Unfolding the dynamics of free-falling folded chain : Experiments and simulations

Athanasios A. Markou*, Djebar Baroudi, Qiang Cheng, Hadi Bordbar

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

1 Citation (Scopus)
126 Downloads (Pure)


Contrary to educated intuition, the tip of a free-falling U-folded chain accelerates faster than gravity without violating the Newtonian laws. In the current work, we study the dynamics of a free-falling U-folded chain experimentally as well as numerically. To this end, high-speed imaging (up to 10000 fps) is used to capture the chain's falling tip by using different openings between the two tips of the chain. Thanks to high-speed digital imaging, the detailed geometry of the dynamic unfolding is captured. The post-processing of captured images has provided detailed quantitative temporal data for displacement, velocity, and acceleration of the falling tip of the chain. The experimental observations have revealed the various phases of dynamics of the falling U-folded chain, including unfolding, whipping, and rebounding phases for the first time. Furthermore, a Henky-type model is developed to capture the associated phenomena related to these phases, such as rebound effect, whip effect, local buckling, and transverse wave propagation. The model that includes nonlinear elastic, dissipative and bilateral gap-contact features, could successfully capture the experimentally observed phases and phenomena of the unfolding dynamics qualitatively.

Original languageEnglish
Article number104257
Number of pages12
Publication statusPublished - Jan 2023
MoE publication typeA1 Journal article-refereed


  • Discrete mechanical model
  • High-speed imaging
  • Nonlinear dynamics
  • U-folded falling chain
  • Variable-mass dynamics
  • Whip cracking


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