Waves within a network of slowly time-modulated interfaces: time-dependent effective properties, reciprocity and high-order dispersion

TL;DR

This paper investigates wave propagation in a 1D periodic network with slowly time-modulated interfaces, deriving effective models that include time-dependent properties and higher-order dispersion effects, validated by simulations.

Contribution

It introduces a homogenisation approach for time-modulated interfaces, deriving effective wave equations with dynamic properties and analyzing higher-order dispersive effects.

Findings

Time-dependent effective mass density and Young's modulus can be engineered through interface modulation.

Second-order homogenisation captures higher-order dispersive effects while maintaining reciprocity.

Time-domain simulations validate the effective models and their limitations.

Abstract

We consider wave propagation through a 1D periodic network of slowly time-modulated interfaces. Each interface is modelled by time-dependent spring-mass jump conditions, where mass and rigidity interface parameters are modulated in time. Low-frequency homogenisation yields a leading-order model described by an effective time-dependent wave equation, i.e.\ a wave equation with effective mass density and Young's modulus which are homogeneous in space but depend on time. This means that time-dependent bulk effective properties can be created by an array where only interfaces are modulated in time. The occurrence of k-gaps in case of a periodic modulation is also analysed. Second-order homogenisation is then performed and leads to an effective model which is reciprocal but encapsulates higher-order dispersive effects. These findings and the limitations of the models are illustrated through time-domain simulations.