Aerodynamic Stability of Long Span Bridges
With a desire to build even longer bridges, it is of interest to improve the numerical tools for aerodynamic response calculations as well as the flutter limit assessment, and to investigate the possibilities for increasing the stability limit. The work conducted within the field of aerodynamic stability and response of long span bridges is summarised in three parts: wind field simulation, bridge aerodynamics, and external damping of suspension bridges. The first part describes the conditional mean field wind simulation method as an efficient and flexible alternative to existing wind simulation methods. The mean field method is an auto regressive process allowing for a stepwise update of the turbulence components based on a relatively compact memory. Hereby, the data storage requirements are limited even for large scale problems and long simulation records. The coefficient matrices of the auto regressive model are determined directly from the wind field covariance relations, and examples show that an exponential distribution of the memory steps included in the model provides high quality results with a minimal number of auto regressive terms. The statistical properties in terms of the auto spectral density and the cross field coherence estimated from simulated records are shown to correspond well with the target results. The second part focuses on the representation of aero elastic forces for bridge response evaluation and flutter assessment. The aero elastic forces are represented as additional state variables in a compact first order state space form of the equation of motion. The aerodynamic matrices used in the representation of the aero elastic forces are identified from the aerodynamic derivatives by a simple identification procedure based on a least squares solution of an over determined equation system. Furthermore, a second order momentum based time integration procedure is described and the modelling and quasi static reduction of a long span suspension bridge are discussed. Finally, the established model was used to obtain results for full structural loading including the bridge deck, pylons, and cables and to evaluate the influence of the wind load correlation on the response based on a consistent anisotropic turbulence representation. It was found that the magnitude of the load depends significantly on the the ratio of the along wind and transverse turbulence length scales. The final part describes a damping system for suspension bridges. The damping system consists of four equally calibrated, symmetrically located devices working on the relative displacement between the pylons and the main suspension cables. Each device consists of a viscous damper and a spring in parallel connected to the structure via a pre tensioned cable. The tuning of the damper system is based on the asymptotic results to a twocomponent subspace approximation with still air modes as calibration input, and the simple procedure is shown to provide very accurate results. The damping system targets the modes of interest for unstable flutter motion and it can be observed that the double symmetrical system of equally tuned dampers is able to provide damping to all modes of interest. Finally, the ability of the damping system to increase the stability limit is illustrated numerically on a full aero elastic model of a long span suspension bridge which shows a significant increase of the critical wind speed for the unset of flutter.