Geodesic
Non-linear free flexural oscillations thin circle cylindrical shells
Dalʹnevostočnyj matematičeskij žurnal, Tome 1 (2000) no. 1, pp. 102-110

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The oscillations with large amplitudes jointly supported on tip of a circle cylindrical shell of finite length are studied. The mathematical model is established on equations of the non-linear theory of pliable shallow shells. Four versions of tangential fastening of tip of a shell are considered which, as against other known solutions, are satisfied precisely. The modal equations were obtained by a method of Boobnov-Galerkin. The periodic solutions were retrieved by a method Krylov-Bogolyubov. Obtained, that the “averaging” satisfaction of tangential bounder conditions, results in an essential error at definition of dynamic characteristics of a shell of finite length. Shown, that irrespective of a way of tangential fastening of tip of a shell, the single mode of motion is characterized by a skeletal curve of a soft type. This conclusion is qualitatively agreed with known experimental data. 
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     title = {Non-linear free flexural oscillations thin circle cylindrical shells},
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N. A. Taranukha; G. S. Leyzerovich. Non-linear free flexural oscillations thin circle cylindrical shells. Dalʹnevostočnyj matematičeskij žurnal, Tome 1 (2000) no. 1, pp. 102-110. http://geodesic.mathdoc.fr/item/DVMG_2000_1_1_a12/