Rayleigh waves in symmetry planes of crystals: explicit secular equations and some explicit wave speeds

TL;DR

This paper derives explicit secular equations for Rayleigh surface waves in crystals with symmetry planes, providing solutions for wave speeds in various crystal classes and directions.

Contribution

It presents explicit quartic and biquadratic secular equations for Rayleigh waves in symmetric crystals, including monoclinic, orthorhombic, and incompressible materials.

Findings

Explicit secular equations are derived for different crystal symmetries.

Solutions for wave speeds are obtained explicitly in certain cases.

Examples include monoclinic, orthorhombic, and incompressible crystals.

Abstract

Rayleigh waves are considered for crystals possessing at least one plane of symmetry. The secular equation is established explicitly for surface waves propagating in any direction of the plane of symmetry, using two different methods. This equation is a quartic for the squared wave speed in general, and a biquadratic for certain directions in certain crystals, where it may itself be solved explicitly. Examples of such materials and directions are found in the case of monoclinic crystals with the plane of symmetry at $x_3=0$. The cases of orthorhombic materials and of incompressible materials are also treated.