Nonlinear oscillations of suspended bridges and footbridges: a regularization technique for non-smooth hangers behavior

Large amplitude oscillations of suspended bridges under wind-induced loads have been observed due to the nonsmooth behavior of the hangers, that behave like unilateral constraints with no resistance to compressive forces. As a consequence, in particular load conditions some hangers may slack and so a part of the bridge deck may experience unacceptable large motion. For long span suspended bridges, such problem has been investigated with different approaches; in particular, some Authors have numerically evaluated the nonlinear oscillations by means of simplified sectional models, while the writers have proposed a continuous approach, that allows to obtain a smooth nonlinear continuous model by means of a regularization technique: as the distance between the hangers is significantly lower than the bridge span, in fact, it can be assumed that the local slackening of hangers produces a smooth variation of the global stiffness of cables and deck, which may be represented by a nonlinear function of their relative displacements. The main advantage is that the dynamical behavior of the continuum model can be evaluated in closed form by means of perturbation methods. This paper generalizes this approach to suspended footbridges and to pedestrian dynamic loads, that is a subject recently dealt with by several Authors. For sample cases of torsional pedestrian-induced loads, the results of the proposed continuous model are discussed in the paper and compared with similar results described in the scientific literature.