Impact of dropped hollow rubber sphere on plate

Abstract

This paper deals with the impact of dropped hollow rubber spheres against a planar surface. Hollow silicon rubber spheres are used as the impact source of the measurement of the floor impact sound insulation of buildings, but the impact characteristics have not been investigated. In order to clear the impact characteristics and show a strategy of a development of another type of source, we have conducted some experiments, FEM simulation on LS-DYNA and a one-dimensional mass-and-spring model analysis. The experiment of the impact of 4 types of rubber spheres, two hollow spheres with an outer radius of 90 mm and two solid spheres with a radius of 60 mm and 40 mm, against a surface plate were conducted. As the FEM solutions corresponded qualitatively with the experimental results, the impact analysis was done based on the FEM results. The FEM solution shows the shock stress propagation in a hollow sphere has two steps; the ‘first period’ is the stress propagation in a solid thickness part similar in a solid sphere and the following period is that to the hollow part of sphere. The frequency response of the impact force shows ‘notch’ frequencies correspond to the natural frequencies of the hollow sphere of free-free boundary condition. This is the key point to analyze the impact characteristics of dropped hollow spheres. We investigated the relations between durations, natural frequencies of free-free boundary condition and notch frequencies of impact in relation to the thickness ratio of hollow sphere. We have presented a simple model to estimate the duration and the peak impact of dropped hollow sphere for an actual design.

Keywords

• impact
• hollow sphere
• rubber sphere
• hertz theory
• natural frequency
• notch frequency