Aerolasticity of suspension bridges using nonlinear aerodynamics and geometrically exact structural models

Wind-induced vibration in super-long-span bridges is a major concern for the designers. There is a need to enhance the structural design technology, through improved computational capabilities, a critical step for a better understanding of fluid-flow physics that induce vibration and fluid- structure dynamics of flexible bridges. The design of bridges with spans significantly longer than those existing today is quite challenging. To refine the computational tools required for such bridges, a multi- disciplinary research effort devoted to the advanced modeling of flexible long-span suspension bridges is proposed. These structures exhibit an aeroelastic behavior quite different from conventional bridges. In the present work, a fully nonlinear model of suspension bridges parameterized by one single space coordinate is proposed to describe the overall three-dimensional motion. The nonlinear equations of motion are obtained via a direct Lagrangian formulation and the kinematics, for the deck-girder and the suspension cables, feature the finite displacements of the associated base lines and the flexural and torsional finite rotations of the deck cross sections. The strain-displacement relationships for the generalized strain parameters - the cable elongations, the deck elongation, and the three curvatures - retain the full geometric nonlinearities. The nonlinear aerodynamic characteristics of the boxed sharp-edge cross section of the Danish Great Belt Bridge are investigated by using two state-of-the-art computational methods, the k-ϵ turbulence model implemented in FLUENT-ANSYS to solve the Reynolds Averaged Navier Stokes (RANS) equations and the Navier Stokes (NS) discrete-vortex method implemented in DVMFLOW-COWI. The computational fluid dynamics tools have been used to develop computationally efficient unsteady aerodynamic models taking into account viscous effects, including flow separation and boundary layer thickening, treated using Reduced-Order Models (ROMs). Frequency-domain representations of the aerodynamic loads in terms of flutter derivatives are obtained for selected values of the wind initial angle of attack. Consequently, nonlinear indicial functions are derived for these angles and incorporated into the proposed ROMs. As a result, a fully nonlinear coupled fluid-structure model for suspension bridges is assembled to study the nonlinear static and dynamic behavior thus addressing problems of static aeroelastic stability, such as torsional divergence, and dynamic aeroelastic instabilities, such as flutter and post-flutter. The geometrically exact formulation developed in this study lends itself naturally to parametric studies about the sensitivity of the static and dynamic limit states of the bridges with respect to variations of the characteristic structural parameters. In addition, the study addresses the dynamic response of the bridges under time- and space-dependent loading conditions due to time- and space-wise distributed gust excitations as well as the study of the effects of spatial nonuniform wind distributions on the critical flutter condition. Finally, the post-flutter behavior is studied by using a continuation method to highlight the post-critical bifurcation scenarios and emphasize the complex nonlinear response of slender self-excited suspended structures.