LARGE-AMPLITUDE PRIMARY AND SUPERHARMONIC RESONANCES IN THE DUFFING OSCILLATOR

Second order perturbation analyses are presented of the order three superharmonic resonance in a Duffing oscillator, and of the primary resonance in a Duffing oscillator with softening non-linearity. It is found in the former case that it is necessary to go to the second order to obtain realistic steady state stability results. In the latter problem, however, the second order solution gives little or no improvement on the first order result. Also presented, for the latter problem, is what is thought to be the first example of a 'double jump' phenomenon for single degree of freedom, harmonically excited oscillators.