Pizzolante, Francesco Battarra, Mattia Mucchi, Emiliano Cochelin, Bruno
The present work proposes the Asymptotic Numerical Method (ANM) combined to the Harmonic Balance Method (HBM) as a valuable approach to solve the nonlinear dynamics of gear pairs. The ANM is a continuation method based on high-order Taylor series expansion of the computed solution branch. The HBM is a periodic solution representation method based o...
DEBEURRE, Marielle GROLET, Aurélien COCHELIN, Bruno THOMAS, Olivier
An original method for the simulation of the dynamics of highly flexible slender structures is presented. The flexible structures are modeled via a finite element (FE) discretization of a geometrically exact two-dimensional beam model, which entirely preserves the geometrical nonlinearities inherent in such systems where the rotation of the cross-s...
Debeurre, Marielle Grolet, Aurélien Cochelin, Bruno Thomas, Olivier
International audience
Debeurre, Marielle Grolet, Aurelien Cochelin, Bruno Thomas, Olivier
An original method for the simulation of the dynamics of highly flexible slender structures is presented. The flexible structures are modeled via a finite element (FE) discretization of a geometrically exact two-dimensional beam model, which entirely preserves the geometrical nonlinearities inherent in such systems where the rotation of the crossse...
Debeurre, Marielle Grolet, Aurélien Mattei, Pierre-Olivier Cochelin, Bruno Thomas, Olivier
A novel method for the numerical computation of the nonlinear normal modes (NNMs) of a highly flexible cantilever beam is presented. The flexible cantilever is modeled using a 2D finite element discretization of the geometrically exact beam model, wherein geometric nonlinearities relating to the rotation are kept entirely intact. The model is then ...
Givois, Arthur
Cette thèse de doctorat concerne l'analyse et la modélisation de structures minces en vibrations de grande amplitude avec transduction piézoélectrique. Ce type de système électromécanique est utilisé dans de nombreuses applications, telles que les microsystèmes électromécaniques (MEMS) ainsi que les systèmes de contrôle ou de récupération d’énergie...
Grenat, Clément Baguet, Sébastien Lamarque, Claude-Henri Dufour, Régis
The aim of this paper is to provide an efficient multi-parametric recursive continuation method of specific solution points of a nonlinear dynamical system such as bifurcation points. The proposed method explores the topology of specific points found on the frequency response curves by tracking extremum points in the successive codimensions of the ...
Grenat, Clément Baguet, Sébastien Dufour, Régis Lamarque, Claude-Henri
This work presents a method for calculating non-conservative Nonlinear Normal Modes (NNMs) based on the conservative NNMs. A specific fictional force is added to the initial non-conservative equation of motion in order to insure the energy balance of the damped nonlinear equation. By doing so, conservative equations corresponding to Phase and Energ...
Bonalli, Riccardo Hérissé, Bruno Trélat, Emmanuel
In this paper, we propose a strategy to solve endo-atmospheric launch vehicle optimal control problems using indirect methods. More specifically, we combine shooting methods with an adequate continuation algorithm, taking advantage of the knowledge of an analytical solution of a simpler problem. This procedure is resumed in two main steps. We first...
Xie, Lihan Baguet, Sébastien Prabel, Benoit Dufour, Régis
The aim of this paper is to provide an efficient frequency-domain method for bifurcation analysis of nonlinear dynamical systems. The proposed method consists in directly tracking the bifurcation points when a system parameter such as the excitation or nonlinearity level is varied. To this end, a so-called extended system comprising the equation of...
