Chaotic Motion Of Cylindrical Shell Under Large Deflection And Its Control

Research of the cylindrical shell only relates to static stability, rarely involves dynamic stability at present, including the problem of chaos. For ordinary thin cylindrical shell, its weight is generally relatively light, and its strength is generally required larger. The structure would lead to a substantial vibration in general. Linear vibration theory that the natural frequencies and mode shapes independent of the amplitude of the situation can’t be met at this time, the presence of non-linear effect makes this assumption is no longer true, the chaos caused by the motion of nonlinear problems need to be solved.Based on Donnell shallow shell theory, chaotic motion of cylindrical shell under large deflection is studied. Using Lagrange equation and Galerkin equations obtained the system of cylindrical shell under large deflection. The threshold region of chaotic systems is determined by Melnikov method. Then analyze chaotic motion of cylindrical shell under large deflection based on the methods of numerical analysis. Then describe the state of the system according to the bifurcation diagrams, Poincare map, time history graph, power spectrum and so on.In this paper, a lot of analysis about cylindrical shell under defect is made to find that nonlinear factors for the chaotic motion of cylindrical shell under large deflection make sense. Comparing the chaotic motion of cylindrical shell under defect and perfect cylindrical shell, it can be concluded that initial defect condition would make the natural frequency of the system increased, the occurrence of chaotic critical load reduced, and the initial defects will make the system easier to be chaotic. After the comparative analysis, we can see a higher degree of chaos of defect system under the same conditions. In this paper, the analysis not only conclude the chaotic motion of isotropic cylindrical shell under large deflection but also the study of the material and geometry to chaos’ s effect of the orthotropic cylindrical shell under large deflection. The study found that material and geometry properties has a significant impact to chaotic threshold for orthotropic shell, directly impact the degree of non-linear to cylindrical shells under large deflection, thus affecting the cylindrical shell under deflection into the chaotic conditions. After a series of comparison, results showed that: the material and geometric nonlinearity parameter values lead to changes in the system, leading to chaotic threshold changes, and not just chaotic threshold will change, along with the degree of chaos in the system will change too.Based on the unpredictability of chaotic systems, we use feedback and non-feedback method to control the chaotic motion of the system. Finally, based on the non-feedback control law, the chaotic state of cylindrical shell under large deflection gets some control, but the effect is not particularly desirable. Then adopting OGY method to control the chaotic state of cylindrical shell under large deflection, then the control effect is very obvious.