Vibration analysis on the original Tacoma Narrows Bridge case using large-scale fluid-structure interaction

The collapse of the Tacoma Narrows Bridge in 1940 is revisited using three-dimensional direct numerical simulation and fluid-structure interaction to study its vibration mechanism. A nonlinear model for suspension bridges (Arioli & Gazzola, 2017) is employed for the structural motion with real-scale parameters. A discrete-forcing immersed-boundary method (Kim et al. 2001) is used for the fluid flow, where Re = 10⁴ is employed instead of the actual Reynolds number (Re =3×10⁶) to avoid enormous computational costs. Nevertheless, a total of 13.4 billion grid points is required to resolve the fluid motion. As observed on the day of the collapse (Ammann et al. 1941), the bridge first exhibits a vertical vibration with a relatively high frequency and short wavelength. Later, a large torsional vibration with a lower frequency and longer wavelength appears. The temporal variations of the vertical displacement, rotational angle and structural energy provide the detailed procedures of the vertical and torsional vibrations, and two different FSI mechanisms (lock-in with vortex shedding and aeroelastic flutter) are analyzed.