A modified incremental harmonic balance method for rotary periodic motions |
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Authors: | Lu Chung-Jen Lin Yu-Min |
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Institution: | (1) Department of Electrical and Control Engineering, National Chiao-Tung University, Hsinchu, 300, Taiwan;(2) Department of Power Mechanical Engineering, National Tsing Hua University, Hsinchu, 300, Taiwan;(3) Department of Mechanical Engineering, Chung-Yuan Christian University, Chung-Li, 320, Taiwan |
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Abstract: | The determination of periodic solutions is an essential step in the study of dynamic systems. If some of the generalized coordinates
describing the configuration of a system are angular positions relative to certain reference axes, the associated periodic
motions divide into two types: oscillatory and rotary periodic motions. For an oscillatory periodic motion, all the generalized
coordinates are periodic in time. On the other hand, for a rotary periodic motion, some angular coordinates may have unbounded
magnitude due to the persistent circulation about their pivots. In this case, although the behaviour of the system is periodic
physically, those angular coordinates are not periodic in time. Although various effective methods have been developed for
the determination of oscillatory periodic motion, the rotary periodic motion can only be determined by brute force integration.
In this paper, the incremental harmonic balance (IHB) method is modified so that rotary periodic motions can be determined
as well as oscillatory periodic motions in a unified formulation. This modified IHB method is applied to a practical device,
a rotating disk equipped with a ball-type balancer, to show its effectiveness. |
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