Fatigue model for elastic bars in turbulent wind

Abstract

Accumulated fatigue damage of an elastic structural bar vibrating in natural turbulent wind may be a primary cause of structural failure. Clumps of strong lateral oscillations may occur randomly with time. These oscillations are due to resonance between the vortex shedding frequency and the natural frequency of the bar. The so-called “lock in” phenomenon apparently extends resonance from a point of coincidence to an interval. An idealized stochastic model is set up on the basis of the empirically observed existence of a critical interval of undisturbed wind velocities upwind of the bar. The upwind velocities are modeled as realizations of a specific stochastic process. A clump of strong lateral, damped harmonic oscillations occurs during any uninterrupted “visit” of the velocity to the critical interval. For velocities outside the critical interval only insignificant lateral oscillations occur. The fatigue damage is assumed to be linearly accumulated according to the Palmgren—Miner rule within each clump and from clump to clump. The goal is to evaluate the structural reliability for any specified period of time. It is expressed in terms of a reliability index.