Dispersion of small amplitute stress waves in pre-stressed elastic, visco-plastic cylindrical bars
Authors:
Jozef Bejda and Tomasz Wierzbicki
Journal:
Quart. Appl. Math. 24 (1966), 63-71
DOI:
https://doi.org/10.1090/qam/99931
MathSciNet review:
QAM99931
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Abstract: The effect of geometrical dispersion on the propagation of longitudinal harmonic stress waves in prestressed elastic, visco-plastic bars is investigated. The solution involves the Hunter and Johnson approximation in which radial and axial displacements and all components of stress tensor are expanded as power series in the radial coordinate. It is shown that the dispersion of the sinusoidal waves is generated by the two simultaneously acting phenomena. These are the purely geometrical dispersion produced by the influence of a free boundary of the bar and the viscous dispersion caused by the viscous properties of material. The obtained solution embraces the combined effect of the phenomena mentioned above. A numerical example is presented in which constants of material characteristic for mild steel were used. The result of the computations provides a plot of phase and group velocities and damping coefficient against the frequency of harmonic waves. The present solution has been compared with the Hunter and Johnson solution for strain-hardening elastic-plastic material and with the exact Pochhammer-Chree solution for elastic rods.
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G. P. De Vault, The effect of lateral inertia on the propagation of plastic strain in a cylindrical rod, J. Mech. Phys. Solids 13, 55–68 (1965)
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E. H. Lee, Wave propagation in anelastic materials, Deformation and Flow of Solids, IUTAM Colloquium, Madrid 1955, 129–136, Springer (1956)
- P. Perzyna, The constitutive equations for rate sensitive plastic materials, Quart. Appl. Math. 20 (1962/63), 321–332. MR 144536, DOI https://doi.org/10.1090/S0033-569X-1963-0144536-3
E. J. Sternglass and D. A. Stuart, An experimental study of the propagation of transient longitudinal deformation in elasto-plastic media, J. Appl. Mech., 20, 427 (1953)
G. Bianchi, Some experimental and theoretical studies on the propagation of longitudinal plastic waves in a strain-rate-dependent materials, Stress Waves in Anelastic Solids, Proc. IUTAM Symposium, Providence 1963, 101–117, Springer (1964)
G. P. De Vault, The effect of lateral inertia on the propagation of plastic strain in a cylindrical rod, J. Mech. Phys. Solids 13, 55–68 (1965)
S. C. Hunter and I. A. Johnson, The propagation of small amplitude elastic-plastic waves in pre-stressed cylindrical bars, Stress Waves in Anelastic Solids, Proc. IUTAM Symposium, Providence 1963, 149–165, Springer (1964)
E. H. Lee, Wave propagation in anelastic materials, Deformation and Flow of Solids, IUTAM Colloquium, Madrid 1955, 129–136, Springer (1956)
P. Perzyna, The constitutive equations for rate sensitive plastic materials, Quart. Appl. Math., 20, 321–332 (1963)
E. J. Sternglass and D. A. Stuart, An experimental study of the propagation of transient longitudinal deformation in elasto-plastic media, J. Appl. Mech., 20, 427 (1953)
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Article copyright:
© Copyright 1966
American Mathematical Society
