Dynamic buckling of conical shells with imperfections

A study has been made to determine the dynamic stability of a truncated thin circular conical shell with various geometrical imperfections and under a wide variety of dynamic loading conditions. The method of solutions utilizes a Galerkin procedure. By assuming the deformation modes, the final nonlinear differential equations of motion are derived by minimizing the total energy of the system with respect to each of the undetermined modal amplitudes. A Runge-Kutta integration scheme is then used to solve these nonlinear differential equations numerically. From the characteristics of the shell response, a criterion for the buckling load is established. It is found that the tendency of dynamic buckling of a conical shell structure decreases with increase of the opening angle of the cone. Conical shells are also found to be less sensitive to initial geometric imperfections than the cylinder.