Calculation of the absorption cross section of a cylindrical gravitational-wave antenna

Eigenfunctions and eigenvalues are calculated in terms of power series in $\frac{R}{L}$ for free axisymmetric longitudinal oscillations of uniform circular cylinders of radius $R$ and length $L$. These are used to compute the cross section for absorption of gravitational waves. Our results are compared with the Pochhamer-Chree solution and other approximate solutions.