Analysis on Bifurcation Behavior of an Acoustic Device with Impact Vibrations

Abstract

An audible warning device (AWD) is a device which generates sound by impact vibrations. The behavior of AWD is a kind of self-inducted vibration in which the suction behavior in AWD depends on its own motion. In specific conditions, period doubling bifurcation occurs and behavior of AWD becomes unstable. Therefore, the bifurcation behavior is investigated by a simple model. We introduced an analytical model which consists of two rigid bodies for a shaft and a pole, two beams for a stay and a sub stay, a diaphragm, and an annular plate for a resonator. The pole and the shaft are 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 to those at the next impact. 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 curve veering is occurred between the two natural vibration modes when length of the sub stay is sufficiently long. Furthermore, the result of bifurcation diagrams has shown that the region of period-1 stable response, which corresponding to the normal condition, becomes narrower when the length of sub stay approaches to the length at which curve veering occurs.