Orateur
Description
In this work, we investigate the role of inertia in the periodic folding of thin viscous sheets. We employ a mathematical framework inspired by concepts from discrete differential geometry (DDG) to track the motion of the sheet midsurface and capture the shape and dynamics of sheet folding in regimes with non-negligible inertia. We observe that the folding frequency undergoes sudden transitions between distinct states as inertial effects become significant, and identify the underlying mechanism as a resonance occurring when the folding frequency at the bottom becomes commensurate with the natural frequency of the oscillating distributed pendulum.
In addition to explaining the coexistence of multiple frequency states observed in experiments, we also explore the strongly inertial regime, where inertia dominates over gravity, and validate the proposed scaling laws in previously unexplored folding regimes. Finally, we present a regime diagram in the control-parameter space, identifying the different folding regimes, namely the kinematic (forced-folding), gravitational, inertio-gravitational, and inertial regimes.