Stability analysis of wind-induced torsional motion of slender bridges

The paper presents a numerical, simulation-based approach to investigate the stability of torsional motion of slender suspension bridges under stochastic wind turbulence. The torsional bridge motion is represented by a linear, single degree of freedom oscillator. Stochastic turbulence in wind velocity is considered in the form of a periodic excitation with random phase modulation. The stability condition refers to the asymptotic sample stability, for which the necessary and sufficient condition is that the largest Lyapunov exponent be negative. Monte Carlo simulation is performed to evaluate the largest Lyapunov exponent, and stochastic differential equations of motion are integrated in polar coordinates using Euler's scheme. Unlike earlier analytical approximations, a quadratic noise term is retained in the present analysis. The turbulence intensity is shown to have a small stabilizing effect on the bridge stability in a sense that an increase in the turbulence intensity moderately increases the critical mean wind velocity beyond the deterministic flutter velocity. The stabilization effect is limited to the case of narrowband detuned excitation. In the proximity of the parametric resonance frequency, an increase in the bandwidth of the excitation process tends to stabilize the bridge motion.