Nonlinear mathematical model of vortex-induced vertical force on a flat closed-box bridge deck

By taking Xiangshan Harbor Bridge located in Ningbo of Zhejiang Province in China, a steel cable-stayed bridge with a main span of 688 m, as a background, the nonlinear vortex-induced vertical force (VIVF) force on the flat closed-box deck was investigated in this study via wind tunnel tests of spring-suspended sectional model at a large scale of 1/20. In the tests, the signals of the dynamic forces acting on the outer cladding of the model at various wind speeds within the lock-in range of vortex-induced resonance (VIR) were measured using four single-component force balances installed in the box of the deck model while the corresponding signals of the dynamic displacement and acceleration responses of the model were measured simultaneously using four laser displacement sensors and four accelerometers. A nonlinear least square fitting (NLSF) method was then applied on the time histories of the VIVFs extracted from the measured dynamic forces to identify the relevant parameters of the Scanlan′s empirical nonlinear model and a new nonlinear mathematic model proposed in this paper for the VIVFs. By comparing both the displacement responses of and the VIVF on the sectional model computed based on the identified model parameters with the corresponding tested results, it was found that the proposed nonlinear mathematical model is adequate, whilst the Scanlan′s empirical nonlinear model may not suitable, for describing the VIVF acting on flat closed-box decks.