Dynamical properties of Duffing oscillator forced by relaxation oscillator and its application to actuators

Abstract

We have developed a Duffing oscillator forced by a relaxation oscillator, the dynamical behavior of which is determined by the duty ratio of discharge to charge duration for the relaxation oscillation as a bifurcation parameter. The forced Duffing oscillator undergoes a period-doubling bifurcation into chaos as the duty ratio increases. We have implemented the Duffing oscillator using an iron cantilever settled between two magnets and the relaxation oscillator using a timer circuit and a programmable accelerator. The actual motion of the forced Duffing oscillator was observed using a high-speed camera to verify its chaotic motion. We discuss the applicability of the coupled nonlinear oscillators to an actuator for mixing fluids.