Hamiltonian system for dynamic buckling of transversely isotropic cylindrical shells subjected to an axial impact

This paper investigates the prebuckling dynamics of transversely isotropic thin cylinder shells in the context of propagation and reflection of axial stress waves. By constructing the Hamiltonian system of the governing equation, the symplectic eigenvalues and eigenfunctions are obtained directly and rationally without the need for any trial shape functions, such as the classical semi-inverse method. The critical loads and buckling models are reduced to the problem of eigenvalues and eigensolutions, in which zero-eigenvalue solutions and nonzero-eigenvalue solutions correspond to axisymmetric buckling and nonaxisymmetric buckling, respectively. Numerical results reveal that energy is concentrated at the unconstrained free ends of the shell and the buckling modes have bigger bell-mouthed shapes at these positions.