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Stability transitions of certain exact periodic responses in undamped helmholtz and duffing oscillators

✍ Scribed by E. Gravador; K.-E. Thylwe; A. Hökback

Publisher: Elsevier Science
Year: 1995
Tongue: English
Weight: 496 KB
Volume: 182
Category: Article
ISSN: 0022-460X
DOI: 10.1006/jsvi.1995.0192

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✦ Synopsis

A linear stability analysis in which phase-integral theory is used is applied to certain exact subharmonic responses of undamped Helmholtz and Duffing oscillators which are valid beyond the limits of perturbation theory. Infinite sequences of stability transitions are identified in terms of the Mathieu parameters, and their limiting behaviours are investigated.

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A peculiar phenomenon of an exact quenching of integer multiples of the fundamental subharmonic frequency in the periodic response is considered. The pure (single-frequency) subharmonic solutions have been found by the exact method of harmonic balance in the undamped oscillator equations with quadra