Characteristics of a Duffing's Oscillator to a Centrifugal Type Stimulating Force.

The responses, excited by a centrifugal type stimulating force, is investigated for a single-degree-of-freedom oscillating system with a Dumng restoring force characteristic. Duffing's oscillator is well known to exhibit a variety of different complex nonlinear dynamical phenomena, which mean sub and superharmonic resonance, cascades of period-doubling bifurcations and chaos. In a wide field of inquiry, this oscillator is prototypical to nonlinear dynamics. This paper shows, in detail, the characteristic of this oscillator under circumstances as above-mentioned, making use of both an approximate procedure, i.e., harmonic balance method, and a numerical technique. Analyses of stabilities for approximate periodic oscillations are accomplished with the aid of Floquet theory, and an easy application of this theory, however, is suggested to likely become pregnant with erronous results. In particular, stability of subharmonic vibrations of order 1/2 is explicitly analyzed and agrees very well with the results of numerical analysis, qualitatively and quntitatively. In addition, numerical analysis reveals that several kinds of isolated subharmonic oscillations of order 1/3 and chaotic responses may occur in this system.