Bucklewaves

Motivated by a selection of results on the plastic buckling of column members within a sandwich plate core where one face of the sandwich is subject to an intense impulse, the problem addressed is one where lateral buckling takes place simultaneously as a compressive axial wave propagates down the member. The bucklewave problem is modeled as an infinitely long column (or wide plate) which is clamped against lateral deflection at the end where velocity is imposed and has a moving clamped condition coinciding with the front of the plastic compression wave. The model reveals that a column or plate suddenly compressed into the plastic range is dynamically stabilized against lateral buckling for lengths that are significantly longer than the corresponding length at which the member would buckle quasi-statically. This stabilization has significant implications for energy absorption under intense dynamic loading. The analysis method is benchmarked against a simpler, but mathematically analogous problem, for which closed form solutions are available: the dynamics of a guitar string lengthening at constant velocity.