Nonlinear Vibrations of Multistable Shells

In this chapter, we investigate nonlinear composite shells as structural elements capable of exhibiting multi-stability. The shells considered here have geometries derived from conical surfaces and are manufactured with unsymmetrical composite layups, making them strong candidates for multi-stable behaviour. Two types of shells are examined: Shell A which has a classical conical geometry and shows two stable equilibrium states, and Shell B, which has a more complex pseudo-conical shape and can exhibit up to five stable equilibria. The static configurations are demonstrated by finite element models and then validated by manufactured prototypes. Finally, based on Helmholtz–Duffing model with asymmetric potential wells strong nonlinear dynamics with softening nonlinear resonance curves, a possible snap-through effect, bifurcations and chaotic oscillations are shown.