Multimodal aeroelastic analysis of suspension bridges with aerostatic nonlinearities

A one-dimensional (1D) continuum model for the multimodal aeroelastic analysis of suspension bridges is presented which refines a previous model by some of the authors. The classical linearized equations governing the (self-excited) bridge vertical and torsional oscillations are enhanced to include geometric stiffness contributions related to the steady lift and drag forces. A multi-degree-of-freedom (MDOF) system is obtained by Galerkin method and, for increasing values of wind speed, the damped linear dynamics, modulated by both the steady and the self-excited aerodynamic forces, is studied in the complex field. Stability thresholds for divergence and flutter are determined by the classical Lyapunov dynamic criterion. Selected engineering case studies are considered to demonstrate the capabilities and the validity of the proposed model and of the relevant numerical code. In a comprehensive dynamic framework, the method allows for: (i) determining the variation of the bridge mode shapes and frequencies for increasing values of wind speed, including an effective description of the coupling between the two displacement components as well as the interaction between different vibration modes; (ii) detecting both single-degree-of-freedom (i.e. damping-driven) and coupled (i.e. stiffness-driven) flutter instability; (iii) detecting static divergence instability; and (iv) investigating geometric nonlinearities associated with the aerostatic load.