Time domain modelling of self-excited aerodynamic forces for bridge decks. An experimental study

Abstract eng:
Modelling of self-excited forces is one of the most important aspects of bridge aerodynamics. The linear model proposed by Scanlan and co-workers in the 1970s where the self-excited forces are modelled with aerodynamic derivatives is still widely used today. It is however well known that nonlinear models need to be applied for bluff cross-sections, which makes the accuracy of Scanlan’s model questionable for some bridge decks. The performance of linear models for self-excited forces for the cross section of the Hardanger Bridge is studied in this paper by comparing numerical predictions with experimental data for random motion histories. INTRODUCTION Models for self-excited forces for bridge decks has been a very active research field since the infamous collapse of the Tacoma Narrows Bridge in 1940. This event made bridge engineers and researchers realise that flutter is of crucial importance in design of cable-supported bridges. Self-excited forces and flutter were already well-known phenomena in aeronautics making the work done in this field a valuable starting point. The early work by Wagner [1] and Theodorsen [2] have in particular received a lot of attention. They developed analytical solutions of the self-excited forces acting on a thin airfoil based on potential flow and the Kutta condition. Theodorsen studied developed expressions for self-excited forces acting on an airfoil in oscillatory motion while Wagner developed expressions for the self-excited forces acting on the aorfoil subjected to a step change in the downwash. Later Garrick [3] pointed out that Wagner’s and Theodorsen’s functions are related by the Fourier transform. Flow separation and possible reattachment makes the flow past a bridge deck very complex. This violates the assumptions introduced to derive analytical expressions by means of potential theory. It is therefore necessary to use empirical methods to describe the wind loads of bridge decks and other bluff bodies. The most well-known model for aerodynamic self-excited forces for bridge decks defines the self-excited forces by means of aerodynamic derivatives and was proposed by Scanlan and Tomko [4] in 1971. The aerodynamic derivatives are function of the reduced frequency of motion similar to Theodorsen’s circulatory function, but needs to be determined by wind tunnel tests. This model is an engineering application that is still widely used. Time domain modelling of self-excited forces have more recently received attention by the research community since it is convenient to model nonlinear structural behaviour in time domain [5–10]. Here the self-excited forces are given by convolution integrals following the convolution theorem of the Fourier transform. The resulting aerodynamic step response, indicial functions or impulse response functions are the empirical counterparts to the Wagner function.

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