Computation of phase nonreciprocity in a nonlinear periodic system

Abstract

Reciprocity is an important property of wave propagation in materials. It ensures that waves can propagate between two points in a material regardless of their direction of travel. Circumventing this property can lead to development of materials and devices that allow directional control over wave propagation and vibration transmission. In this work, we provide a computational analysis of nonreciprocal vibration transmission in a discrete model of a nonlinear periodic material. The periodic system consists of eight unit cells, each with two nonlinearly coupled masses. To ensure the possibility of nonreciprocal response, the unit cells have broken mirror symmetry. Specifically, we identify response regimes that are characterized by a nonreciprocal phase shift in vibration transmissibility (phase nonreciprocity). We discuss the influence of different system parameters on phase nonreciprocity. We hope this new functionality enables new designs for periodic materials.