Arnold tongues and mode-jumping in the supercritical post-buckling of an archetypal elastic structure

The buckling and post-buckling of a classical simply supported elastic stru t on a stiffening elastic foundation is treated as a nonlinear dynamical sy stem. For super critical loads this fourth-order system has a pair of imagi nary eigenvalues, indicating the possibility of either a double or a quasi- periodic response. Finite lengths impose constraints that restrict such res ponses to the rational positions on the real line of the ratio of competing wavelengths: for irrational positions the response locks onto a single per iodic wave. The extent of the mode-locking is described in parameter space by the geometry of Arnold tongues. Critical positions on the tongues are id entified which. mark conditions for mode-jumping from one wavelength to ano ther.