Equilibria and vibration of a heavy pinched loop
A thin strip is bent such that the two ends are brought together and clamped (pinched) to form a teardrop shape. The clamped end is held at various angles with the loop either upright, horizontal, downward, or halfway between these positions. The length of the loop is increased, and the resulting equilibrium shapes, as well as small in-plane vibrations about equilibrium, are investigated analytically and experimentally. When the loop is held upright, in-plane buckling occurs at a critical length, and subsequent postbuckling deflections can be large. For the other orientations, except the hanging one, deflections also become large as the length is increased. In the analysis, the strip is assumed to be an inextensible elastica which is unstrained when straight, and its self-weight is included. A shooting method is applied to obtain numerical solutions to the nonlinear equilibrium boundary value problem and the linear vibration boundary value problem. Polycarbonate strips are used in the experiments, and data are acquired with a laser vibrometer. The experimental deflections, frequencies, and mode shapes exhibit excellent agreement with the analytical solutions. © 2005 Elsevier Ltd. All rights reserved.
Santillan, S; Virgin, LN; Plaut, RH
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