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arXiv · 2603.27641

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

Michaël Darche·Raphaël Assier·Sébastien Guenneau·Bruno Lombard·Marie Touboul
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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.

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Michaël Darche, Raphaël Assier, Sébastien Guenneau, Bruno Lombard, Marie Touboul. 2026-03-29. Waves within a network of slowly time-modulated interfaces: time-dependent effective properties, reciprocity and high-order dispersion. https://arxiv.org/abs/2603.27641

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