduce the forced response amplification. The main technologic solutions to introduce detuning are based on modifying blade material properties, the interface between blade and disk, or the blade shape. This paper presents a sensitivity analysis of mistuning for a given detuning in unsteady aeroelasticity. Detuning is performed by modifying blade shapes. The different kinds of blades obtained by those modifications are then distributed on the disk circumference. A new reduced-order model of the detuned disk is constructed using the cyclic modes of the different sectors which can be obtained from a usual cyclic symmetry modal analysis. Finally a stochastic analysis using a nonparametric probabilistic method to take model and system parameters uncertainties into account in the computational model is performed

Robust analysis of design in vibration of turbomachines

International audienceIn the context of turbomachinery design, a small variation in the blade characteristics due to manufacturing tolerances can affect the structural symmetry creating mistuning which increases the forced response. However, it is possible to detune the mistuned system in order to reduce the forced response amplification. The main technologic solutions to introduce detuning are based on modifying blade material properties, the interface between blade and disk, or the blade shape. This paper presents a sensitivity analysis of mistuning for a given detuning in unsteady aeroelasticity. Detuning is performed by modifying blade shapes. The different kinds of blades obtained by those modifications are then distributed on the disk circumference. A new reduced-order model of the detuned disk is constructed using the cyclic modes of the different sectors which can be obtained from a usual cyclic symmetry modal analysis. Finally a stochastic analysis using a nonparametric probabilistic method to take model and system parameters uncertainties into account in the computational model is performed

Uncertain rotating dynamical systems with cyclic geometry

International audienceThe aim of this paper is to propose probabilistic methodologies for the dynamic analysis of the mistuning of rotating bladed-disks with cyclic symmetry in the low frequency range. A recent nonparametric probabilistic model of random uncertainties is used for modeling the random uncertainties in the context of the blade mistuning. An inverse probabilistic approach, based on the identification of the dispersion parameters controlling the nonparametric probability model with respect to the blade tolerances is constructed in order to define the blade geometric tolerances yielding a given probability level of the dynamic amplification of the forced response. A numerical application is presented in details

Robust analysis of design in vibration of turbomachines

International audienceIn the context of turbomachinery design, a small variation in the blade characteristics due to manufacturing tolerances can affect the structural symmetry creating mistuning which increases the forced response. However, it is possible to detune the mistuned system in order to reduce the forced response amplification. This paper presents a robustness analysis of mistuning for a given detuning in blade geometry. Detuning is performed by modifying blade shapes. The different types of blades, obtained by those modifications, are then distributed on the disk circumference. A new reducedorder model of the detuned disk is introduced. It is based on the use of the cyclic modes of the different sectors which can be obtained from a usual cyclic symmetry modal analysis. Finally, the robustness of the computational model responses with respect to uncertainties, is performed with a stochastic analysis using a nonparametric probabilistic approach of uncertainties which allows both the system-parameter uncertainties and the modeling errors to be taken into account