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

[+] Author and Article Information
R. A. Williams

Department of Mechanics, University of Wisconsin-Milwaukee, Milwaukee, Wis.

L. E. Malvern

Department of Metallurgy, Mechanics, and Material Science, Michigan State University, East Lansing, Mich.

J. Appl. Mech 36(1), 59-64 (Mar 01, 1969) (6 pages) doi:10.1115/1.3564586 History: Received February 23, 1968; Revised July 10, 1968; Online September 14, 2011


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.

Copyright © 1969 by ASME
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