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.
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March 2018
Research-Article
Stochastic Bifurcations of a Nonlinear Acousto-Elastic System
W. Dheelibun Remigius,
W. Dheelibun Remigius
Department of Aerospace Engineering,
IIT Madras,
Chennai 600036, India
e-mail: remigius.dheelibun@gmail.com
IIT Madras,
Chennai 600036, India
e-mail: remigius.dheelibun@gmail.com
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Sunetra Sarkar
Sunetra Sarkar
Department of Aerospace Engineering,
IIT Madras,
Chennai 600036, India
e-mail: sunetra.sarkar@gmail.com
IIT Madras,
Chennai 600036, India
e-mail: sunetra.sarkar@gmail.com
Search for other works by this author on:
W. Dheelibun Remigius
Department of Aerospace Engineering,
IIT Madras,
Chennai 600036, India
e-mail: remigius.dheelibun@gmail.com
IIT Madras,
Chennai 600036, India
e-mail: remigius.dheelibun@gmail.com
Sunetra Sarkar
Department of Aerospace Engineering,
IIT Madras,
Chennai 600036, India
e-mail: sunetra.sarkar@gmail.com
IIT Madras,
Chennai 600036, India
e-mail: sunetra.sarkar@gmail.com
1Corresponding author.
Manuscript received February 26, 2017; final manuscript received May 23, 2017; published online September 7, 2017. Assoc. Editor: Yan Wang.
ASME J. Risk Uncertainty Part B. Mar 2018, 4(1): 011007 (7 pages)
Published Online: September 7, 2017
Article history
Received:
February 26, 2017
Revised:
May 23, 2017
Citation
Dheelibun Remigius, W., and Sarkar, S. (September 7, 2017). "Stochastic Bifurcations of a Nonlinear Acousto-Elastic System." ASME. ASME J. Risk Uncertainty Part B. March 2018; 4(1): 011007. https://doi.org/10.1115/1.4037460
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