Propagation of Love waves in linear elastic isotropic Cosserat materials

TL;DR

This paper presents a new, simplified numerical method for analyzing Love wave propagation in Cosserat materials, confirming their existence without artificial surface layers and addressing unresolved issues in Cosserat continuum theories.

Contribution

It introduces an algebraic Riccati equation approach for Love wave analysis in Cosserat materials, ensuring existence and uniqueness of wave speeds without traditional formalisms.

Findings

The method guarantees the existence of subsonic Love wave speeds.

Love waves do not require artificial surface layers for their existence.

The approach simplifies numerical analysis of wave propagation in Cosserat media.

Abstract

We investigate the propagation of Love waves in an isotropic half-space modelled as a linear {elastic isotropic} Cosserat material. To this aim, we show that a method commonly used to study Rayleigh wave propagation is also applicable to the analysis of Love wave propagation. This approach is based on the explicit solution of an algebraic Riccati equation, which operates independently of the traditional Stroh formalism. The method provides a straightforward numerical algorithm to determine the wave amplitudes and speed{s}. Beyond its numerical simplicity, the method guarantees the existence and uniqueness of a subsonic wave speed, addressing a problem that remains unresolved in most Cosserat solids generalised {continua} theories. Although often overlooked, proving the existence of an admissible solution is, in fact, the key point that validates or invalidates the entire analytical approach used to derive the equation determining the wave speed. Interestingly, it is confirmed that the Love waves do not need the artificial introduction of a surface layer, as indicated in the literature.