Impedance matrices are obtained for radially inhomogeneous structures usingthe Stroh-like system of six first order differential equations for the timeharmonic displacement-traction 6-vector. Particular attention is paid to thenewly identified solid-cylinder impedance matrix ${\mathbf Z} (r)$ appropriateto cylinders with material at $r=0$, and its limiting value at that point, thesolid-cylinder impedance matrix ${\mathbf Z}_0$. We show that ${\mathbf Z}_0$is a fundamental material property depending only on the elastic moduli and theazimuthal order $n$, that ${\mathbf Z} (r)$ is Hermitian and ${\mathbf Z}_0$ isnegative semi-definite. Explicit solutions for ${\mathbf Z}_0$ are presentedfor monoclinic and higher material symmetry, and the special cases of $n=0$ and1 are treated in detail. Two methods are proposed for finding ${\mathbf Z}(r)$, one based on the Frobenius series solution and the other using adifferential Riccati equation with ${\mathbf Z}_0$ as initial value. %in aconsistent manner as the solution of an algebraic Riccati equation. Theradiation impedance matrix is defined and shown to be non-Hermitian. Theseimpedance matrices enable concise and efficient formulations of dispersionequations for wave guides, and solutions of scattering and related waveproblems in cylinders.
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