Erosion of the safe basin for the transversal oscillations of a suspension bridge

The time evolution of the lowest order transversal oscillation mode of a suspension bridge is studied by means of a piecewise-linear forced and damped one-dimensional oscillator, in which the loss of smoothness is due to the asymmetric response of the bridge hangers with respect to stretching and compression. If the midpoint roadbed deflection is outside a specified safe region, the bridge is supposed to collapse. We analyze the relative area of the safe basin, or the fraction of initial conditions in the phase space for which the bridge does not collapse with respect to the damping and forcing parameters. The safe basin erosion is enhanced by the appearance of incursive fingers caused by the exponential accumulation of safe basin lobes towards an invariant manifold of a periodic orbit which undergoes a homoclinic bifurcation.