Smoothed "slack cable" models for large amplitude oscillations of suspension bridges

This paper proposes a technique to study the dynamics of suspension bridges in those cases where the use of traditional models is not possible, i.e., when the deformed shape of the structure allows the simultaneous presence of taut and slack hangers. The typical unilateral behavior of these suspension elements, which are unable to transmit compressive forces, introduces a discontinuity in the stiffness that implies strong computational difficulties in the solution of the equations governing the motion; as a consequence, the response of the continuous or discrete models proposed may be evaluated only through step by step time integration. In this paper an alternative technique is proposed, which replaces the distribution of unilateral hangers with a smooth nonlinear regular system made equivalent to the effective one by means of an energy criterion. The proposed technique, referred to as "equivalent nonlinearization," allows description of the motion through partial differential equations that are nonlinear but regular and, therefore, can be solved through classical perturbation techniques. The paper also describes two models formulated on the basis of the previously mentioned technique and some classes of solutions corresponding to particular characteristics of the forcing action.