JUMP AND BIFURCATION OF DUFFING OSCILLATOR UNDER NARROW-BAND EXCITATION

The jump and bifurcation of Duffing oscillator with hardening springsubject to narrow-band random excitation are systematically and comprehensivelyexamined. It is shown that, in a certain domain of the space of the oscillator andexcitation parameters, there are two types of more probable motions in the stationaryresponse of the Duffing oscillator and jumps may occur. The jump is a transition ofthe response from one more probable motion to another or vise versa. Outside thedomain the stationary response is either nearly Gaussian or like a diffused limit cycle.As the parameters change across the boundary of the domain the qualitative behaviorof the stationary response changes and it is a special kind of bifurcation. It is alsoshown that, for a set of specified parameters, the statistics are unique and they areindependent of initial condition. It is pointed out that some previous results andinterpretations on this problem are incorrect.