Exploiting dynamic bifurcation in elastic ribbons for mode skipping and selection

TL;DR

This study explores the dynamic snap-through behavior of elastic ribbons, revealing how controlled rotation can induce mode skipping and selection, with implications for designing advanced mechanical systems.

Contribution

It introduces a comprehensive analysis combining theory, simulations, and experiments to control snap-through pathways in elastic ribbons, a novel approach compared to classical bistable beam studies.

Findings

Snap-through paths differ in 3D ribbons versus 2D beams.

Controlled rotation enables mode skipping and selection.

Scaling laws govern the delay in snap-through processes.

Abstract

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, which is different from the classical snap-through of a two-dimensional (2D) bistable beam. Our theoretical model for the static bifurcation analysis is derived based on the Kirchhoff equations, and dynamical numerical 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 the saddle-node bifurcation, the same scaling law for the delay applies. We further demonstrate that, in elastic ribbons, by controlling the rotating velocity at the end, distinct snap-through pathways can be realized by selectively skipping specific modes, 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.