Study on Vibration with Collision (4th Report)

Considerations in Stability of Steady-state Impact Motion

Abstract

This paper deals with the stability on damped forced colliding vibration with one degree of freedom system, consists of a spring suspended impacter and a fixed rigid stop. Following problems are solved by a stability analysis based on a perturbation technique : It determines a stable gap region of actual impact motion within a setting gap range of the stop which is obtained by the steadystate conditions, chooses the alternative of the actual phase lag among its two values in the gap of the outside of forced vibration amplitude. It is also described on the characteristics of undamped impact motion at resonance and its stability in this report. Whatever gap is get up, the colliding velocity doesn't change. It is stable over the infinite gap range. The other results of this paper are as follows : The limit of the gap range agrees with the one side boundary of the stable region. There is the gap of the maximum velocity within the stable region. The phase lag with larger impact velocity causes stable motion in the gap of the outside of forced vibration amplitude. Over-all region of the setting gap is stable in the neutral type.