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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November 2015
Research-Article
Nonlinear Dynamics of a Rotating Flexible Link
B. Sandeep Reddy,
B. Sandeep Reddy
Department of Mechanical Engineering,
e-mail: bsandeep@mecheng.iisc.ernet.in
Indian Institute of Science
,Bangalore 560012
, India
e-mail: bsandeep@mecheng.iisc.ernet.in
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Ashitava Ghosal
Ashitava Ghosal
1
Professor
Department of Mechanical Engineering,
e-mail: asitava@mecheng.iisc.ernet.in
Department of Mechanical Engineering,
Indian Institute of Science
,Bangalore 560012
, India
e-mail: asitava@mecheng.iisc.ernet.in
1Corresponding author.
Search for other works by this author on:
B. Sandeep Reddy
Department of Mechanical Engineering,
e-mail: bsandeep@mecheng.iisc.ernet.in
Indian Institute of Science
,Bangalore 560012
, India
e-mail: bsandeep@mecheng.iisc.ernet.in
Ashitava Ghosal
Professor
Department of Mechanical Engineering,
e-mail: asitava@mecheng.iisc.ernet.in
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. Nov 2015, 10(6): 061014 (8 pages)
Published Online: November 1, 2015
Article history
Received:
June 10, 2014
Revision Received:
October 24, 2014
Online:
April 9, 2015
Citation
Sandeep Reddy, B., and Ghosal, A. (November 1, 2015). "Nonlinear Dynamics of a Rotating Flexible Link." ASME. J. Comput. Nonlinear Dynam. November 2015; 10(6): 061014. https://doi.org/10.1115/1.4028929
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