Wind-Induced Instability Mechanism of Old Tacoma Narrows Bridge from Aerodynamic Work Perspective

Abstract

Postflutter limit cycle oscillations (LCOs) are typical nonlinear aeroelastic phenomena for bridge girders. An H-shaped section with a roughly 5:1 aspect ratio, treated as a simplified section of the Old Tacoma Narrows Bridge, was chosen for wind-induced instability re-evaluation, considering its vibration amplitude-dependent aerodynamics characteristics and nonlinear structural damping effects from the energy perspective of aerodynamic work. Forced vibrations at large torsional amplitudes in a wind tunnel were realized with the help of an improved forced motion apparatus (FMA), and synchronous measurements of forces and displacements on the FMA were achieved. Self-excited forces (SEFs) were extracted, and an energy map showing quantitative relationships between vibration amplitude, reduced velocity, and aerodynamic work acting on the section were established. Furthermore, the postflutter LCOs phenomena originating from the energy balance between nonlinear aerodynamic work input and energy consumption by structural damping effects were reillustrated, and nonlinear structural damping effects of prototype bridges are therefore discussed. Moreover, the instability paths of the bridge were investigated by the energy map, considering its vibration amplitude-dependent aerodynamics and structural damping effects from an aerodynamic work perspective. The results show that LCO velocity basically increases with vibration amplitude at different structural damping ratios in torsional degree of freedom, characterizing postflutter LCOs phenomena. The structural damping ratio at the bridge’s collapse is also re-estimated as about 0.0115 with better coincidence of on-the-spot observation and theoretical analysis. In addition, both the aerodynamic damping ratio considering nonlinear characteristics of the SEFs and the structural damping ratio basically increasing with vibration amplitude contribute to postflutter LCOs phenomena of the Tacoma Bridge. The instability paths of the bridge essentially rely on the competitive relationships between structural damping ratios, structural stiffness degeneration, and oncoming wind velocities in the process of collapse.