Keywords: catenary cables, flutter derivative, geometric nonlinear analysis, aerodynamics, cable-supported bridges, aerodynamic instability, dead loads, wind forces, critical wind speed, vibration modes
Aerodynamic instability of cable-supported bridges considering the initial deformed shape due to dead loads
The aerodynamic instability of cable-supported bridges is studied, with due account taken of the initial deformed shape of the bridge due to the dead loads. The two-node catenary cable element is adopted to model the non-linear behaviours of cables with sags of various magnitudes. Self-excited wind loads are expressed in terms of flutter derivatives. The aerodynamic instability analysis is conducted in two stages. In the first stage, a geometric non-linear analysis is performed for the dead loads to find the deformed shape. In the second stage, the aerodynamic stiffness and damping matrices due to the self-excited wind forces are considered in forming the system matrices. Then a complex eigenvalue analysis formulated in the state space is conducted to find the critical wind speed by an incremental-iterative procedure, in which all vibration modes of the bridge are considered. Both the lumped mass and consistent mass approaches are adopted for comparison. The solutions obtained by the present procedure are compared with the existing ones and discussed.