Exact Quenching Phenomenon Of Undamped Driven Helmholtz And Duffing Oscillators

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...

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Bibliographic Details
Published in:Journal of sound and vibration 1993-02, Vol.161 (2), p.203-211
Main Author: Thylwe, K.-E.
Format: Article
Language:English
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Summary: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 quadratic (Helmholtz oscillator) and cubic (Duffing oscillator) non-linear local forces. In contrast to known approximate solutions, the amplitudes of these exact solutions become arbitrarily large in the limit where the strength of the non-linearity vanishes. The stability of the subharmonic motions is briefly discussed.
ISSN:0022-460X
1095-8568
DOI:10.1006/jsvi.1993.1066