Abstract
The transient and steady-state response of a very general non-linear oscillator subject to a finite number of harmonic forcing terms is studied by the asymptotic perturbation method. We consider three cases: (i) the forcing frequencies are not close to each other or close to the primary resonance of the oscillator; (ii) the forcing frequencies are close to each other but not close to the primary resonance; and (iii) all the forcing frequencies are close to the primary resonance. We determine both the conditions for the quenching of the free oscillation and the conditions for its persistence. Analytical results are validated by numerical integration.
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