A sextic formalism for three–dimensional elastodynamics of cylindrically anisotropic radially inhomogeneous materials

Elasticity of arbitrary cylindrically anisotropic radially inhomogeneous media is considered. The system of six first-order ordinary differential equations describing time-harmonic cylindrical waves propagating along the cylinder axis is obtained. The matrix of the system coefficients has a specific algebraic symmetry underlying the structure of the formalism. The matricant solution in the form of the Peano expansion is discussed. The Wentzel-Kramers-Brillouin approximation is derived. Algebraic features of the solution are analysed and their physical content is elucidated. The dispersion equation for waves in a hollow cylinder with free or clamped lateral surfaces is formulated in terms of the impedance/admittance matrices. Their analytical properties are established, which are useful for analysis of the resulting frequency spectrum. The theory is extended to anisotropic radially inhomogeneous piezoelectric cylinders, for which the octet generalization of the formalism is developed and studied.