Transient wave propagation in an isotropically elastic, hollow rod is studied experimentally to help appraise existing and new rod analyses. The study involves a comparison between the actual dynamic response of a hollow rod determined from experiments and the response of the same rod as predicted using the method of characteristics and an approximate theory. Not only is the method itself appraised but insight (though limited by experimental data) is gained into what order approximate theory is appropriate for a rod of a particular cross‐sectional geometry. Two approximate theories are presented: a membrane theory which is already in existence and a two‐mode theory which is new. The governing equations of motion for this latter theory are derived and the frequency equation is established. The experimental results are due to Heimann and Kolsky and are in the form of responses, at two stations, to an impact on the end of the rod. Comparison with theory is obtained by treating the response at the first arrival station as an input. By this device, an input is formulated in which the actual, complicated dependency on time is known at the expense of the radial dependency. The trade is based on the belief that for hollow rods, except perhaps when the walls are thick, an assumed distribution of strains through the thickness that is consistent with the boundary conditions and the kinematics of the approximate theory will differ little from the actual strains. The responses from experiment and theory at the second station are remarkably close to one another, which would seem to establish the value of the method of characteristics for the type of problem considered here.
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May 01 1973
Comparison of experimental and theoretical responses in hollow rods to a transient input
G. Pernica;
G. Pernica
Department of Civil Engineering, University of California, Berkeley, California 94720
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H. D. McNiven
H. D. McNiven
Department of Civil Engineering, University of California, Berkeley, California 94720
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J. Acoust. Soc. Am. 53, 1365–1376 (1973)
Article history
Received:
November 15 1971
Citation
G. Pernica, H. D. McNiven; Comparison of experimental and theoretical responses in hollow rods to a transient input. J. Acoust. Soc. Am. 1 May 1973; 53 (5): 1365–1376. https://doi.org/10.1121/1.1913482
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