On the Properties of a Traveling Ruck in a Flexible Strip

Abstract

This paper concerns the analysis of a traveling ruck. A ruck is the resulting postbuckled shape created when the ends of a slender, flexible, flat-lying strip of non-negligible self-weight are displaced toward one another. We consider the case of a semi-infinite strip with a fixed end displacement such that the shape of the ruck remains constant. The first mode of vibration of such a ruck is a translational rolling motion parallel to the length of the strip. In this paper, we calculate the potential energy of the static ruck and determine the relationship between the translational velocity and the kinetic energy of the traveling ruck. The results are formulated as nondimensional terms so that the methodology, developed in this paper, can be applied more generally. Results of physical testing show good comparison to predictions. The results from the study are applied to establish the feasibility of creating a large-scale kinetic sculpture, Sun, Land, and Sea. Sun, Land, and Sea is a kinetic sculpture proposed by internationally renowned artist Len Lye. The sculpture would feature a 3 m tall ruck that travels a distance of 45 m along a stainless steel strip.