Complex vibrations of closed cylindrical shells of circular cross section and finite length subjected to nonuniform sign-changeable external load in the frame of classical nonlinear theory are studied. A transition from partial differential equations to ordinary differential equations (Cauchy problem) is carried out using the higher order Bubnov–Galerkin’s approach and Fourier’s representation. On the other hand, the Cauchy problem is solved using the fourth-order Runge–Kutta method. Results are analyzed owing to the application of nonlinear dynamics and qualitative theory of differential equations. The present work is devoted to the analysis of influence of the system dynamics of the following parameters: length of pressure width $φ0$, relative linear shell dimension $λ=L∕R$, and frequency $ωp$ and amplitude $q0$ of external transversal load. Some new scenarios of vibrations of closed cylindrical shells exhibiting a transition from harmonic to chaotic vibrations are illustrated and studied.

1.
Awrejcewicz
,
J.
, and
Krysko
,
V. A.
, 2001, “
Feigenbaum Scenario Exhibited by Thin Plate Dynamics
,”
Nonlinear Dyn.
0924-090X,
24
, pp.
373
398
.
2.
Awrejcewicz
,
J.
,
Krysko
,
V.
, and
Krysko
,
A.
, 2002, “
Spatial-Temporal Chaos and Solitons Exhibited by Von Karman Model
,”
Int. J. Bifurcation Chaos Appl. Sci. Eng.
0218-1274,
12
(
7
), pp.
1465
1513
.
3.
Awrejcewicz
,
J.
, and
Krysko
,
A. V.
, 2003, “
Analysis of Complex Parametric Vibrations of Plates and Shells using Bubnov-Galerkin Approach
,”
Archive of Applied Mathematics
,
73
, pp.
495
504
.
4.
Awrejcewicz
,
J.
, and
Krysko
,
V.
, 2003,
Nonclassic Thermoelastic Problem in Nonlinear Dynamics of Shells
,
Springer
,
Berlin, Germany
.
5.
Awrejcewicz
,
J.
,
Krysko
,
V. A.
, and
Vakakis
,
A. F.
, 2004,
Nonlinear Dynamics of Continuous Elastic Systems
,
Springer
,
Berlin, Germany
.
6.
Volmir
,
A. S.
, 1963,
Stability of Elastic Systems
,
Fizmatgiz
, Moscow (in Russian).
7.
Krysko
,
V. A.
, and
Kucemako
,
A. N.
, 1999,
Stability and Vibrations of Non-Uniform Shells
,
Saratov University Press
,
Russia, Saratov
(in Russian).
8.
Krysko
,
V. A.
, and
Saveleva
,
N. E.
, 2003, “
Vibrations of Closed Cylindrical Shells at Non-Axis-Symmetrical Sign-Variable External Load
,”
Works of the International Conference “Nonlinear Fluctuations of Mechanical and Biological Systems,”
Saratov University Press
,
Russia, Saratov
(in Russian).
9.
Krysko
,
V. A.
, and
Saveleva
,
N. E.
, 2003,
,
Saratov University Press
,
Russia, Saratov
(in Russian).
10.
Krysko
,
V. A.
, and
Saveleva
,
N. E.
, 2004, “
,”
Works of the International Conference “Problems of Durability of Materials and Designs on Transport,”
St.-Petersburg
,
Russia
(in Russian).
11.
Landau
,
D.
, 1944,
On the Problem of Turbulence, Lectures Academy of Sciences of USSR
,
Moscow
,
Russia
(in Russian),
44
, pp.
339
342
.
12.
Ruelle
,
D.
, and
Takens
,
F.
, 1971, “
On the Nature of Turbulence
,”
Comp. Math. Phys
,
20
(
2
), pp.
167
192
.
13.
Feigenbaum
,
M. J.
, 1978, “
Quantitative Universally for a Class of Nonlinear Transformation
,”
J. Stat. Phys.
0022-4715,
19
(
1
), pp.
25
52
.
14.
Manneville
,
P.
, and
Pomeau
,
Y.
, 1980, “
Different ways to turbulence in dissipative dynamical systems
,”
Physica D
0167-2789,
1
, pp.
219
228
.
15.
Krysko
,
V. A.
, and
Saveleva
,
N. E.
, 2003, “
Ruelle-Takens-Feigenbaum Scenario and Counting of Feigenbaum constant
,”
Proceedings of the 7th Conference on “Dynamical Systems—Theory and Applications
,
J.
Awrejcewicz
,
A.
Owczarek
,
J.
Mrozowski
,
Łódź Poland
, December 8-11, pp.
179
188
.