NONLINEAR OSCILLATIONS WITH MULTIPLE RESONANT OR NONRESONANT FORCING TERMS

The transient and steady-state response of a very general non-linear o scillator subject to a finite number of harmonic forcing terms is stud ied 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 det ermine both the conditions for the quenching of the free oscillation a nd the conditions for its persistence. Analytical results are validate d by numerical integration. (C) 1998 Elsevier Science Ltd. All rights reserved.