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Stochastic bifurcations of a nonlinear acousto-elastic system
W. Dheelibun Remigius,
Published in American Society of Mechanical Engineers (ASME)
2018
Volume: 4
   
Issue: 1
Abstract
The nonlinear stochastic behavior of a nonconservative acousto-elastic system is in focus in the present work. The deterministic acousto-elastic system consists of a spinning disk in a compressible fluid filled enclosure. The nonlinear rotating plate dynamics is coupled with the linear acoustic oscillations of the surrounding fluid, and the coupled field equations are discretized and solved at various rotation speeds. The deterministic system reveals the presence of a supercritical Hopf bifurcation when a specific coupled mode undergoes a flutter instability at a particular rotation speed. The effect of randomness associated with the damping parameters are investigated and quantified on the coupled dynamics and the stochastic bifurcation behavior is studied. The quantification of the parametric randomness has been undertaken by means of a spectral projection based polynomial chaos expansion (PCE) technique. From the marginal probability density functions (PDFs), it is observed that the stochastic system exhibits stochastic phenomenological bifurcations (P-bifurcation). The study provides insights into the behavior of the stochastic system during its P-bifurcation with reference to the deterministic Hopf bifurcation. Copyright © 2018 by ASME.
About the journal
JournalASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part B: Mechanical Engineering
PublisherAmerican Society of Mechanical Engineers (ASME)
ISSN23329017
Open AccessNo
Concepts (17)
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    Bifurcation (mathematics)
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    ELASTICITY
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    Nonlinear equations
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    Probability density function
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    Random processes
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    Rotation
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    Shafts (machine components)
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    Stochastic systems
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    ACOUSTIC OSCILLATION
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    COUPLED FIELD EQUATIONS
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    DETERMINISTIC SYSTEMS
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    MARGINAL PROBABILITY
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    Polynomial chaos expansion (pce)
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    SPECTRAL PROJECTIONS
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    STOCHASTIC BIFURCATION
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    Supercritical hopf bifurcation
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    Hopf bifurcation