Harmonic Dispersion Analysis of Incremental Waves in Uniaxially Prestressed Plastic and Viscoplastic Bars, Plates, and Unbounded Media

Abstract

The equations governing the propagation of infinitesimal incremental loading stress waves in a medium prestressed uniaxially into the plastic region are derived for a strain-rate-independent and a strain-rate-dependent constitutive equation. These equations, applied to a circular rod, a flat plate, and an unbounded medium, are solved using harmonic analysis to give the phase-velocity dispersion curves for component waves as a function of frequency. The results of this analysis are compared to the corresponding elastic dispersion curves.