Stress waves in pyramids by photoelasticity
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.
KeywordsAttenuation Epoxy Fluid Dynamics Longitudinal Wave Pyramid
cross-sectional area, in.2
Young's modulus, lb/in.2
applied force, lb
fringe order, dimensionless
strain-gage factor, dimensionless
stress-optic coefficient, psi/fringe/in.
strain-optic coefficient, (in./in.)/fringe/in.
dilatational wave velocity, in./sec
rod wave velocity, in./sec
- pσ,qσ andrσ
principal stresses, lb/in.2
- pε,qε andrε
principal strains, in./in.
wavelength of the shortest significant Fourier component
mass density, lb-sec2/in.4
- λ, μ
Lamé constants, lb/in.2
Unable to display preview. Download preview PDF.
- 1.Tuzi, Z., andNisida, M., “Photoelastic Study of Stresses Due to Impact,”Phil. Mag.,21,448–473 (1936).Google Scholar
- 2.Senior, D. A., andWells, A. A., “Photoelastic Study of Stress Waves,”Phil. Mag.,37,463–469 (1945).Google Scholar
- 3.Feder, J. C., Gibbons, R. A., Gilbert, J. T., andOffenbacher, E. L., “The Study of the Propagation of Stress Waves by Photoelasticity,”Proc. Soc. Exp. Stress Anal., XIV (1),109–118 (1957).Google Scholar
- 4.Föppl, L., “Slow-Motion Pictures of Impact Tests by Means of Photoelasticity,”Jnl. Appl. Mech.,16,173–177 (1946).Google Scholar
- 5.Goldsmith, W., “Dynamic Photoelasticity,” U. S. Naval Ordnance Test Station, China Lake, Calif., Report No. NAVWEPS 8037, Nov. 1962, or in Experimental Techniques in Shock and Vibration published from winter annual meeting of the American Society of Mechanical Engineer 25–54 (Nov. 27, 1962).Google Scholar
- 6.Clark, Austin B. J., “Static and Dynamic Calibration of Photoelastic Model Material, CR-39,”Proc. Soc. Exp. Stress Anal., XIV (1),195–204 (1957).Google Scholar
- 7.Dove, R. C., andAdams, P. H., Experimental Stress Analysis and Motion Measurements, Charles E. Merrill Books Inc., Ohio (1964).Google Scholar
- 9.Meier, J. H., “Dynamic Determination of the Photoelastic Fringe Constant for Hysol 4290 Plastic,” IBM Technical Report TR.01.13. 172662 (Oct. 1961).Google Scholar
- 11.Taylor, C. E., Bowman, C. E., North, W. P. T., and Swinson, W. F., “Applications of Lasers to Photoelasticity,” Dept. of Theoretical and Applied Mechanics, University of Illinois, Report No. TAM 276.Google Scholar
- 12.Flynn, P. D., “Photoelastic Studies of Dynamic Stresses in High Modulus Materials,”Jnl. Soc. Motion Picture Television Engrs.,75 (8),729–734 (August 1966).Google Scholar
- 13.Landon, J. W., andQuinney, J., “Experiments with Hopkinson Pressure Bar,”Proc. Roy. Soc. (London), A 103,639–643 (1943).Google Scholar
- 14.Kenner, V., “Wave Propagation in Conical Bars,” M.S. Thesis, University of California (1967).Google Scholar
- 15.Drucker, D. C., “Photoelastic Separation of Principal Stresses by Oblique Incidence,” Jnl. Appl. Mech., A156–A160 (Sept. 1943).Google Scholar
- 16.Woodward, W. B., “A Photoelastic Investigation of the Stress Distribution in a Cone with a Band of Pressure at the Vertex,”Proc. Soc. Exp. Stress Anal., XVII (1)85–98 (1960).Google Scholar
- 18.Cunningham, D. M., andGoldsmith, W., “Short-Time Impulses Produced by Longitudinal Impact,”Proc. Soc. Exp. Stress Anal., XVI (2),153–164 (1959).Google Scholar
- 19.Cistaro, J., Dally, J. W., Isakson, K., Miller, R., Riley, W. F., and Viera, J., “Feasibility Study of Methods for Dynamic Three-Dimensional Photoelasticity,” Technical Report No. AFSWC-TDR-63-48, Kirkland Air Force, N. M. (June 1963).Google Scholar
- 21.Goldsmith, W., and Norris, G. W., Jr., “Stresses in Curved Beams due to Transverse Impact,” Proc. of the 3rd. U.S. Nat. Cong. Appl. Mech., 153–162 (1958).Google Scholar
- 23.Kolsky, H., “Stress Waves in Solids,” Dower Publications, Inc. Google Scholar