Stochastic energy absorbers based on analogies with soft-wall billiards

Abstract

A few degrees-of-freedom Hamiltonian model exhibiting one-directional long-term trends in energy exchange flows is introduced. The model includes a massive potential well—a container with one or few light non-interacting particles—attached to a linearly elastic spring. Intentionally, no phenomenological dissipation is imposed. Nonetheless, due to the similarity of container shapes to various types of stochastic soft-wall billiards, the energy is transferred from the container (donor) to the inner particle (acceptor) in almost irreversible way during physically reasonable time intervals. The potential well is introduced in such a way that, in the rigid-body limit, it resembles one of the two most common types of billiards, with either dispersing- or stadium-type boundaries, as the signature of main geometrical parameter of the well changes. In particular, we found conditions of stochasticity of the model’ dynamics based on the nonlinear normal mode stability concept. Such an approach points to the link between stability properties of normal modes and the typical dynamics of billiards. Possible applications to macro-level energy harvesters and the design of artificial energy-absorbing materials are discussed.