Vibrations of Solid Cylinders

A series solution of the general three-dimensional equations of linear elasticity is developed and used to find accurate natural frequencies for the vibrations of solid elastic cylinders with traction-free surfaces. The series solution is found to converge to accurate frequencies with the use of very few terms. Results are given for height-to-diameter ratios from zero to two and a frequency parameter ωR/Cs from zero to five and for modes of circumferential order from zero to four. Comparisons of these analytical results with previous experimental results shows excellent agreement.