Identification of the High-Order Rational Function of Bridge Decks by SDOF Forced Vibration Testing

Abstract

The high-order rational function provides an accurate and effective model of self-excited forces for flutter analysis of bridges. This study proposes a direct identification method for the rational function of a bridge deck, which enables high-order modeling. In this method, the single degree of freedom (SDOF) forced vibration test is first carried out on the sectional model of the bridge deck. The tested results are then processed by a harmonic function-based filter, yielding force time histories with high signal-to-noise ratios. Formulas are derived to identify parameters of the high-order rational function from these time histories. To deal with the numerical difficulties of the formulas, two practical optimal nonlinear fitting procedures were proposed, which simplify the identification but at the same time maintain a reasonable accuracy. A thin flat plate and a streamlined box section under various wind angles of attack were used as examples to elucidate the effectiveness and feasibility of the proposed identification method. Results showed that the identified high-order rational function could accurately replicate the self-excited force. In contrast, a significant deviation was observed if the first-order rational function was utilized as an alternative. Finally, the high-order rational function model identified was applied in the flutter analysis by a state-space method. The yielded critical flutter wind speed matched satisfactorily with the free-vibration wind tunnel test results, confirming the advantage of the proposed model.