Bifurcations and chaotic motions of a forced nonlinear oscillating system

摘要

The steady-state responses which the damped Duffing oscillator with a softening spring property under a harmonically stimulating force exhibited in the main resonant frequency region have been analyzed by using both an approximate analytical procedure; that is, the harmonic balance scheme, and a numerical procedure. With regard to the structure which the system reveals in this region, there exists another branch which seems to be caused by bifurcation from the resonant branch at a certain frequency as well as to the usual resonant and nonresonant branches. It has also been shown that chaotic phenomena, which are related to the fundamental harmonics in the region of interest, arise due to period doubling bifurcation and develop only along the path of the new branch.