Nonlinear breathing vibrations of eccentric rotating composite laminated circular cylindrical shell subjected to temperature, rotating speed and external excitations

The internal resonances and the nonlinear breathing vibrations of an eccentric rotating composite laminated circular cylindrical shell rounding a parallel axis are studied for the first time, which is subjected to the lateral excitation and the temperature excitation. Based on Love thin shear deformation theory and von Kármán-type nonlinear relation, the nonlinear partial differential governing equations of motion for the eccentric rotating composite laminated circular cylindrical shell are established by Hamilton’s principle. The nonlinear partial differential govern equations are discretized into a set of coupled nonlinear ordinary differential equations by Galerkin approach. Considering the effects of the eccentricity ratio, the geometric parameters and the excitation conditions, the internal resonance and nonlinear breathing vibrations of the eccentric rotating composite laminated circular cylindrical shell rounding a parallel axis are studied. The method of multiple scales is employed to obtain four-dimensional nonlinear averaged equations. Corresponding to several selected parameters, the frequency-response curves are obtained and the nonlinear dynamic behaviors and the jump phenomena are exhibited. The effects of different parameters on the nonlinear resonant responses are also studied. The periodic and chaotic motions of the eccentric rotating composite laminated circular cylindrical shell rounding a parallel axis are found when the rotating speed corresponds to the internal resonant point at the certain excitations.