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Complex and chaotic response of a non-linear oscillator with an isothermal gas spring

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Abstract

In this paper we study the dynamics of a non-linear one-degree-of-freedom system subjected to an external harmonic excitation, representing a simplified model for the synchronous hydraulic oscillations that can occur in the draft tube of Francis turbines at partial loads. The application of different typical numerical techniques has shown the existence of multiple coexisting periodic solutions, and the non-periodic bounded solutions which exhibit deterministic chaotic behaviour. The relevant strange attractor has been defined and the loss of memory associated with an exponential divergence in time of close initial conditions resulting in chaotic dynamics have been found and measured. A partial classification of qualitatively different dynamical behaviours for the system has been outlined in the control parameter space.

Sommario

In questo articolo viene studiata la dinamica di un sistema non-lineare ad un singolo grado di liberta' soggetto ad una forzante armonica esterna, rappresentante un modello semplificato per le oscillazioni idrauliche sincrone che hanno luogo nei diffusori delle turbine tipo Francis a carico parziale. Applicando differenti tecniche numeriche, viene mostrata l'esistenza di soluzioni periodiche multiple, oltre che soluzioni non-periodiche limitate con tipico comportamento caotico deterministico. L'attrattore strano corrispondente e' stato definito e caratterizzato: la perdita di memoria associata alla divergenza esponenziale di orbite inizialmente vicine, tipica della dinamica caotica, e' stata individuata e calcolata numericamente. Una prima parziale classificazione dei vari comportamenti dinamici per il sistema viene evidenziata attraverso la rappresentazione nello spazio parametrico.

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Authors and Affiliations

  1. E.N.E.L.-D.S.R.-C.R.I.S., via Ornato, 90, 14-20162, Milano, Italy

    M. Fanelli

  2. (Applied Mathematics Section), C.I.S.E., via Reggio Emilia, 39, 20090, Segrate (MI), Italy

    S. Sello

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  1. M. Fanelli
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  2. S. Sello
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Fanelli, M., Sello, S. Complex and chaotic response of a non-linear oscillator with an isothermal gas spring. Meccanica 27, 297–306 (1992). https://doi.org/10.1007/BF00424370

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  • DOI: https://doi.org/10.1007/BF00424370

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