Analytical predictions of chaos in a non-linear rod

The resonant and chaotic conditions for non-dampened, non-linear, planar rods are developed through the Chirikov criterion, and the subharmonic bifurcation conditions for weakly dampened, non-linear, planar rods are also presented through the Melnikov method. The analytical conditions are based on a simply supported, geometrically non-linear, planar rod model with a specific single-mode response, but these conditions are applicable to geometrically non-linear planar rods with different supports. Chaos and transient motion from chaos to periodic motion in the non-linear rod are simulated through the approximate rod model, and they are illustrated through the Poincare mapping section. (C) 1999 Academic Press.