  Impedance matrices are obtained for radially inhomogeneous structures using
the Stroh-like system of six first order differential equations for the time
harmonic displacement-traction 6-vector. Particular attention is paid to the
newly identified solid-cylinder impedance matrix ${\mathbf Z} (r)$ appropriate
to cylinders with material at $r=0$, and its limiting value at that point, the
solid-cylinder impedance matrix ${\mathbf Z}_0$. We show that ${\mathbf Z}_0$
is a fundamental material property depending only on the elastic moduli and the
azimuthal order $n$, that ${\mathbf Z} (r)$ is Hermitian and ${\mathbf Z}_0$ is
negative semi-definite. Explicit solutions for ${\mathbf Z}_0$ are presented
for monoclinic and higher material symmetry, and the special cases of $n=0$ and
1 are treated in detail. Two methods are proposed for finding ${\mathbf Z}
(r)$, one based on the Frobenius series solution and the other using a
differential Riccati equation with ${\mathbf Z}_0$ as initial value. %in a
consistent manner as the solution of an algebraic Riccati equation. The
radiation impedance matrix is defined and shown to be non-Hermitian. These
impedance matrices enable concise and efficient formulations of dispersion
equations for wave guides, and solutions of scattering and related wave
problems in cylinders.
