1. Scattering from a Bi-stable Elastica Arm

In this contribution, we study the transient scattering of waves from a structural bi-stable element modelled as a Euler elastica. The non-linear elastic element has localized inertia at its end points, each of which is connected to a semi-infinite straight rod. The focus is on longitudinal waves reflected and transmitted into the semi-infinite rods by the non-linear structural interface. The derivation of the transient governing ordinary differential equations for the reflected and transmitted amplitudes is outlined. The key point is the assumption that the semi-infinite rods are linear elastic, with non-linearity embedded into special transient transmission conditions for the scattering amplitudes. The governing equations are solved using standard numerical integration techniques. From a physical point of view, we focus on the effect of the bi-stability on the transmission resonances, identified in the linearized regime. Special attention is given to the up- and downconversion of the frequency content of scattered amplitudes as a function of the amplitude of a harmonic impinging wave.