Vortex-induced oscillations of bridges: theoretical linkages between sectional model tests and full bridge responses

Vortex-induced oscillation is a type of aeroelastic phenomenon, to which extended structures such as long-span bridges are most susceptible. The vortex-induced vibration (VIV) behaviors of a concerned bridge were investigated conventionally in virtue of wind tunnel tests on string-mounted sectional models. This necessitates the building of a linkage between the response of the sectional model and that of the prototype structure. Although many released literatures have related to this issue and provided suggestions, there is a lack of consistency among them. In this study, some theoretical models describing the vortex-induced structural motion, including the linear empirical model, the nonlinear empirical model and the modified (or generalized) nonlinear empirical model, are firstly reviewed. Then, the concept of equivalent mass density is introduced based on the principle that an equal input of energy should result in identical structural amplitudes. Based on these, the theoretical linkages between the amplitude of a section model and that corresponding to the prototype bridge are discussed with different analytical models. Theoretical derivation indicates that such connections are dependent mainly on two factors, one is the presupposed shape of deformation, and the other is the theoretical VIV model employed. The theoretical analysis in this study shows that, in comparison to the nonlinear empirical models, the linear one can result in obvious larger estimations of the full bridges' responses, especially in cases of cable-stayed bridges.