Deformations and Stability of an Elastica Subjected to an Off-Axis Point Constraint
Resource
JOURNAL OF APPLIED MECHANICS-TRANSACTIONS OF THE ASME, 77(3), 031006
Journal
Journal of Applied Mechanics
Pages
31006
Date Issued
2010
Date
2010
Author(s)
Ro, Wei-Chia
Abstract
This paper studies, both theoretically and experimentally, the deformation, the vibration, and the stability of a buckled elastic strip (also known as an elastica) constrained by a space-fixed point in the middle. One end of the elastica is fully clamped while the other end is allowed to slide without friction and clearance inside a rigid channel. The point constraint is located at a specified height above the clamping plane. The elastic strip buckles when the pushing force reaches the conventional buckling load. At this buckling load, the elastica jumps to a symmetric configuration in contact with the point constraint. As the pushing force increases, a symmetry-breaking bifurcation occurs and the elastica evolves to one of a pair of asymmetric deformations. As the pushing force continues to increase, the asymmetric deformation experiences a second jump to a self-contact configuration. A vibration analysis based on an Eulerian description taking into account the sliding between the elastica and the point constraint is described. The natural frequencies and the stability of the calculated equilibrium configurations can then be determined. The experiment confirms the two jumps and the symmetry-breaking bifurcation predicted theoretically. © 2010 by ASME.
Type
journal article
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