Sudden lateral asymmetry and torsional oscillations of section models of suspension bridges

Cable-supported bridges typically exhibit minimal torsional motion under traffic and wind loads. If symmetry of the bridge about the deck's centerline is suddenly lost, such as by the failure of one or more cables or hangers (suspenders), torsional motion of the deck may grow and angles of twist may become large. The initiation of the disastrous torsional oscillations of the original Tacoma Narrows Bridge involved a sudden lateral asymmetry due to loosening of a cable band at midspan. The effects of these types of events on two-degree-of-freedom and four-degree-of-freedom section models of suspension bridges are analyzed. Vertical and rotational motions of the deck, along with vertical motions of the cables, are considered. A harmonic vertical force and an aerodynamic moment proportional to angular velocity are applied to the deck. Resistance is provided by translational and rotational springs and dashpots. Flutter instability and large oscillations occur under the aerodynamic moment, which provides “negative damping.” In order to model the occurrence of limit cycles, nonlinear damping of the van der Pol type is included in one case, and nonlinear stiffness of the hangers in others. The frequencies of the limit cycles are compared to the natural frequencies of the system.