Large amplitude oscillations can arise in bridges due to the geometry of their construction, as shown by the models considered above. We have not addressed how large amplitude torsional oscillations arise.
In a 1999 paper by P. J. McKenna, he proposed that the geometry coupled with a more physically realistic description of the cables allows the vertical oscillations to generate horizontal oscillations.
McKenna's cable idea discards the assumption that the suspending cables of the bridge always act like Hooke's law springs. As everyone that has tried to push a string knows, if you grab one end of a cable, you can move the other end by pulling, but if you try to move the other end by pushing, the cable simply folds into itself. McKenna argues that the suspending cables of these bridges should act this way too. Therefore, they cannot be Hooke's law springs because they don't create a force when they are shortened.
McKenna suggests that cable springs are Hooke's law springs when x is positive, but when x is negative they do not generate a force. A mathematical description is:
The cable springs modeled this way can induce large torsional oscillations.