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Technical Brief

Chaotic Motion in a Flexible Rotating Beam and Synchronization

[+] Author and Article Information
B. Sandeep Reddy

Department of Mechanical Engineering,
Indian Institute of Science,
Bangalore 560012, India
e-mail: bsandeep@mecheng.iisc.ernet.in

Ashitava Ghosal

Professor
Department of Mechanical Engineering,
Indian Institute of Science,
Bangalore 560012, India
e-mail: asitava@mecheng.iisc.ernet.in

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received November 5, 2016; final manuscript received January 10, 2017; published online February 8, 2017. Assoc. Editor: Hiroshi Yabuno.

J. Comput. Nonlinear Dynam 12(4), 044505 (Feb 08, 2017) (7 pages) Paper No: CND-16-1537; doi: 10.1115/1.4035825 History: Received November 05, 2016; Revised January 10, 2017

A rotating flexible beam undergoing large deformation is known to exhibit chaotic motion for certain parameter values. This work deals with an approach for control of chaos known as chaos synchronization. A nonlinear controller based on the Lyapunov stability theory is developed, and it is shown that such a controller can avoid the sensitive dependence of initial conditions seen in all chaotic systems. The proposed controller ensures that the error between the controlled and the original system, for different initial conditions, asymptotically goes to zero. A numerical example using the parameters of a rotating power generating wind turbine blade is used to illustrate the theoretical approach.

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References

Figures

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Fig. 1

Schematic of a rotating flexible beam (from Ref. [5]): (a) flexible rotating beam and (b) planar beam element

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Fig. 2

Synchronization errors without control for the undamped equations: (a) plot of e1(t), (b) plot of e2(t), (c) plot of e3(t), and (d) plot of e4(t)

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Fig. 3

Synchronization errors without control for the damped equations: (a) plot of e1(t), (b) plot of e2(t), (c) plot of e3(t), and (d) plot of e4(t)

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Fig. 4

Synchronization errors with control for the undamped equations: (a) plot of e1(t), (b) plot of e2(t), (c) plot of e3(t), and (d) plot of e4(t)

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Fig. 5

Synchronization errors with control for the damped equations: (a) plot of e1(t), (b) plot of e2(t), (c) plot of e3(t), and (d) plot of e4(t)

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Fig. 6

Phase plots for the damped equations showing both the z, w state variables going to zero: (a) Ug = 400 and (b) Ug = 100

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