New Stochastic Theory for Bridge Stability in Turbulent Flow

Abstract

Theoretical explanation is provided on why turbulence in the wind flow can sometimes stabilize an essentially single‐degree‐of‐freedom motion of a flexible bridge. The theory is based on a new turbulence model, which has a finite mean‐square value and a versatile spectral shape, and is capable of matching closely a target spectrum. It is shown that, without turbulence, the onset of flutter instability is associated with a critical wind velocity and an eigenvector describing a combined critical structure‐fluid mode. This particular composition strikes a balance between the energy inflow from fluid to structure, and the energy outflow from structure to fluid, so that an undamped structural motion becomes sustainable. At the introduction of turbulence, the combined structure‐fluid mode is changed continuously and randomly, and the new energy flow balance, in the sense of statistical average, renders the stabilizing or destabilizing effect of turbulence possible. Numerical results are presented for the boundary of asymptotic sample stability for a bridge model undergoing a single‐degree‐of‐freedom torsional motion.