Abstract
The recently developed time transformation method [1–3] is extended to the analysis of forced vibration of the strongly non-linear undamped oscillator, u+u+ef(u)=P(t) , where f(u) is a non-linear function of the displacement u(t) and e is not necessarily small. Two types of external loading P(t) are considered: a step input and a simple harmonic input. The frequency-amplitude relation is obtained through a slight modification of the results developed in reference [2] for the unforced oscillator. A comparison with the results of numerical and other analytic methods is made. It can be deduced that the time transformation approach offers simple and accurate approximations for the oscillators considered.
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