Full bridge analysis of nonlinear vortex-induced vibration considering incomplete span-wise correlation of vortex-induced force

Responses of vortex-induced vibration (VIV) of long-span bridges are commonly measured at first via wind tunnel tests of sectional model and then converted to the prototype ones of the corresponding full bridges by some approximate formulae. In this paper, a time-domain full bridge analysis method was presented for predicting nonlinear VIV responses mode-by-mode based on a polynomial type of nonlinear mathematical model of vortex-induced force (VIF) on bridge deck cross section. In this method, the motion-dependant self-excited force (SEF) components of VIF were regarded as fully correlated span-wise in the case of smooth flow, while the motion-independent harmonic pure vortex-shedding force (PVSF) component of VIF was regarded as incompletely correlated along the bridge span. To take into account the incomplete span-wise correlation of PVSF, an equivalent generalized PVSF including the effect of the incomplete span-wise correlation of PVSF was defined by using a span-wise correlation coefficient of PVSF which could be obtained through a sectional model wind tunnel test of simultaneous pressure measurement. As an application example, the VIV responses of 12 vertical modes of a steel box deck cable stayed bridge with a main span of 688 m were analysed, and were compared with those converted with two approximate converting formulae, respectively, based on Scanlan’s linear and nonlinear mathematical model of VIF. It is found that the influence of the incomplete span-wise correlation of PVSF on the bridge VIV response is very small and can then be ignored.