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  • 1
    Electronic Resource
    Electronic Resource
    Nonlinear dynamics 10 (1996), S. 333-357 
    ISSN: 1573-269X
    Keywords: Pipes ; parametric excitation ; nonlinearity ; chaos ; multiple time scales ; harmonic balancing ; stability
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Chaotic motions of a simply supported nonlinear pipe conveying fluid with harmonie velocity fluetuations are investigated. The motions are investigated in two flow velocity regimes, one below and above the critical velocity for divergence. Analyses are carried out taking into account single mode and two mode approximations in the neighbourhood of fundamental resonance. The amplitude of the harmonic velocity perturbation is considered as the control parameter. Both period doubling sequence and a sudden transition to chaos of an asymmetric period 2 motion are observed. Above the critical velocity chaos is explained in terms of periodic motion about the equilibrium point shifting to another equilibrium point through a saddle point. Phase plane trajectories, Poincaré maps and time histories are plotted giving the nature of motion. Both single and two mode approximations essentially give the same qualitative behaviour. The stability limits of trivial and nontrivial solutions are obtained by the multiple time scale method and harmonic balance method which are in very good agreement with the numerical results.
    Type of Medium: Electronic Resource
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