Starting from Flügge's three equations of motion for a uniform thin cylindrical shell, the paper gives a general solution, from which the dependence of natural frequencies on shell dimensions and mode number can be investigated for any end conditions. This solution requires the assumption of a natural frequency and the determination of the corresponding shell length for the prescribed end conditions. Numerical results are given for shells with clamped ends and for shells with free ends; the variation of frequency factor and of mode shape with dimensional and mode parameters is shown and the accuracy of approximate theories assessed.
Get full access to this article
View all access options for this article.
References
1.
ArnoldR. N.WarburtonG. B.‘Flexural vibrations of the walls of thin cylindrical shells having freely supported ends’, Proc. roy. Soc.1949197 (Series A), 238.
2.
ArnoldR. N.WarburtonG. B.‘The flexural vibrations of thin cylinders’, Proc. Instn mech. Engrs, Lond.1953167 (A), 62.
3.
ForsbergK.‘Influence of boundary conditions on the modal characteristics of thin cylindrical shells’, A.I.A.A. Journal19642 (No. 12), 2150.
4.
FlüggeW.Statik und Dynamik der Schalen, second edition, 1957 (Springer, Berlin).
5.
RayleighLordTheory of sound, vol. 1, second edition, 1894 (Macmillan, London).
6.
TimoshenkoS.Theory of plates and shells, first edition, 1940 (McGraw-Hill, New York).
7.
LoveA. E. H.The mathematical theory of elasticity, fourth edition, 1927 (Cambridge University Press).
8.
WarburtonG. B.‘The vibration of rectangular plates’, Proc. Instn mech. Engrs, Lond.1954168, 371.
9.
BishopR. E. D.JohnsonD. C.Vibration analysis tables1956 (Cambridge University Press).
