On dynamic quasi-bifurcation of simple shell-like systems under impulsive loads

Abstract

The nonlinear dynamic response and buckling of a simple, two degree of freedom system is investigated in this work under an impulsive load that simulates a nearby detonation-like explosion. The model considered in this work was originally studied by other researchers to explore static buckling. The system includes force and moment springs in much the same way as membrane and bending effects develop in shell structures. The static response is first obtained to evaluate bifurcation states and nonlinear equilibrium paths including geometric imperfections. The dynamic problem is modeled using Lagrange equation of motion involving the total potential and kinetic energies. The nonlinear dynamic response under impulsive load is next computed for the perfect configuration under increasing load levels. The presence of quasi-bifurcations is detected using stability coefficients based on second order derivatives of the total potential energy. For a given load level, it is found that one stability coefficient vanishes at the first maximum in the displacement versus time trajectory, at which the system passes through a state of zero velocity. This occurs for the same displacement configuration as in the static buckling mode. The results show that quasi-bifurcation loads thus obtained are independent of the amplitude of the geometric imperfection considered but display high sensitivity to changes in the membrane to bending stiffness ratio. Extensions of the present model to account for the behavior of oil storage tanks under loads due to nearby explosions are suggested.