Skip to Main content Skip to Navigation

Dynamique non linéaire des structures mécaniques: application aux systèmes à symétrie cyclique

Abstract : In an industrial context, the design of new mechanical systems requires long design processes in order to define and to anticipate the behavior of all the constitutive parts. In the particular case of aeronautical structures such as plane engines, design is especially critical since they have to meet various and strict needs (life duration, performances...). Then, anticipating vibratory behavior is very important as this provides information about cyclic solicitations and fatigue. Most often, numerical models are used to mimic the structure and mechanical behavior is simulated by solving a set of differential equations. In the case of industrial structures, such models can be quite large and their resolution very time-consuming. Moreover, in order to model experimental behavior realistically, it is often necessary to take nonlinear phenomena into account and thus increase the required computational effort. The work presented in this PhD deals with the study of mechanical nonlinear systems. It focuses on two principal directions : model reduction and multiple solutions computation. The goal of the first direction is to contribute to the building of numerical reduced order models usable in industrial context and to propose tools to exploit an interpret them. Particularly, Galerkin projection methods are investigated in the context of nonlinear systems reduction, showing that those methods are, under certain conditions, able to give a reliable picture of full system behavior. In the case of the harmonic balance method, complementary methods are also proposed to reduce the size of the algebraic equations system by using harmonic selection techniques. The presented methods are firstly illustrated and compared on a simple nonlinear beam example ; they are then applied to an industrial model of open rotor blade. The second direction of this work deals with the computation of multiple solutions arising in nonlinear dynamical systems. Indeed, it has been shown that such systems can present different stable configurations for a given solicitation. The objective here is to provide tools for computing such multiple solutions. We only consider the case of periodic solutions for systems with polynomial nonlinearities, treated with harmonic balance method. These hypotheses enable one to search for multiple states as solutions of polynomial algebraic systems of equations, for which some methods exist to compute the entire set of solutions. In particular, we propose to use methods relying on Groebner basis computation, in order to compute the whole set of solutions. The proposed methods are illustrated and compared on simple examples, showing that even such simple systems can present very complex dynamical behavior.
Complete list of metadatas

Cited literature [1 references]  Display  Hide  Download
Contributor : Aurelien Grolet <>
Submitted on : Friday, March 9, 2018 - 3:14:04 PM
Last modification on : Thursday, January 2, 2020 - 12:56:30 AM
Long-term archiving on: : Sunday, June 10, 2018 - 2:36:33 PM


Files produced by the author(s)


Distributed under a Creative Commons Attribution 4.0 International License


  • HAL Id : tel-01727750, version 1



Aurelien Grolet. Dynamique non linéaire des structures mécaniques: application aux systèmes à symétrie cyclique. Vibrations [physics.class-ph]. Ecole centrale de Lyon, 2013. Français. ⟨tel-01727750⟩



Record views


Files downloads