The explicit secular equation for surface acoustic waves in monoclinic elastic crystals

TL;DR

This paper derives an explicit quartic secular equation for surface acoustic waves in monoclinic elastic crystals using the method of first integrals, and computes wave speeds for specific crystals.

Contribution

It presents a direct derivation of the secular equation for monoclinic crystals, extending previous orthorhombic results, and provides numerical wave speed calculations.

Findings

Explicit quartic secular equation derived for monoclinic crystals

Wave speeds computed for twelve specific monoclinic crystals

Equation consistent with orthorhombic case

Abstract

The secular equation for surface acoustic waves propagating on a monoclinic elastic half-space is derived in a direct manner, using the method of first integrals. Although the motion is at first assumed to correspond to generalized plane strain, the analysis shows that only two components of the mechanical displacement and of the tractions on planes parallel to the free surface are nonzero. Using the Stroh formalism, a system of two second order differential equations is found for the remaining tractions. The secular equation is then obtained as a quartic for the squared wave speed. This explicit equation is consistent with that found in the orthorhombic case. The speed of subsonic surface waves is then computed for twelve specific monoclinic crystals.