Abstract
An audible warning device (AWD) is a device which sounds by impact vibrations. The behavior of AWD is a kind of self-induced vibration in which the suction behavior in AWD depends on its own motion. In specific condition, period doubling bifurcation occurs and behavior of AWD becomes unstable. Therefore, the bifurcation behavior is investigated by a simple model. First, a simple analytical model consists of a shaft, a pole, and a resonator of AWD is introduced, which is 3 degree-of-freedom system accompanied by impacts, and suction force between the pole and the shaft is modeled as a ramp function which starts to increase from zero-value at the time of an impact. Then, a map from state variables of an impact to those at the next impact is derived. Fixed points of the map and their stabilities are numerically calculated, and arc-length continuation method is used to obtain those. It was found that the saddle-node bifurcation occurs when time duration from an impact to the next impact coincide with a natural period of the mode that the resonator mainly vibrates. Furthermore, the bifurcation of impact behavior is drastically influenced by the phase of the vibration of the resonator at the time of impact.
