Non-linear free flexural oscillations thin circle cylindrical shells

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.