2,338 research outputs found
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
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
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 . 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 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
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
Robust correlation analyses: false positive and power validation using a new open source Matlab toolbox
Pearson’s correlation measures the strength of the association between two variables. The technique is, however, restricted to linear associations and is overly sensitive to outliers. Indeed, a single outlier can result in a highly inaccurate summary of the data. Yet, it remains the most commonly used measure of association in psychology research. Here we describe a free Matlab(R) based toolbox (http://sourceforge.net/projects/robustcorrtool/) that computes robust measures of association between two or more random variables: the percentage-bend correlation and skipped-correlations. After illustrating how to use the toolbox, we show that robust methods, where outliers are down weighted or removed and accounted for in significance testing, provide better estimates of the true association with accurate false positive control and without loss of power. The different correlation methods were tested with normal data and normal data contaminated with marginal or bivariate outliers. We report estimates of effect size, false positive rate and power, and advise on which technique to use depending on the data at hand
LIMO EEG: A Toolbox for hierarchical LInear MOdeling of ElectroEncephaloGraphic data
Magnetic- and electric-evoked brain responses have traditionally been analyzed by comparing the peaks or mean amplitudes of signals from selected channels and averaged across trials. More recently, tools have been developed to investigate single trial response variability (e.g., EEGLAB) and to test differences between averaged evoked responses over the entire scalp and time dimensions (e.g., SPM, Fieldtrip). LIMO EEG is a Matlab toolbox (EEGLAB compatible) to analyse evoked responses over all space and time dimensions, while accounting for single trial variability using a simple hierarchical linear modelling of the data. In addition, LIMO EEG provides robust parametric tests, therefore providing a new and complementary tool in the analysis of neural evoked responses
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