Modelling of nonlinear aerodynamic self-excited forces on bridge decks

Abstract

The continuous demand for increasing the height and length of structures pushes the boundaries for state-of-the-art engineering. Climate change increases the complexity of the task even further. Precise wind engineering is essential for achieving appropriate structural reliability for large structures. Large-scale weather systems modulated by local topography provide the basis for the wind conditions at a specific site. These wind conditions, which are typically simplified as statistical properties of wind speed, direction, and turbulence, serve as inputs to the wind–structure interaction, which, in turn, outputs the forces on the structure. Self-excited forces, also called motion-induced forces, are changes in the forces from wind caused by the motion of the structure. Aeroelastic flutter is a prime example of a design state requiring adequate models of motion-induced aerodynamic behavior for long-span bridges. Current engineering practice treats flutter and related motion-induced effects as linear phenomena by introducing several simplifications. However, the evolving trends in bridge design, characterized by longer spans and innovative double- and triple-deck configurations, challenge the accuracy of these approximations. Understanding and modeling nonlinear aerodynamic forces are therefore necessary. Recognizing this challenge, the Norwegian University of Science and Technology developed a stateof- the-art forced vibration rig for sectional model wind tunnel testing. This facility presents novel opportunities for evaluating self-excited forces by imposing arbitrary three-degree-of-freedom motion while continuously measuring the forces on the sectional model. The initial part of this thesis involves conducting wind tunnel tests on a double-deck section model. The experimental findings are compared to predictions obtained by traditional linear theory, and various types of aerodynamic nonlinearities are identified. The effects such as amplitude dependency, frequency shifts, and the presence of subharmonics and superharmonics in the test results deviate from linear theories. A simple nonlinear model for selfexcited forces based on response surface methodology is proposed. Further insight into the nonlinear properties in the experimental results was gained by adding and removing terms from the model. It was observed that increased accuracy was achieved when including higher-order terms in the response surface model and that including products of the vertical and pitching motion in the response surface model enhanced accuracy. Accurate modeling of the observed nonlinear self-excited forces is essential for assessing the buffeting response and aeroelastic instability of long-span bridges. While several nonlinear models have been proposed in the literature for predicting self-excited forces, a definitive solution has not yet been achieved. The Volterra series is a general nonlinear model that can model a wide range of nonlinear phenomena and was therefore investigated in detail in this thesis. This thesis presents a thorough investigation into the performance of the Volterra series in modeling nonlinear self-excited forces by fitting the model to measured forces from wind tunnel experiments and validating the obtained model in a separate set of experiments. It is concluded that the Volterra models can model the observed aerodynamic nonlinearities. Volterra models were also further developed by addressing some of their major drawbacks, namely, susceptibility to overfitting and high computational effort. Regularization was introduced to avoid overfitting by introducing penalties on the unknown parameters in the least squares problem. This results in smooth and more realistic Volterra kernels. A comparison of the performances of models with and without regularization considering both synthetic and experimental data shows that models with regularization perform better than models without regularization when considering data with measurement noise. The performance of models with regularization is also better in cases where extrapolation is necessary. It is well known that higher-order Volterra models are very computationally demanding since higherorder terms involve multiple integrals. This work uses Laguerrian filters as the expansion basis for the Volterra kernels to reduce the computational effort. In this approach, the unknown kernels are approximated by a weighted superposition of linear filters and products of linear filters. A weighted sum of filters is used in a linear model, while higher-order Volterra kernels are implicitly constructed by multiplying two or more filters for higher-order models. The performances of models that apply Laguerrian filters and standard nonparametric kernels are evaluated considering both experimental and synthetic data. Models using Laguerrian filters perform equally well or better than the standard Volterra models, and the Laguerrian models require far less computational effort, opening the opportunity to use higher-order models with more inputs. In recent years, nonlinear flutter has received significant attention from the research community. For certain cross-sections, the observed flutter response in experimental tests manifests as a nonlinear limit cycle oscillation, presenting potential advantages in bridge design. Accurate estimation of the response for dynamic systems with nonlinear self-excited forces is crucial. In this context, a framework utilizing the Laguerre filter basis was developed. Experimental data from section models tested in free vibration serve as a benchmark for nonlinear torsional flutter phenomena, and the Laguerrian Volterra model is trained using data from a section model tested in the forced vibration rig. Response prediction is accomplished through a stepwise linear state-space scheme. The framework shows promise in predicting nonlinear flutter, but more work needs to be conducted to verify the performance of the presented framework.