Elastic Strain Produced by Sudden Application of Pressure to One End of a Cylindrical Bar. I. Theory

Abstract

A double transform method is used to solve the problem of determining the elastic strain in a semi‐infinite cylindrical bar with a stress free lateral surface, subject to the end conditions that the stress applied normally to the end is uniform and has a step function time dependence and that the radial displacement at the end is always zero. The exact solution appears as a sum of Fourier integrals whose integrands have the form of Pochhammer‐Chree waves. These integrals cannot be evaluated in general by simple means, but asymptotic solutions have been obtained which are valid for large distances of travel. The theoretical predictions are compared with the results of experiment in a companion report.