Abstract
Donnell equations are used to simulate free nonlinear oscillations of cylindrical shells with imper- fections. The expansion, which consists of two conju- gate modes and axisymmetric one, is used to analyze shell oscillations. Amplitudes of the axisymmetric mo- tions are assumed significantly smaller, than the con- jugate modes amplitudes. Nonlinear normal vibrations mode, which is determined by shell imperfections, is analyzed. The stability and bifurcations of this mode are studied by the multiple scales method. It is dis- covered that stable quasiperiodic motions appear at the bifurcations points. The forced oscillations of circular cylindrical shells in the case of two internal resonances and the prin- ciple resonance are analyzed too. The multiple scales method is used to obtain the system of six modulation equations. The method for stability analysis of standing waves is suggested. The continuation algorithm is used to analyze fixed points of the system of the modulation equations.
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