Abstract
DURING measurements of the resonant frequencies of torsional vibrations in cylindrical bars, it was observed that variation in the diameter of the bar along its axis caused the resonant frequencies to depart from a harmonic series. In order to relate the resonant frequencies to the shape of the bar, we have adapted a method described by P. M. Morse1 for calculating the modes of vibrating strings in which the tension varies from point to point along the length.
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References
Morse, P. M., “Vibration and Sound”, 2nd edit., 122 (McGraw-Hill, 1948).
Love, A. E. H., “The Mathematical Theory of Elasticity”, 4th edit., 289 (Dover Publications, 1944).
Pochhammer, L., I.C. Math. (Crelle), 81, 324 (1876).
Bancroft, D., Phys. Rev., 59, 588 (1941).
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PURSEY, H. Effect of Variation in Diameter on the Torsional Vibration of Bars. Nature 170, 502 (1952). https://doi.org/10.1038/170502a0
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DOI: https://doi.org/10.1038/170502a0
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