Abstract
In [1] a dispersion relation for the vibrations of an elastic rod of circular cross section with an electric current flowing over its surface was obtained, and a detailed study was made of the particular case of axially symmetric vibrations. The present paper is devoted to an examination of the longwave bending vibrations of elastic rods with an electric current flowing over their surface. These vibrations are of special interest since they have the lowest frequency and hence the last stability.
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References
N. I. Dolbin, “Propagation of elastic wavesin a current-carrying rod,” PMTF, no. 2, 104, 1962.
H. Kolsky, Stress Waves in Solids, Oxford, 1953.
M. A. Leontovich and V. D. Shafranov, “Stability of a flexible conductor in a longitudinal magnetic field,” in: Plasma Physics and Problems of Controlled Thermonuclear Reactions [in Russian], Izd-vo AN SSSR, vol. 1, 1958.
N. W. McLachlan, Theory and Application of Mathieu Functions, [Russian translation], Izd. inostr. lit., 1953.
E. T. Whittaker and G. N. Watson, Modern Analysis, Vol. 2 [Russian translation], Fizmatgiz, 1963.
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Dolbin, N.I., Morozov, A.I. Elastic bending vibrations of a rod carrying electric current. J Appl Mech Tech Phys 7, 59–62 (1966). https://doi.org/10.1007/BF00914701
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DOI: https://doi.org/10.1007/BF00914701