Resonance, Tacoma Narrows bridge failure, and undergraduate physics textbooks

The dramatic Tacoma Narrows bridge disaster of 1940 is still very much in the public eye today. Notably, in many undergraduate physics texts the disaster is presented as an example of elementary forced resonance of a mechanical oscillator, with the wind providing an external periodic frequency that matched the natural structural frequency. This oversimplified explanation has existed in numerous texts for a long time and continues to this day, with even more detailed presentation in some new and updated texts. Engineers, on the other hand, have studied the phenomenon over the past half‐century, and their current understanding differs fundamentally from the viewpoint expressed in most physics texts. In the present article the engineers’ viewpoint is presented to the physics community to make it clear where substantial disagreement exists. First it is pointed out that one misleading identification of forced resonance arises from the notion that the periodic natural vortex shedding of the wind over the structure was the source of the damaging external excitation. It is then demonstrated that the ultimate failure of the bridge was in fact related to an aerodynamically induced condition of self‐excitation or ‘‘negative damping’’ in a torsional degree of freedom. The aeroelastic phenomenon involved was an interactive one in which developed wind forces were strongly linked to structural motion. This paper emphasizes the fact that, physically as well as mathematically, forced resonance and self‐excitation are fundamentally different phenomena. The paper closes with a quantitative assessment of the Tacoma Narrows phenomenon that is in full agreement with the documented action of both the bridge itself in its final moments and a full, dynamically scaled model of it studied in the 1950s.