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.

Propagation and attenuation of guided waves in stressed viscoelastic waveguides

“…Actually, the exploration of wave propagation in predeformation or prestress solids started from the mathematical treatment in the works by Biot [5] and Hayes [6]. Williams and Malvern [7] analyzed the dispersion curves of phase velocity in prestressed structures and media with different strain-rate constitutive equations. Mott [8] considered the lower flexural wave modes in solid cylinders subjected to a static axial stress and strain.…”

Guided waves dispersion analysis for prestressed viscoelastic waveguides by means of the SAFE method

“…Through the years, the problem has been subjected to an intensive research. Williams and Malvern (1969) used the harmonic analysis to get the phase-velocity dispersion curves for prestressed circular rods, flat plates and unbounded mediums considering both strain-rate-independent and strain-rate-dependent constitutive equations. The effect of tensile and compressive axial loads on the dispersive characteristic of elastic waves propagating in submerged beams was investigated by Cook and Holmes (1981).…”