Stability and response of suspension bridges under turbulent wind excitation

This research addresses the linear flutter theory for bridges. A new model for the self-excited loads is proposed in which oscillatory variation in the loads due to motion-induced vortex activity in the wake, is accounted for. The addition of complex exponential terms generalizes the traditional Prony series representation of the indicial function for the self-excited loads. Turbulence in the flow direction is included in the self-excited loads. Hence the system is parametrically excited and its governing equations have randomly varying coefficients. The state vector of the response is approximated by a Markov vector process. Stochastic averaging is utilized to convert the physical equations into Ito's stochastic differential equations which govern the Markov vector process. Ito's differential rule is then used to construct the equations for the second statistical moments. Motion stability of the system is interpreted as stability of the first and second statistical moments. The computed stability boundaries for the first and second moments are shown to be crucially dependent upon the coupled loads. Unfortunately, parameters for the indicial functions calculated indirectly from the frequency-domain flutter derivatives, are nonunique. Nevertheless, it can be concluded that a bridge deck that exhibits oscillatory self-excited load behavior is generally less stable (in the mean square) than one with nonoscillatory behavior. The new model that captures the oscillatory behavior concisely, reduces the critical wind speed by more than 10%. Buffeting loads result essentially from the vertical turbulence component. In the present thesis the buffeting loads are expressed as convolution integrals, that account for past history of the fluid flow. Thus the buffeting model considered is based on unsteady aerodynamics rather than the quasi-steady model that has been traditionally used in many previous analyses. The time domain unsteady buffeting response analysis, that also incorporates the randomly varying parameters of the self-excited loads, is the first of its kind. In the illustrative examples, the unsteady buffeting effect is shown to be significant on a single-degree-of-freedom system, whereas it is comparatively less significant with a coupled two-degree-of-freedom system.