Exploiting dynamic bifurcation in elastic ribbons for mode skipping and selection

• Published in: Journal of the mechanics and physics of solids Vol. 190; p. 105721
• Main Authors: Huang, Weicheng, Yu, Tian, Vella, Dominic, Hsia, K. Jimmy, Liu, Mingchao
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.09.2024
• Subjects: Delayed bifurcation; Discrete model; Elastic ribbon; Snap-through; Structural dynamics; Structural dynamics; Delayed bifurcation; Discrete model; Elastic ribbon; Snap-through
• ISSN: 0022-5096
• DOI: 10.1016/j.jmps.2024.105721

In this paper, we systematically study the dynamic snap-through behavior of a pre-deformed elastic ribbon by combining theoretical analysis, discrete numerical simulations, and experiments. By rotating one of its clamped ends with controlled angular speed, we observe two snap-through transition paths among the multiple stable configurations of a ribbon in three-dimensional (3D) space; this is different from the classical snap-through of a two-dimensional (2D) bistable beam. Our theoretical model for the static bifurcation analysis is based on the Kirchhoff rod equations, and dynamical simulations are conducted using the Discrete Elastic Rods (DER) algorithm. The planar beam model is also employed for the asymptotic analysis of dynamic snap-through behaviors. The results show that, since the snap-through processes of both planar beams and 3D ribbons are governed by a saddle–node bifurcation, the same scaling law for the delay applies. We further demonstrate that by controlling the velocity of end-rotation, distinct snap-through pathways can be realized. In this way, we may selectively skip specific modes and, moreover, particular final modes can be strategically achieved. Through a parametric study using numerical simulations, we construct general phase diagrams for both mode skipping and selection of snapping ribbons. The work serves as a benchmark for future investigations on dynamic snap-through of thin elastic structures and provides guidelines for the novel design of intelligent mechanical systems.