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

Abstract

In this paper, the nonlinear breathing vibrations of an eccentric rotating composite laminated circular cylindrical shell are studied for the first time, which is subjected to the lateral and temperature excitations. Based on Donnell thin shear deformation theory, von Kármán-type nonlinear relation and Hamilton’s principle, the nonlinear partial differential governing equations of motion are established for the eccentric rotating composite laminated circular cylindrical shell. The nonlinear partial differential governing equations of motion are discretized into a set of coupled nonlinear ordinary differential equations of motion by Galerkin approach. Based on the case of 1:2 internal resonance and principal parametric resonance-1/2 subharmonic resonance, the method of multiple scales is employed to obtain four-dimensional nonlinear averaged equations. Considering the effects of different parameters, for example, the eccentricity ratio, the geometric parameters and the excitations, the nonlinear dynamic behaviors and the jumping phenomena are exhibited for the frequency-response curves and the amplitude-response curves. The periodic and chaotic motions of the eccentric rotating composite laminated circular cylindrical shell are found when the rotating speed corresponds to the internal resonant point at the certain conditions for different lateral and temperature excitations.