Research Papers

Nonlinear Dynamics of a Rotating Flexible Link

[+] 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

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 June 10, 2014; final manuscript received October 24, 2014; published online April 9, 2015. Assoc. Editor: Stefano Lenci.

J. Comput. Nonlinear Dynam 10(6), 061014 (Nov 01, 2015) (8 pages) Paper No: CND-14-1151; doi: 10.1115/1.4028929 History: Received June 10, 2014; Revised October 24, 2014; Online April 09, 2015

This paper deals with the study of the nonlinear dynamics of a rotating flexible link modeled as a one dimensional beam, undergoing large deformation and with geometric nonlinearities. The partial differential equation of motion is discretized using a finite element approach to yield four nonlinear, nonautonomous and coupled ordinary differential equations (ODEs). The equations are nondimensionalized using two characteristic velocities—the speed of sound in the material and a velocity associated with the transverse bending vibration of the beam. The method of multiple scales is used to perform a detailed study of the system. A set of four autonomous equations of the first-order are derived considering primary resonances of the external excitation and one-to-one internal resonances between the natural frequencies of the equations. Numerical simulations show that for certain ranges of values of these characteristic velocities, the slow flow equations can exhibit chaotic motions. The numerical simulations and the results are related to a rotating wind turbine blade and the approach can be used for the study of the nonlinear dynamics of a single link flexible manipulator.

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Fig. 1

Schematic of a rotating flexible beam and an ith element: (a) flexible rotating beam and (b) planar beam element

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Fig. 2

Poincaré maps for various Ug—undamped case: (a) Ug = 250, (b) Ug = 150, (c) Ug = 100, and (d) Ug = 50

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Fig. 3

Plot of Lyapunov exponents at Ug = 50—undamped case

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Fig. 4

Phase plots for various Ug—damped case: (a) Ug = 155, (b) Ug = 105, and (c) Ug = 50

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Fig. 5

Spectra of Lyapunov exponents at Ug = 105—damped case



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