Lyapunov stability of suspension bridges in turbulent flow

Abstract

In the era of sleek, super slender suspension bridges, facing the issue of stability against dynamic wind actions represents an increasingly complex challenge. Despite the significant progress over the last decades, the impact of atmospheric turbulence on bridge stability remains partially not understood, evoking the need for innovative research approaches. This study aims to address a gap in current research by investigating the random flutter stability associated with variations in the angle of attack due to turbulence, which has not formally been addressed yet. The present investigation employs the 2D rational function approximation (2D RFA) model to express self-excited forces in a turbulent flow. The application of this type of models to bridge dynamics yields a viscoelastic coupled dynamic system characterized by memory effects and driven by broad-band long-time-scale noise, described here by a linear homogeneous time-variant differential equation, which shows apparent nonlinear features, and which has rarely been matter of research. Utilizing a Monte Carlo methodology, this work innovates in applying the largest Lyapunov exponent (LE) and the moment Lyapunov exponents (MLE) to study bridge random flutter stability. The calculation of LE and MLE under diverse turbulent wind conditions uncovers lower flutter stability than without turbulence effects. In most cases, sample and low-order p-th moment stability thresholds closely align with the bridge dynamic response pattern; therefore, the flutter critical wind speed is unequivocal. However, under certain turbulence scenarios, it is necessary to resort to MLE for a complete description of stability, evoking some additional consideration of which statistical moments should be considered for the engineering assessment of the flutter limit. Finally, this work provides a qualitative insight into the instability mechanisms by approximating the random parametric excitation with a sinusoidal gust and evaluating the time-periodic system stability via Floquet theory.