An Explicit Model for Simplified Flutter Analysis of Long-span Bridges
Abstract
The collapse of the First Tacoma Bridge in 1940 at a wind speed of about 18m/s triggered the need to recognize aerodynamic stability as a design constraint for long-span bridges. The advancement in understanding and modeling of dynamic wind effects has played a significant role in the realization of long-span bridges with a clear span of up to 2 km. However, the need to span longer, the risk of windstorms exceeding the strongest recorded in the past, and consequently, the quest for optimized design solutions continue to evolve.
A rigorous nature of aerodynamic stability analysis techniques poses a challenge to automate aerodynamic design optimization tools for long-span bridges. The analysis may involve evaluating flutter wind speed, aerodynamic damping, aerodynamic derivatives, or aerodynamic force coefficients through wind tunnel testing and computational fluid dynamics (CFD) simulations. On the other hand, approximate methods such as iterative flutter analysis using an existing aerodynamic database or flutter formula are non-costly to implement for design optimizations during conceptual and preliminary design stages. However, these methods are bound to certain aerodynamic and structural constraints. Existing explicit flutter formulas, such as Selberg’s formula, are applicable for bridges with well-spaced torsional and vertical bending frequencies and require empirical factors to account for aerodynamic effects. The empirical factors may not necessarily adaptable for shape-modification studies of innovative bridge decks.
This study focuses on formulating analytical models for computing (i) the coupled flutter wind speed of contemporary long-span bridges with semi-streamlined deck cross-sections and. (ii) the natural vibration frequency of suspension bridges. Unlike existing methods, the developed flutter formula accounts for the frequency coalescence effect of vibration modes. It also allows to explore sensitivity of bridge designs for shape-specific aerodynamic signatures through aerodynamic drag, lift and moment coefficients from either CFD simulations or static section model tests. Furthermore, non-linear finite element and iterative flutter analysis models are coded in MATLAB to analyze the relative role of gravity and elasticity on the dynamics of suspension bridges and to explore the genesis of negative aerodynamic damping linked to the onset of coupled flutter.