Research Papers

Stochastic Bifurcations of a Nonlinear Acousto-Elastic System

[+] Author and Article Information
W. Dheelibun Remigius

Department of Aerospace Engineering,
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

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 4(1), 011007 (Sep 07, 2017) (7 pages) Paper No: RISK-17-1035; doi: 10.1115/1.4037460 History: Received February 26, 2017; Revised May 23, 2017

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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Fig. 1

Schematic of a spinning disk in a compressible fluid filled enclosure

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Fig. 2

Variation of the imaginary part of the coupled frequencies with disk rotation speed

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Fig. 3

Variation of the real part of the coupled frequencies with disk rotation speed

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Fig. 4

Deterministic bifurcation diagram of the (3, 0)R mode for Cr = 0.01 and Cg = 0.1

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Fig. 5

Time response of (3, 0)R mode at Ω = 5

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Fig. 6

Time response of (3, 0)R mode at Ω = 14.8

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Fig. 7

Random Cr: PDF, pA(a), for Ω = 4 at t = 1250. In all figures under Sec. 3, n indicates the order of PCE expansion, and p indicates the total number of collocation points.

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Fig. 8

Random Cr: PDF, pA(a) for Ω = 6.81 at t = 1250

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Fig. 9

Random Cr: PDF, pA(a), for Ω = 12 at t = 1250

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Fig. 10

Random Cr: Error bar plot on stochastic bifurcation

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Fig. 11

Random Cg: PDF, pA(a), for Ω = 4 at t = 1490

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Fig. 12

Random Cg: PDF, pA(a), for Ω = 6.81 at t = 1490

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Fig. 13

Random Cg: PDF, pA(a), for Ω = 12 at t = 1490

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Fig. 14

Random Cg: Error bar plot on stochastic bifurcation




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