%0 Conference Proceedings
%T A harmonic-based method for computing the stability of periodic oscillations of non-linear structural systems
%+ Laboratoire de Mécanique des Structures et des Systèmes Couplés (LMSSC)
%+ Unité de Mécanique (UME)
%A Thomas, Olivier
%A Lazarus, Arnaud
%A Touzé, Cyril
%< avec comité de lecture
%B ASME IDETC 2010 International Design Engineer ing Technical Conferences
%C Montreal, Canada
%8 2010-08-15
%D 2010
%R 10.1115/DETC2010-28407
%Z Engineering Sciences [physics]/Mechanics [physics.med-ph]
%Z Nonlinear Sciences [physics]
%Z Engineering Sciences [physics]/Mechanics [physics.med-ph]/Vibrations [physics.class-ph]Conference papers
%X In this paper, we present a validation on a practical example of a harmonic-based numerical method to determine the local stability of periodic solutions of dynamical systems. Based on Floquet theory and Fourier series expansion (Hill method), we propose a simple strategy to sort the relevant physical eigenval-ues among the expanded numerical spectrum of the linear periodic system governing the perturbed solution. By mixing the Harmonic Balance Method and Asymptotic Numerical Method continuation technique with the developed Hill method, we obtain a purely-frequency based continuation tool able to compute the stability of the continued periodic solutions in a reduced computation time. This procedure is validated by considering an externally forced string and computing the complete bifurcation diagram with the stability of the periodic solutions. The particular coupled regimes are exhibited and found in excellent agreement with results of the literature, allowing a method validation.
%G English
%2 https://ensta-paris.hal.science/hal-01148758/document
%2 https://ensta-paris.hal.science/hal-01148758/file/ASME2010OTALCT.pdf
%L hal-01148758
%U https://ensta-paris.hal.science/hal-01148758
%~ ENSTA
%~ CNAM
%~ ENSTA_UME
%~ LMSSC-CNAM
%~ HESAM-CNAM
%~ HESAM