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Analysis of forced non-linear undamped oscillators by a time transformation method

✍ Scribed by M.N. Hamdan; T.D. Burton

Publisher: Elsevier Science
Year: 1986
Tongue: English
Weight: 547 KB
Volume: 110
Category: Article
ISSN: 0022-460X
DOI: 10.1016/s0022-460x(86)80206-1

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✦ Synopsis

The recently developed time transformation method [1-3] is extended to the analysis of forced vibration of the strongly non-linear undamped oscillator, ii + u + el(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 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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