The Chaotic Motion of an Axially Compressed Cylindrical Shell Subjected to Radial Disturbance
Using the logarithmic hoop strain，a nonlinear dynamic equation governing the axisymmetric radial motion of an axially compressed cylindrical shell subjected to radial disturbance is derived. By means of Bubnov-Galerkin approach the partial differential equation can be transformed into an ordinary differential equation containing second-order nonlinear term. The qualitative analysis indicates that the autonomous dynamic systems corresponding to two cases of pre-buckling and post-buckling has the form-same homoclinic orbits and two orbits locate different positions on the horizontal axis of phase plane. The threshold condition for the occurrence of Smale horseshoe-type chaos in disturbed system is obtained by Melnikov’s method. Finally, the bifurcation diagram, time-history curve, phase portrait and Poincare’s map are calculated.
T. Zhang and S. Y. Zhang, "The Chaotic Motion of an Axially Compressed Cylindrical Shell Subjected to Radial Disturbance", Applied Mechanics and Materials, Vols. 29-32, pp. 454-459, 2010