Abstract
This paper presents a systematic analysis approach for the study of two non-linearly coupled oscillators, with incommensurable fundamental frequencies. The asymptotic perturbation method is used to analyze a bifurcation problem of codimension two. It is found that the amplitude modulation equations are equal to normal forms equations available in the literature. Approximate analytic solutions for generic quadratic and cubic non-linearities can be constructed. The results obtained from a computer simulation based on a fifth order Runge–Kutta–Fehlberg scheme confirm the validity of the asymptotic perturbation method. The method is illustrated by applying it to a two-rod system subjected to aerodynamic excitation.
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