Exact Quenching Phenomenon Of Undamped Driven Helmholtz And Duffing Oscillators

✍ Scribed by K.-E. Thylwe

• Publisher: Elsevier Science
• Year: 1993
• Tongue: English
• Weight: 276 KB
• Volume: 161
• Category: Article
• ISSN: 0022-460X
• DOI: 10.1006/jsvi.1993.1066

✦ Synopsis

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.