Universitätsbibliothek
Weimar Open Access

The phenomenon of aerodynamic instability caused by the wind is usually a major design criterion for long-span cable-supported bridges. If the wind speed exceeds the critical flutter speed of the bridge, this constitutes an Ultimate Limit State. The prediction of the flutter boundary, therefore, requires accurate and robust models. The complexity and uncertainty of models for such engineering problems demand strategies for model assessment. This study is an attempt to use the concepts of sensitivity and uncertainty analyses to assess the aeroelastic instability prediction models for long-span bridges. The state-of-the-art theory concerning the determination of the flutter stability limit is presented. Since flutter is a coupling of aerodynamic forcing with a structural dynamics problem, different types and classes of structural and aerodynamic models can be combined to study the interaction. Here, both numerical approaches and analytical models are utilised and coupled in different ways to assess the prediction quality of the coupled model.

Wind-induced vibrations often represent a major design criterion for long-span bridges. This work deals with the assessment and development of models for aerodynamic and aeroelastic analyses of long-span bridges. Computational Fluid Dynamics (CFD) and semi-analytical aerodynamic models are employed to compute the bridge response due to both turbulent and laminar free-stream. For the assessment of these models, a comparative methodology is developed that consists of two steps, a qualitative and a quantitative one. The first, qualitative, step involves an extension of an existing approach based on Category Theory and its application to the field of bridge aerodynamics. Initially, the approach is extended to consider model comparability and completeness. Then, the complexity of the CFD and twelve semi-analytical models are evaluated based on their mathematical constructions, yielding a diagrammatic representation of model quality. In the second, quantitative, step of the comparative methodology, the discrepancy of a system response quantity for time-dependent aerodynamic models is quantified using comparison metrics for time-histories. Nine metrics are established on a uniform basis to quantify the discrepancies in local and global signal features that are of interest in bridge aerodynamics. These signal features involve quantities such as phase, time-varying frequency and magnitude content, probability density, non-stationarity, and nonlinearity. The two-dimensional (2D) Vortex Particle Method is used for the discretization of the Navier-Stokes equations including a Pseudo-three dimensional (Pseudo-3D) extension within an existing CFD solver. The Pseudo-3D Vortex Method considers the 3D structural behavior for aeroelastic analyses by positioning 2D fluid strips along a line-like structure. A novel turbulent Pseudo-3D Vortex Method is developed by combining the laminar Pseudo-3D VPM and a previously developed 2D method for the generation of free-stream turbulence. Using analytical derivations, it is shown that the fluid velocity correlation is maintained between the CFD strips. Furthermore, a new method is presented for the determination of the complex aerodynamic admittance under deterministic sinusoidal gusts using the Vortex Particle Method. The sinusoidal gusts are simulated by modeling the wakes of flapping airfoils in the CFD domain with inflow vortex particles. Positioning a section downstream yields sinusoidal forces that are used for determining all six components of the complex aerodynamic admittance. A closed-form analytical relation is derived, based on an existing analytical model. With this relation, the inflow particles’ strength can be related with the target gust amplitudes a priori. The developed methodologies are combined in a synergistic framework, which is applied to both fundamental examples and practical case studies. Where possible, the results are verified and validated. The outcome of this work is intended to shed some light on the complex wind–bridge interaction and suggest appropriate modeling strategies for an enhanced design.

Reliable modelling in structural engineering is crucial for the serviceability and safety of structures. A huge variety of aerodynamic models for aeroelastic analyses of bridges poses natural questions on their complexity and thus, quality. Moreover, a direct comparison of aerodynamic models is typically either not possible or senseless, as the models can be based on very different physical assumptions. Therefore, to address the question of principal comparability and complexity of models, a more abstract approach, accounting for the effect of basic physical assumptions, is necessary. This paper presents an application of a recently introduced category theory-based modelling approach to a diverse set of models from bridge aerodynamics. Initially, the categorical approach is extended to allow an adequate description of aerodynamic models. Complexity of the selected aerodynamic models is evaluated, based on which model comparability is established. Finally, the utility of the approach for model comparison and characterisation is demonstrated on an illustrative example from bridge aeroelasticity. The outcome of this study is intended to serve as an alternative framework for model comparison and impact future model assessment studies of mathematical models for engineering applications.

Innerhalb der Arbeit wird der Einfluss der Querschnittssteifigkeit und der Lagerungsbedingungen von Brücken auf das Schwingungsverhalten in Querrichtung infolge Windeinwirkung untersucht. Am Beispiel der Talbrücke Schwarza (A71) wird die Schwingungsanfälligkeit des Tragwerkes durch Vergleich der Tragwerksreaktionen infolge einer statischen Ersatz-Windlast und der dynamischen Windlast untersucht. Dazu wird ein FE-Modell der Brücke mit dem Programmsystem ANSYS erstellt. Die Windlastannahmen basieren auf dem EC 1991 - Teil 2-4. Für das untersuchte Tragwerk kann gezeigt werden, das aufgrund der geringen Eigenfrequenzen der Brücke in Querrichtung keine Schwingungsanfälligkeit besteht.

Zur Berechnung der Böeneinwirkungen auf ein Brückenbauwerk wird ein stochastisches Modell vorgestellt. Die Windkraft aus der Böenbelastung wird dabei als systemunabhängige Luftkraft betrachtet welche in mathematischer Hinsicht dadurch gekennzeichnet ist, daß die aeroelastischen Bewegungsdifferentialgleichungen inhomogener Natur sind und der Bewegungsablauf den Charakter einer erzwungenen abklingenden Schwingung hat. Ausgehend von den nicht linearen partiellen Differentialgleichungen für Verschiebung und Torsion wird mittels der Galerkin Prozedur ein System von totalen Differentialgleichungen abgeleitet. Die äußeren Luftkräfte werden als gefilterter Poissonprozess von Dirac Impulsen dargestellt. Zur Berechnung der statistischen Momente des Differentialgleichungssystem wird die Itô'sche Differentialformel erweitert und in ein System von algebraischen nicht linearen Gleichungen transformiert. Diese dienen zur Berechnung des Momentenverlaufs für den stationären Anteil des stochastischen Prozesses. Der Abschluß des so erhaltenen nicht linearen Gleichungssystems erfolgt über die Methode der Kumulantenabschlußtechnik.