Snapping of a Planar Elastica with Fixed End Slopes
Resource
ASME Journal of Applied Mechanics,75,0-041024.
ASME Journal of Applied Mechanics
Journal
ASME Journal of Applied Mechanics
Journal Volume
75
Journal Issue
4
Pages
-
Date Issued
2008
Date
2008
Author(s)
Lin, Yong-Zhi
Abstract
In this paper, we study the deformation and stability of a planar elastica. One end of the elastica is clamped and fixed in space. The other end of the elastica is also clamped, but the clamp itself is allowed to slide along a linear track with a slope different from that of the fixed clamp. The elastica deforms after it is subjected to an external pushing force on the moving clamp. It is observed that when the pushing force reaches a critical value, snapping may occur as the elastica jumps from one configuration to another remotely away from the original one. In the theoretical investigation, we calculate the static load-deflection curve for a specified slope difference between the fixed clamp and the moving clamp. To study the stability of the equilibrium configuration, we superpose the equilibrium configuration with a small perturbation and calculate the natural frequencies of the deformed elastica. An experimental setup is designed to measure the loaddeflection curve and the natural frequencies of the elastica. The measured load-deflection relation agrees with the theoretical prediction very well. On the other hand, the measured natural frequencies do not agree very well with the theoretical prediction, unless the mass of the moving clamp is taken into account. Copyright © 2008 by ASME.
Other Subjects
Forecasting; System stability; Critical values; Elastica; Equilibrium configurations; Experimental set ups; Fixed clamp; Linear tracking; Load deflections; Planar elastica; Pushing forces; Small perturbations; Static loads; Natural frequencies
Type
journal article
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