Existence and uniqueness of Rayleigh waves in isotropic elastic Cosserat materials and algorithmic aspects

TL;DR

This paper introduces a new algebraic method for analyzing Rayleigh surface waves in isotropic Cosserat elastic materials, proving existence and uniqueness of solutions, and providing algorithms for numerical computation of wave properties.

Contribution

It develops a novel algebraic approach independent of the Stroh formalism, establishing the secular equation and algorithms for wave analysis in Cosserat materials.

Findings

Proved existence and uniqueness of subsonic solutions.

Developed algorithms for wave speed and amplitude calculation.

Performed numerical calculations for alumunium-epoxy.

Abstract

We discuss the propagation of surface waves in an isotropic half space modelled with the linear Cosserat theory of isotropic elastic materials. To this aim we use a method based on the algebraic analysis of the surface impedance matrix and on the algebraic Riccati equation, and which is independent of the common Stroh formalism. Due to this method, a new algorithm which determines the amplitudes and the wave speed in the theory of isotropic elastic Cosserat materials is described. Moreover, the method allows to prove the existence and uniqueness of a subsonic solution of the secular equation, a problem which remains unsolved in almost all generalised linear theories of elastic materials. Since the results are suitable to be used for numerical implementations, we propose two numerical algorithms which are viable for any elastic material. Explicit numerical calculations are made for alumunium-epoxy in the context of the Cosserat model. Since the novel form of the secular equation for isotropic elastic material has not been explicitly derived elsewhere, we establish it in this paper, too.