Multiple Rayleigh waves guided by the planar surface of a continuously twisted structurally chiral material.

Tom G Mackay,Akhlesh Lakhtakia

doi:10.1098/rspa.2020.0314

Abstract

The Stroh formalism was adapted for Rayleigh-wave propagation guided by the planar traction-free surface of a continuously twisted structurally chiral material (CTSCM), which is an anisotropic solid that is periodically non-homogeneous in the direction normal to the planar surface. Numerical studies reveal that this surface can support either one or two Rayleigh waves at a fixed frequency, depending on the structural period and orientation of the CTSCM. In the case of two Rayleigh waves, each wave possesses a different wavenumber. The Rayleigh wave with the larger wavenumber is more localized to the surface and has a phase speed that changes less as the angular frequency varies in comparison with the Rayleigh wave with the smaller wavenumber.

Highlights

Elastodynamic surface waves [1,2] have been studied from the 1880s, when Rayleigh [3] hinted at their significance for earthquakes, which was subsequently borne out both experimentally and theoretically [4,5,6]
The theory is followed by a section on numerical studies wherein we demonstrate the existence of more than one Rayleigh wave, depending on the structural period and orientation of the continuously twisted structurally chiral material (CTSCM)
The half-space x3 > 0 is occupied by a CTSCM and the plane x3 = 0 is traction-free so that it can guide a Rayleigh wave along the x1 direction

Summary

Introduction

Elastodynamic surface waves [1,2] have been studied from the 1880s, when Rayleigh [3] hinted at their significance for earthquakes, which was subsequently borne out both experimentally and theoretically [4,5,6]. We develop the theory underpinning Rayleigh-wave propagation guided by the traction-free surface of a CTSCM. The theory is followed by a section on numerical studies wherein we demonstrate the existence of more than one Rayleigh wave, depending on the structural period and orientation of the CTSCM. The half-space x3 > 0 is occupied by a CTSCM and the plane x3 = 0 is traction-free so that it can guide a Rayleigh wave along the x1 direction. Where q denotes the wavenumber of the Rayleigh wave As both τ(x) and ε(x) are symmetric [45], the following column vectors are defined in accordance with the Kelvin notation:. In order to find the stress and displacement vectors of the Rayleigh wave, as well as the corresponding surface wavenumber q, equation (2.15) must be solved. While equation (2.33) is analytically intractable, graphical methods can be implemented to extract the Rayleigh wavenumber(s) q as functions of the constitutive parameters of the CTSCM

Numerical studies

Findings

Closing remarks