Chaotic and regular dynamics of a morphing shell with a vanishing-stiffness mode

Abstract

Thin elastic shells are almost inextensible but easy to bend. In the presence of prestresses, geometric frustrations can produce complex elastic energetic landscapes, which have been tailored for the design of morphing structures with multiple stable equilibria or neutrally stable manifolds. We show that the co-existence of stiff and floppy modes leads to unexploited dynamical features. We build a neutrally stable cylindrical shell that under dynamical excitation alternates a chaotic behavior with a surprisingly regular regimes with a continuous precession of the curvature axis at a constant speed. We explain the experimental findings with a minimal model, showing how the intriguing dynamics is due to the subtle coupling between the prestress, geometrical nonlinearity, material anisotropy and inertial effects. Our results shed a new light on morphing structures dynamics and can be exploited in engineering applications such as energy harvesting.