期刊
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING
卷 67, 期 5, 页码 629-671出版社
JOHN WILEY & SONS LTD
DOI: 10.1002/nme.1632
关键词
quasi-periodic oscillation; averaging method; Fourier method; invariant torus; Van der Pol oscillator
Quasi-periodic oscillations and invariant tori play an important role in the study of forced or coupled oscillators. This paper presents two new numerical methods for the investigation of quasi-periodic oscillations. Both algorithms can be regarded as generalizations of the averaging and the harmonic (spectral) balance methods. The algorithms are easy to implement and require only minimal a priori knowledge of the system. Most importantly, the methods do not depend on an a priori co-ordinate transformation. The methods are applied to a number of illustrative examples from non-linear electrical engineering and the results show that the methods are efficient and reliable. In addition, these examples show that the presented algorithms can also continue through regions of sub-harmonic (phase-locked) resonance even though they are designed only for the quasi-periodic case. Copyright (c) 2006 John Wiley & Sons, Ltd.
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