Research Papers

On the Properties of a Traveling Ruck in a Flexible Strip

[+] Author and Article Information
A. N. O'Keefe

Department of Mechanical Engineering,
University of Canterbury,
20 Kirkwood Avenue,
Upper Riccarton,
Christchurch 8041, New Zealand
e-mail: alex.okeefe@pg.canterbury.ac.nz

S. D. Gooch

Department of Mechanical Engineering,
University of Canterbury,
20 Kirkwood Avenue,
Upper Riccarton,
Christchurch 8041, New Zealand
e-mail: shayne.gooch@canterbury.ac.nz

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received September 15, 2014; final manuscript received January 29, 2015; published online February 26, 2015. Assoc. Editor: Nick Aravas.

J. Appl. Mech 82(4), 041002 (Apr 01, 2015) (7 pages) Paper No: JAM-14-1425; doi: 10.1115/1.4029697 History: Received September 15, 2014; Revised January 29, 2015; Online February 26, 2015

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.

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Fig. 1

Schematic of a long ruck

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Fig. 2

Predicted ruck shape in a flexible strip using Eq. (1)

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Fig. 3

Numerical and analytical approximation of potential energy of a static ruck

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Fig. 4

Ruck elements of a traveling ruck showing positive element velocity

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Fig. 5

Sequence of ruck profiles showing the shape of the element path

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Fig. 6

Schematic showing derivation of ruck element travel over dT

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Fig. 7

Example set of profiles recorded for a traveling ruck. The bold profile highlights the shape of the ruck and dots identify the peak of each ruck profile.

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Fig. 8

Plot of ruck peak position versus time for stainless steel and polycarbonate test strips

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Fig. 10

Comparison between measured and predicted ruck speeds (Eq. (13)) for given kinetic energy in the polycarbonate strip, plotted on the same scale as Fig. 9 for direct comparison

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Fig. 9

Comparison between measured and predicted ruck speeds (Eq. (13)) for given kinetic energy in the steel strip

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Fig. 11

Len Lye's maquette showing the intended form and motion of his proposed kinetic sculpture Sun, Land, and Sea

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Fig. 12

Sequence showing the motion used to create a traveling ruck in test rig strip. (a) Creating the initial ruck, (b) initial ruck shape, (c) sending the traveling ruck, and (d) the traveling ruck.




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