The Deformation and Stability Analysis of a Planar Elastica with Fixed End Angles
Date Issued
2007
Date
2007
Author(s)
Lin, Yong-Zhi
DOI
zh-TW
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 angle different from that of the fixed clamp. The elastica deforms after it is subject 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. Moreover, in order to transfer motion or force by this structure, we will make a research into the relation between longitudinal forces of the two ends. In the theoretical investigation, we calculate the static load-deflection curves and the longitudinal forces transmission for a specified angle 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. In addition, the condition where two ends with identical angles are introduced will be researched. An experimental set-up is designed to measure the load-deflection 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.
Subjects
彈性板條
大變形
穩定性
自然頻率
折斷式挫曲
elastica
stability
natural frequency
Snap
Type
thesis
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