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Elastic waves in truncated cones

Experimental and theoretical investigation is undertaken by authors to study the propagation of waves produced by impact of projectiles on truncated cones

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Abstract

An experimental investigation of elastic waves produced by the axial collision of strikers with truncated 2024 aluminum cones with apex angles of 0.48, 5.38, 20, and 30 deg was performed. Wave propagation was initiated at the small end of all four cones and at the large end of the 0.48-deg and 5.38-deg cones. The striker consisted of a 1/2-in.-diam steel ball or a soft phenol-impregnated fiber cylinder. In most cases, impact was caused by firing the striker from an air gun at approximately 1300 ips; in an additional series of tests, a steel ball was dropped on the cone. The metamorphosis of the pulse at the surface of the target was recorded using both foil and semiconductor resistance strain gages. Data were obtained for periods ranging from 200 to 500 μsec; this permitted the observation of several reflections from the ends of the specimen. In several instances, cylindrical aluminum rods were glued to the cone to form a composite target; this permitted observation of the initial pulse incident on the conical section both from surface strain gage and sandwiched crystal records. Studies were also conduced to ascertain the stress distribution across the base of the 20-deg cone.

Initial pulse records were employed to predict the surface response in the target using the one-dimensional equation of elastic wave propagation in a cone of infinite length. Reasonable agreement between the data and the results of calculations based on the analysis was obtained.

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Abbreviations

A :

area of cross section

c :

phase velocity

c 0 :

rod wave velocity

c s :

shear wave velocity

E :

Young's modulus

f,F :

function

g :

acceleration of gravity

r :

distance from cone apex

R :

radius of cross section

t :

time

u :

displacement

v 0 :

initial velocity of striker

v f :

final velocity of striker

α:

total cone angle

ε:

strain

Δ:

wavelength

μ:

Poisson's ratio

ρ:

density

σ:

stress

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Authors and Affiliations

  1. Department of Mechanical Engineering, University of California, Berkeley, Calif

    V. H. Kenner (Research Assistant) & W. Goldsmith (Professor of Applied Mechanics)

Authors
  1. V. H. Kenner
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  2. W. Goldsmith
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Kenner, V.H., Goldsmith, W. Elastic waves in truncated cones. Experimental Mechanics 8, 442–449 (1968). https://doi.org/10.1007/BF02327408

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  • DOI: https://doi.org/10.1007/BF02327408

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