Geodesic
Roots of the circular cylindrical shell characteristic equation
Applications of Mathematics, Tome 17 (1972) no. 6, pp. 409-421
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In this paper the following fact is proved: the complete characteristic equation of 8-th degree for the closed circular cylindrical shell in Goldenweiser's version (Love-Timoshenko's approach to the change of circumferential curvature) has not real roots for harmonics $n=2$, so that this version is not in contradiction to the law of conservation of energy. If we neglect little members in this equation, real roots appear. Solving this equation, two regions of the numerical instability arise. For the calculation of the roots a) algebraic algol-procedure RADICES, b] iteration method and c) asymptitic series, which is suitable in the instability region, are introduced.
In this paper the following fact is proved: the complete characteristic equation of 8-th degree for the closed circular cylindrical shell in Goldenweiser's version (Love-Timoshenko's approach to the change of circumferential curvature) has not real roots for harmonics $n=2$, so that this version is not in contradiction to the law of conservation of energy. If we neglect little members in this equation, real roots appear. Solving this equation, two regions of the numerical instability arise. For the calculation of the roots a) algebraic algol-procedure RADICES, b] iteration method and c) asymptitic series, which is suitable in the instability region, are introduced.
DOI : 10.21136/AM.1972.103434
Classification : 65H05, 74-04, 74K15, 74K25 
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Geryk, Milan. Roots of the circular cylindrical shell characteristic equation. Applications of Mathematics, Tome 17 (1972) no. 6, pp. 409-421. doi: 10.21136/AM.1972.103434

[1] M. Geryk:: Closed circular cylindrical shell. (Czech). Diss, VUT Brno 1963.

[2] D. A. Royak: Circular cylindrical shell characteristic equation. (Russian). Izvěstija AN SSSR - Mechanika i mašinostrojenije No 5/1961.

[3] W. S. Wlasow: Allgemeine Schalentheorie und ihre Anwendung in der Technik. Berlin 1958.

[4] A. L. Goldenweiser: Theory of elastic shells. New York 1961.

[5] W. Flügge: Stresses in shells. Springer 1962. | MR

[6] Š. Schwarz: On equations. (Czech). JČMF, Praha 1947.

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