The Main Parameters Affecting the Stability of Rotating Pretwisted Cylindrical Shells

Abstract

In the paper, the main parameters affecting the stability of a rotating pretwisted cylindrical shell model with a presetting angle are found by the extended singularity theory. Based on the nonlinear second-order ordinary differential equations of rotating pretwisted cylindrical shell, the universal unfoldings of these equations are given, such that the derivative terms of these equations are treated as periodic perturbation parameters. Analysis results show that these equations have: one form of the universal unfolding codimension 4; one form of the universal unfolding codimension 2; one form of the universal unfolding codimension 2. Calculating the transition set of the universal unfolding codimension 2, the transition set covers all parameters which affect the stability of the rotating pretwisted cylindrical shell. The numerical results show that the amplitudes of periodic excitation and part of the functions of the geometric and physical parameters have strong effect on bifurcation and hysteresis of the rotating pretwisted cylindrical shell subjected to small perturbations near the singularity; however, small external disturbances have weak effect on bifurcation and hysteresis. Due to the periodicity of perturbation parameters, settled in different persistent regions by change in other parameters, the governing equations produce chaotic solutions. The present results are validated by comparison with those in the existing literature.