The Method of Strained Coordinates for Vibrations with Weak Unilateral Springs

We study some spring mass models for a structure having a unilateral spring of small rigidity $\epsilon$. We obtain and justify an asymptotic expansion with the method of strained coordinates with new tools to handle such defects, including a non negligible cumulative effect over a long time: T_\eps \sim \eps^{-1} as usual; or, for a new critical case, we can only expect: T_\eps \sim \eps^{-1/2}. We check numerically these results and present a purely numerical algorithm to compute "Non linear Normal Modes" (NNM); this algorithm provides results close to the asymptotic expansions but enables to compute NNM even when $\epsilon$ becomes larger

Double scale analysis of periodic solutions of some non linear vibrating systems

We consider {\it small solutions} of a vibrating system with smooth non-linearities for which we provide an approximate solution by using a double scale analysis; a rigorous proof of convergence of a double scale expansion is included; for the forced response, a stability result is needed in order to prove convergence in a neighbourhood of a primary resonance.Comment: 36 page

Periodic solutions of o.d.e. systems with a lipchitz non linearity

In this report, we address differential systems with Lipschitz non linearities; this study is motivated by the subject of vibrations of structures with unilateral springs or non linear stress-strain law close to the linear case. We consider existence and solution with fixed point methods; this method is constructive and provides a numerical algorithm which is under study. We describe the method for a static case example and we address periodic solutions of differential systems arising in the vibration of structures

Finite Elements for a Beam System With Nonlinear Contact Under Periodic Excitation

Solar arrays are structures which are connected to satellites; during launch, they are in a folded position and submitted to high vibrations. In order to save mass, the flexibility of the panels is not negligible and they may strike each other; this may damage the structure. To prevent this, rubber snubbers are mounted at well chosen points of the structure; a prestress is applied to the snubber; but it is quite difficult to check the amount of prestress and the snubber may act only on one side; they will be modeled as one sided springs (see figure 2). In this article, some analysis for responses (displacements) in both time and frequency domains for a clamped-clamped Euler-Bernoulli beam model with a spring are presented. This spring can be unilateral or bilateral fixed at a point. The mounting (beam +spring) is fixed on a rigid support which has a sinusoidal motion of constant frequency. The system is also studied in the frequency domain by sweeping frequencies between two fixed values, in order to save the maximum of displacements corresponding to each frequency. Numerical results are compared with exact solutions in particular cases which already exist in the literature. On the other hand, a numerical and theoretical investigation of nonlinear normal mode (NNM) can be a new method to describe nonlinear behaviors, this work is in progress

Time course and robustness of ERP object and face differences

Conflicting results have been reported about the earliest “true” ERP differences related to face processing, with the bulk of the literature focusing on the signal in the first 200 ms after stimulus onset. Part of the discrepancy might be explained by uncontrolled low-level differences between images used to assess the timing of face processing. In the present experiment, we used a set of faces, houses, and noise textures with identical amplitude spectra to equate energy in each spatial frequency band. The timing of face processing was evaluated using face–house and face–noise contrasts, as well as upright-inverted stimulus contrasts. ERP differences were evaluated systematically at all electrodes, across subjects, and in each subject individually, using trimmed means and bootstrap tests. Different strategies were employed to assess the robustness of ERP differential activities in individual subjects and group comparisons. We report results showing that the most conspicuous and reliable effects were systematically observed in the N170 latency range, starting at about 130–150 ms after stimulus onset

Quantifying the time course of visual object processing using ERPs: it's time to up the game

Hundreds of studies have investigated the early ERPs to faces and objects using scalp and intracranial recordings. The vast majority of these studies have used uncontrolled stimuli, inappropriate designs, peak measurements, poor figures, and poor inferential and descriptive group statistics. These problems, together with a tendency to discuss any effect p < 0.05 rather than to report effect sizes, have led to a research field very much qualitative in nature, despite its quantitative inspirations, and in which predictions do not go beyond condition A > condition B. Here we describe the main limitations of face and object ERP research and suggest alternative strategies to move forward. The problems plague intracranial and surface ERP studies, but also studies using more advanced techniques – e.g., source space analyses and measurements of network dynamics, as well as many behavioral, fMRI, TMS, and LFP studies. In essence, it is time to stop amassing binary results and start using single-trial analyses to build models of visual perception

Flutter of articulated pipes at finite amplitude

Previous studies of the behavior of pipes conveying fluid have assumed that the fluid velocity relative to the pipe is a known quantity and is unaffected by the motion of the pipe. This approach eliminates the need to find the flow equations of motion, and is adequate for infinitesimal transverse amplitudes of motion of the pipe system, but is incapable of predicting what will be the effect of larger amplitudes. This last shortcoming may be of importance when flow velocities are near critical velocities, that is, velocities at which the system begins to flutter. It is the purpose of the present study to investigate in greater detail the dynamic behavior of pipes in the vicinity of critical velocities

Les figures de la laïcité postsoviétique en Russie

L’État russe est formellement un État laïque. Plusieurs éléments tendent pourtant à prouver que le principe de laïcité a bel et bien fait long feu en Russie : l’absence de vrai débat sur cette question précise, le contrôle accru de l’État sur les forces sociales, la visibilité de plus en plus grande de l’Église russe dans l’espace public et les persécutions dont sont victimes de nombreuses minorités religieuses. Au-delà de ce constat, fondé sur une approche normative de la laïcité, une réflexion sur la construction sociale des relations entre Églises et État permet de saisir le seuil de laïcisation atteint par la Russie. Celui-ci est le résultat de conflits et de compromis entre acteurs sociaux qui se réclament des principes laïques ou qui, à l’inverse, les condamnent, pour défendre leurs positions. Les relations entre le politique et le religieux sont définies en Russie selon le principe du « pluralisme hiérarchisé » et s’expliquent par une prédominance, dans les représentations, du collectif sur l’individu. En tant qu’élément central de la Tradition, la religion est un facteur légitimateur de l’ordre social. Quant aux représentations de la laïcité, elles se nourrissent autant de l’héritage soviétique que de perceptions libérales. [Premier paragraphe