Edge Waves and Transmissions for Temporal Laminates and Imperfect Chiral Interfaces

TL;DR

This paper investigates wave behaviors at spatial and temporal interfaces in periodic structures, focusing on edge waves, growth regimes, and the effects of imperfect chiral interfaces in elastic systems, supported by analytical and numerical analysis.

Contribution

It introduces a comprehensive analysis of edge waves and wave transmission in structures with temporal and spatial periodicity, including the effects of imperfect chiral interfaces, which is a novel extension.

Findings

Edge waves are characterized and regimes with solution growth are identified.

Imperfect chiral interfaces cause discontinuities affecting wave transmission.

Analytical and asymptotic methods effectively model complex wave phenomena.

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 edge 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.