Characteristic of the Duffing Oscillator in the Main Resonant Region

Abstract

The characteristic which the Duffing oscillator with a softening spring property under harmonically stimulating force presents in the main resonant region has been investigated numerically. With regard to the structure which the system exhibits in this region, there exists another branch which appears due to bifurcation from the resonant branch at a certain frequency, in addition to the resonant and nonresonant branches. It has been clarified that many kinds of periodic solutions exist in the region between this new branch and the resonant one. Furthermore, besides the traditional harmonic solutions, i. e., resonant and nonresonant solutions, it has been shown that another harmonic solution appears, although it is unstable. This unstable solution enables us to reasonably explain the constitution of attractors in this resonant region. Chaotic phenomena, which appear due to period doubling bifurcation also exist.