Arnold tongue predictions of secondary buckling in thin elastic plates

The stability of post-buckled states for simply-supported flat elastic plates under compression is investigated for a range of in-plane boundary conditions. The von Karman plate equations are reduced to a series of ODEs which are solved numerically under parametric variation of both load and length. Results are checked against full numerical solutions of the PDEs, and comparison with a modal analysis highlights the dominant passive contaminations. The nondimensional amplitude at secondary bifurcation, for any combination of modes and all plate lengths, is presented in a concise form using the parameter space of Arnold tongues. This demonstrates that compound bifurcation represents a worst case for post-buckling reserve, and that long plates have inherently more such reserve than short plates. It is also shown that stiffening the boundaries against inplane movement is destabilizing, in that it induces mode jumping at secondary bifurcation to occur at an earlier stage in the post-buckling regime. (C) 1999 Elsevier Science Ltd. All rights reserved.