Exact Analysis of the Plane-Strain Vibrations of Thick-Walled Hollow Cylinders

Abstract

The plane-strain vibrations of a thick-walled hollow cylinder are investigated in the framework of the linear theory of elasticity. Approximate expressions for the frequencies of free modes are derived for moderately thick shells. The transition from the shell vibrations to the Pochhammer vibrations of a solid cylinder is investigated by means of a numerical solution of the frequency equation using an IBM 704 digital computer.