The dynamic buckling response of a spring-mass, geometrically imperfec
t, dissipative model with 3 degrees of freedom simulating a relatively
deep cylindrical shell panel under step loading is comprehensively an
alyzed. The main feature of the real continuous structure and its corr
esponding model is that, under the same Loading statically applied, bo
th exhibit snapping. Energy, topological, and geometric considerations
allow us to establish qualitative and quantitative criteria leading t
o dynamic buckling loads of both dissipative and nondissipative models
without integrating the highly nonlinear equations of motion. An a pr
iori knowledge of the accuracy of these buckling estimates is successf
ully obtained by discussing the geometry of the channel in which the m
otion takes place before reaching the escape passage through a saddle
(or its neighborhood) with very small negative total potential energy.
A comparison of the numerical results obtained by the proposed method
with those of Runge-Kutta-Verner scheme shows the reliability and eff
iciency of the proposed method.