The Chaotic Motion of an Axially Compressed Cylindrical Shell Subjected to Radial Disturbance

Abstract:

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.

• Periodical: Applied Mechanics and Materials (Volumes 29-32)
• Pages: 454-459
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.29-32.454
• Online since: August 2010
• Authors: Tao Zhang, Shan Yuan Zhang
• Keywords: Axial Compression, Chaotic Motion, Cylindrical Shell, Logarithmic Hoop Strain, Melnikov Function, Radial Periodic Disturbance

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