Frontal waves and transmissions for temporal laminates and imperfect chiral interfaces

Abstract

The analysis of wave patterns in a structure which possesses periodicity in the spatial and temporal dimensions is presented. The topic of imperfect chiral interfaces is also considered. Although causality is fundamental for physical processes, natural wave phenomena can be observed when a wave is split at a temporal interface. A wave split at a spatial interface is a more common occurrence; however, when the coefficients of the governing equations are time-dependent, the temporal interface becomes important. Here, the associated frontal waves are studied, and regimes are analysed where the growth of the solution in time is found. Imperfect interfaces, across which the displacements are discontinuous, are also considered in the vector case of chiral elastic systems. Analytical study and asymptotic approximations are supplied with illustrative numerical examples. This article is part of the theme issue ‘Wave generation and transmission in multi-scale complex media and structured metamaterials (part 1)’.

Gravity-induced dispersion in a chiral waveguide: transient regimes and imperfect temporal interfaces

“…This jump is governed by the velocity g at time t=0−. It is also observed that, when the gravity is finite, the jump conditions across the temporal chiral interface are not affected by gravity, and are similar to those studied in [20].…”

“…The applications of the dynamic materials with temporal interfaces are discussed in [15,19], and the wave patterns in such materials are also analysed in [16][17][18]20].…”

“…The energy balance relations for waves in a spatio-temporal material composite is addressed in [19]. The modelling of frontal waves, incorporating the analysis of the transient wave phenomena in structures that have stratification in the temporal dimension, is discussed in [20]. The study of temporal modulation of frontal waves is emphasized, with special regimes being identified where the solution shows growth in time.…”

“…The study of temporal modulation of frontal waves is emphasized, with special regimes being identified where the solution shows growth in time. Imperfect interfaces, across which the displacements are discontinuous, are also considered in [20] for the vector case of chiral elastic systems.…”

High-order homogenization of the time-modulated wave equation: non-reciprocity for a single varying parameter

“…We could further explore optimal design of time-modulated media [51]. As another perspective, our asymptotic analysis can be applied to time-modulated conductivity, hydrodynamic and elasticity equations (we note in passing the fascinating work [52] on temporal elastic laminates with imperfect chiral interfaces), as well as other governing equations in physics described by linear partial differential equations, where we expect that similar non-reciprocal effects can be unveiled in the homogenization regime. Another perspective concerns the case of locally resonant media [53,54], to combine both low-frequency non-reciprocity and low-frequency resonances for more important macroscopic effects.…”