Finite element analysis of the axisymmetric vibrations of cylinders

A finite element analysis is developed for finite and infinite solid or hollow cylinders in axisymmetric vibration. The elements themselves are solid or annular cylinders, and have 16 degrees of freedom. Results are given for the propagation constants of solid and hollow infinite cylinders, and excellent agreement is found with those from the exact Pochhammer theory and Mindlin and McNiven's three-mode theory. Frequency spectra are presented for the symmetric and antisymmetric modes of solid and hollow finite rods. Excellent agreement is found with experimental results, and this suggests that some of the results obtained from the three-mode theory by McNiven et al., and in particular the frequency of the end mode, are in error by more than 10%. Details of the finite element inertia and stiffness matrices appear in an appendix.