Far Eastern Mathematical Journal

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Non-linear free flexural oscillations thin circle cylindrical shells

N. A. Taranukha, G. S. Leyzerovich

2000, issue 1, Ń. 102–110

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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[1] D. A. E'vensen, “Nelinejnye kolebaniya krugovyx cilindricheskix obolochek”, Tonkostennye obolochechnye konstrukcii, Mashinostroenie, M., 1980, 156–176.
[2] V. D. Kubenko, P. S. Koval'chuk, T. S. Krasnopol'skaya, Nelinejnoe vzaimodejstvie form izgibnyx kolebanij cilindricheskix obolochek, Nauk. dumka, Kiev, 1984.
[3] T. K. Varadan, Dzh. Pratxap, X. V. Ramani, “Nelinejnye svobodnye izgibnye kolebaniya tonkostennyx krugovyx cilindricheskix obolochek”, Ae'rokosmicheskaya texnika, 1990, ¹ 5, 21–24.
[4] E. V. Ladygina, A. I. Manevich, “Nelinejnye svobodnye izgibnye kolebaniya cilindricheskoj obolochki s uchetom vzaimodejstviya sopryazhennyx form”, Izv. AN MTT, 1977, ¹ 3, 169–175.
[5] G. S. Lejzerovich, “O formax kolebanij tonkostennyx krugovyx cilindricheskix obolochek”, Problemy mexaniki sploshnyx sred, Materialy trudov mezhd. nauch.-texn. konf., Ch. 1, KnAGTU, Komsomol'sk-na-Amure, 1998, 53–55.
[6] A. S. Vol'mir, Nelinejnaya dinamika plastin i obolochek, Nauka, M., 1972.

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