Non-axisymmetric Dynamic Buckling And Chaotic Behavior Of Cylindrical Shell

Cylindrical shells have been widely applied in aerospace, weapons manufacturing and nuclear engineering etc. because of its excellent properties and satisfactory design performance. They often work in complex and extreme conditions such as explosion, high speed impact. The dynamic behavior of cylindrical shells under high speed impact is very different from static behavior. So the research on the dynamic buckling of cylindrical shells is of great significance. Current research to non-axisymmetric dynamic buckling of cylindrical shells focuses on aspects of computer simulation and experimental study due to the complexity of theory. The research includes the following aspects:(1) The research status of dynamic buckling and chaos effect of cylindrical shells at home and abroad is reviewed. The research methods are summarized.(2) Considering the effect of stress wave and first-order shear deformation, the non-axisymmetric dynamic buckling governing equation of cylindrical shells is derived by using the Hamilton principle. The expression of radial displacement function along the circumferential direction is got since the cylindrical shell is closed. The buckling modes and analytical solution of the critical load can be obtained based on Variable Separation method and the periodic properties of trigonometric functions before the reflection of stress wave. The influences of shear effect, boundary conditions, diameter-thickness ratio, modes etc. on critical load are discussed.(3) Considering the effect of stress wave, the non-axisymmetric dynamic buckling governing equation of composite cylindrical shells under axial step load is derived by using the Hamilton principle. The expression of radial displacement function along the circumferential direction is got since the cylindrical shell is closed. The buckling modes and analytical solution of the critical load on the dynamic buckling of composite cylindrical shell can be obtained b ased on Variable Separation method before the reflection of stress wave. Comparing the analytical solution with the result got by Ritz method. The influences of diameterthickness ratio, ply orientations, etc. on critical load are discussed by using MATLAB software.(4) Considering geometrical nonlinearity, the nonlinear controlling equations of composite cylindrical shells are established, the formula of displacement function is given based on the simple supported boundary condition and the stress function can be obtained. Transforming governing equations into Duffing equation based on Galerkin principle. Chaotic Thresholds are solved by the function of Melnikov. The bifurcation diagrams, displacement-time curve graph, the space trajectory, the Poincare? map are got by Runge-Kutta Method are used to describe the chaotic behavior of cylindrical shells. In the end, the chaos effect of different ply orientations is discussed.