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Research Papers

Vibration and Snap-Through of Bent Elastica Strips Subjected to End Rotations

[+] Author and Article Information
R. H. Plaut

Department of Civil and Environmental Engineering, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061-0105

L. N. Virgin1

Department of Civil and Environmental Engineering, Duke University, Durham, NC 27708-0287l.virgin@duke.edu.

1

Corresponding author.

J. Appl. Mech 76(4), 041011 (Apr 23, 2009) (7 pages) doi:10.1115/1.3086783 History: Received June 18, 2008; Revised December 29, 2008; Published April 23, 2009

A flexible strip is rotated at its ends until it forms a deep circular arc above its ends. Then the ends are kept immovable and are rotated downward until the arch suddenly snaps into an inverted configuration. The strip is analyzed as an inextensible elastica. Two-dimensional equilibrium shapes, vibration modes and frequencies, and critical rotations for snap-through are determined using a shooting method. Experiments are also conducted and results are compared with those from the analysis. The agreement is good. In addition, a microelectromechanical systems (MEMS) example is analyzed, in which an electrostatic force below a buckled strip causes the strip to snap downward, and the critical force is obtained as a function of the vertical gap.

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Copyright © 2009 by American Society of Mechanical Engineers
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Figures

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Figure 1

Schematic of bent strip

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Figure 2

Photo of experimental system

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Figure 3

End rotation as function of midpoint vertical deflection for α0=30 deg, 60 deg, 90 deg, and 120 deg

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Figure 4

End rotation as function of midpoint vertical deflection for α0=90 deg; dots denote experimental data

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Figure 5

End rotation as function of midpoint vertical deflection for (a) α0=30 deg, (b) 60 deg, and (c) 120 deg; dots denote experimental data

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Figure 6

End rotation as function of lowest frequency for α0=30 deg, 60 deg, 90 deg, and 120 deg

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Figure 7

End rotation as function of lowest frequencies for α0 equal to (a) 30 deg, (b) 60 deg, (c) 90 deg, and (d) 120 deg

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Figure 8

Mode shapes for α0=90 deg and ϕ=149 deg

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Figure 9

Expansion of the end rotation as function of lowest frequencies for α0=120 deg

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Figure 10

Self-contact equilibrium shape for α0=150 deg

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Figure 11

End rotation as function of midpoint vertical deflection for α0=150 deg. The shaded area for ϕ>171 deg indicates self-contact.

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