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Disk Position Nonlinearity Effects on the Chaotic Behavior of Rotating Flexible Shaft-Disk Systems

Published online by Cambridge University Press:  09 August 2012

H. M. Khanlo ,
M. Ghayour  and
S. Ziaei-Rad
H. M. Khanlo*
Affiliation:
Department of Aerospace Engineering, Aeronautical University of Science and Technology, Tehran 13846-73411, Iran
M. Ghayour
Affiliation:
Department of Mechanical Engineering, Isfahan University of Technology, Isfahan 84156-83111, Iran
S. Ziaei-Rad
Affiliation:
Department of Mechanical Engineering, Isfahan University of Technology, Isfahan 84156-83111, Iran
*
*Corresponding author ([email protected])
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Abstract

This study investigates the effects of disk position nonlinearities on the nonlinear dynamic behavior of a rotating flexible shaft-disk system. Displacement of the disk on the shaft causes certain nonlinear terms which appears in the equations of motion, which can in turn affect the dynamic behavior of the system. The system is modeled as a continuous shaft with a rigid disk in different locations. Also, the disk gyroscopic moment is considered. The partial differential equations of motion are extracted under the Rayleigh beam theory. The assumed modes method is used to discretize partial differential equations and the resulting equations are solved via numerical methods. The analytical methods used in this work are inclusive of time series, phase plane portrait, power spectrum, Poincaré map, bifurcation diagrams, and Lyapunov exponents. The effect of disk nonlinearities is studied for some disk positions. The results confirm that when the disk is located at mid-span of the shaft, only the regular motion (period one) is observed. However, periodic, sub-harmonic, quasi-periodic, and chaotic states can be observed for situations in which the disk is located at places other than the middle of the shaft. The results show nonlinear effects are negligible in some cases.

Keywords

Rotating shaftDynamic behaviorNonlinearitiesBifurcationChaoticGyroscopic
Type
Articles
Information
Journal of Mechanics , Volume 28 , Issue 3 , September 2012 , pp. 513 - 522
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2012

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