Exact solution of the Stroh characteristic equation for Cosserat elastic materials

Derive exact analytical solutions of the characteristic equation r^6 + P1 r^4 + P2 r^2 + P3 = 0 arising from the Stroh matrix eigenvalue problem for Love-wave propagation in isotropic elastic Cosserat materials, enabling explicit determination of the associated eigenvectors and amplitudes within the Stroh formalism.

Background

The authors present the standard Stroh formalism for surface-wave analysis, deriving a first-order system and the associated sextic characteristic polynomial for the complex attenuation factor r in Cosserat elasticity.

They explicitly state that the exact solution of this characteristic equation could not be found in Cosserat elastic materials, which motivates their adoption of the Riccati-based impedance method to avoid spurious roots and to prove existence and uniqueness of the subsonic speed.