Deformation and vibration of a spatial elastica with fixed end slopes

In this paper we study the static deformations and vibration frequencies of a clamped–clamped spatial elastica. One clamp is fixed in space, and the other is attached to a slider which is allowed to slide without friction on a linear track. Emphasis is placed on the effect of the slope difference between the two clamps on the response of the elastica when the slider is under the action of an edge thrust. The equations of motion of the elastica are formulated within the framework of director theory, and the static deformations and vibration frequencies are calculated by shooting method. An experimental set-up is designed to examine the theoretical predictions. When the slope difference between the two clamps is smaller than 68°, two separate load-deflection curves can be found; one for spatial deformation and the other for purely planar deformation. In force control, the elastica-slider assembly may jump between planar and spatial deformations as the edge thrust increases or decreases monotonically. In displacement control, on the other hand, no jump will occur. In the case when the slope difference is greater than 68°, only planar deformation exists.