Propagating buckles in undersea pipelines – A model problem

Steady state propagation of a buckle on an elastic beam resting on a non-linear foundation is studied by analytical methods. Besides serving as a prototype model for propagating instabilities in solids and structures, it may be refined with parameters based on experimental input to serve as a quantitative model for pipeline collapse. An approximate analytical approach based on matched asymptotic expansions is pursued including effects of axial tension in the beam and inertia at steady state propagation of the buckle. The model is in good agreement with numerical results.