S. Pernot

Application of neural networks to the modelling of some constitutive laws

This study investigates the modelling of constitutive laws of materials by neural networks. Material behaviour is no longer represented mathematically but is described by neuronal modelling. The main aim is to build a neural network directly from experimental results (the learning phase). We give several examples of constitutive laws (Hooke, Sargin, etc.) using a backpropagation algorithm. Then we show that abilities of adjustment, memorisation and anticipation of neural networks permit us to develop a method of classification of constitutive laws.

A Wavelet-Balance Method to Investigate the Vibrations of Nonlinear Dynamical Systems

The scope of this paper is to introduce a new wavelet-balanceprocedure allowing to give a genuine time-scale representation ofvibrations of nonlinear dynamical systems by adopting a waveletmultiresolution approach. In a former paper, a wavelet-Galerkinoriented procedure was developed to analyze vibrations of lineartime-periodic systems. The topic is here to extend the process tothe nonlinear case using a perturbation technique. The underlyingidea consists in successively balancing the linearized equationsof motion into wavelet spaces with increasing resolution scales.Here we demonstrate the wavelet-balance procedure may accuratelyexhibit both transient and stationary vibrations of any nonlinearproblem in general, whatever smooth nonlinearity shape or externalforcing may be. In addition, wavelets inherit of fairly goodtime-frequency localization properties that are likely to permitthe investigation of strong nonlinear problems. Numericalexperiments achieved on a well known Duffing oscillator involvinga cubic nonlinearity then illustrate the procedure. Simulationsattest the relevance of the method by comparison with eitherpurely numerical results obtained with a Runge–Kutta integrationscheme or with an analytical study based on the multiple scalesmethod. We demonstrate that this semi-analytical semi-numericalperturbation method permits to capture stable limit cycles of theDuffing oscillator and its related amplitude spectrum response orstill responses to pulse-like excitations. Finally, key propertiesof the method are discussed and future prospective works areoutlined.

Nonlinear Energy Pumping With Strongly Nonlinear Coupling: Identification of Resonance Captures in Numerical and Experimental Results

The present work aims to study the effect of a nonlinear energy sink (NES) with relatively small mass on the dynamics of a coupled system under impulsion with free oscillations. The process of energy transfer is governed by structure of damped nonlinear normal modes of the system. In particular the energy pumping occurs if the nonlinear normal mode is quickly broken down with rather abrupt decrease of both amplitudes, i.e. a bifurcation (brutal change of frequency) is associated with the breakdown of the resonant regime of vibrations. The theoretical effects are experimentally verified with a mechanical experiment which confirms the above results by using a small building model. To identify those frequency migrations, a new wavelet-based methodology, namely quasi-continuous wavelet method, is used.© 2005 ASME

Nonlinear Parametric Resonances in a Stay of the Iroise Cable-Stayed Bridge: Analytical Model and Experiments

Recent experimental campaigns led on the Iroise cable stayed bridge near Brest, France, revealed repeated vibratory events in some cable stays likely to provoke durability problems. A spectral analysis emphasized two regimes in which either the fundamental or the third cable mode were excited. Yet, wavelet scalograms of tests allowed to exhibit a global pylon mode excited by traffic environment through deck-cable-tower interaction and which again excites local cable modes by means of a nonlinear parametric resonance mechanism with vertical bending modes of the girder. Preliminary results are introduced as an attempt to explain such a scenario.Copyright