Experimental Mechanics

, Volume 8, Issue 7, pp 289–299 | Cite as

Stress waves in pyramids by photoelasticity

Experimental investigation was undertaken for the purpose of gaining a better understanding of how a doubly tapered section conditions stress waves
  • A. Okada
  • D. M. Cunningham
  • W. Goldsmith
Article

Abstract

The propagation of stress waves in pyramids was studied photoelastically with the application of a laser-photomultiplier tube system and an internal polariscope for recording moving fringes. Dispersion and attenuation of stress waves were considered in a straight bar, a 5-deg pyramid, and a 20-deg pyramid made of Hysol 4290 epoxy plastic. In the straight bar and 5-deg pyramid, longitudinal waves propagate without any dispersion even though the waves attenuate as they progress down the models; in the 20-deg pyramid, however, the dispersion of the stress waves is quite significant. The distributions of the axial and radial stresses and the photoelastic fringe patterns obtained on the 20-deg pyramid show that the stress wave front is spherical with the maximum stress along the central axis of the pyramid. A one-dimensional theory of wave propagation without correction factors in a small-angle infinite cone compares well with the experimental results.

Keywords

Attenuation Epoxy Fluid Dynamics Longitudinal Wave Pyramid 

Nomenclature

A

cross-sectional area, in.2

E

Young's modulus, lb/in.2

F

applied force, lb

N

fringe order, dimensionless

G.F.

strain-gage factor, dimensionless

d

diameter, in.

f

stress-optic coefficient, psi/fringe/in.

g

strain-optic coefficient, (in./in.)/fringe/in.

h

thickness, in.

m

mass, lb-sec2/in.

r

radius, in.

t

time, μsec

u

displacement, in.

ω

weight, lb

cD

dilatational wave velocity, in./sec

co

rod wave velocity, in./sec

pσ,qσ andrσ

principal stresses, lb/in.2

pε,qε andrε

principal strains, in./in.

Λ

wavelength, in.

Λs

wavelength of the shortest significant Fourier component

σ

stress, lb/in.2

ε

strain, in./in.

ρ

mass density, lb-sec2/in.4

λ, μ

Lamé constants, lb/in.2

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Copyright information

© Society for Experimental Mechanics, Inc. 1968

Authors and Affiliations

  • A. Okada
    • 1
  • D. M. Cunningham
    • 2
  • W. Goldsmith
    • 2
  1. 1.Rocketdyne Corp.North American Rockwell Corp.Canoga Park
  2. 2.University of CaliforniaBerkeley

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