Growth of longitudinal and torsional waves through a rod for second order elasticity

Abstract

A boundary value problem connected with the propagation and growth of wave through a rod of second order elastic materials is studied. Two one-dimensional equations of motions are derived from the exact three dimensional equations which govern the torsional and longitudinal wave motions. The torsional wave does not grow at all while there is a distinct possibility for a compressive wave to grow into a shock. For Seth's stress strain relations the compressive wave grows into a shock while a tension wave decays.