A HARMONIC-BASED METHOD FOR COMPUTING THE STABILITY OF PERIODIC OSCILLATIONS OF NON-LINEAR STRUCTURAL SYSTEMS

Abstract : 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.
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Communication dans un congrès
ASME IDETC 2010 International Design Engineer ing Technical Conferences, Aug 2010, Montreal, Canada. 2010, 〈10.1115/DETC2010-28407〉
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Olivier Thomas, Arnaud Lazarus, Cyril Touzé. A HARMONIC-BASED METHOD FOR COMPUTING THE STABILITY OF PERIODIC OSCILLATIONS OF NON-LINEAR STRUCTURAL SYSTEMS. ASME IDETC 2010 International Design Engineer ing Technical Conferences, Aug 2010, Montreal, Canada. 2010, 〈10.1115/DETC2010-28407〉. 〈hal-01148758〉

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