New Stochastic Theory for Bridge Stability in Turbulent Flow

Abstract

Motion stabilty of a long-span bridge in turbulent wind is studied. The bridge motion is represented by a torsional mode and a bending mode, and the new wind turbulence model proposed in an earlier paper is used in the analysis. This turbulence model is capable of matching closely a target spectral density, such as the well-known von-Karman and Dryden spectrums. It is shown that the presence of turbulence changes the combined structure-fluid critical mode and results in a new energy balance. The asymptotic behavior of the combined structure-fluid system is determined by the largest Lyapunov exponent, and the motion is asymptotically stable if the largest Lyapunov exponent is negative. In this sense, the turbulence has a stabilizing or a destabilizing effect, depending on whether it increases or decreases the critical mean wind velocity at which the largest Lyapunov exponent vanishes. For a particular bridge model investigated, it is found that the peak location of the spectral density of the turbulence is crucial to the stability condition. By changing the peak location of the spectrum, a stabilizing turbulence can become destabilizing, even when the mean-square value remains the same.