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.
|Translated title of the contribution||Fourier methods for quasi-periodic oscillations|
|Pages (from-to)||629 - 671|
|Number of pages||43|
|Journal||International Journal for Numerical Methods in Engineering|
|Publication status||Published - Jul 2006|