A parametric one-dimensional model of suspension bridges is employed to investigate their static and dynamic aeroelastic behavior in response to a gust load and at the onset of flutter. The equilibrium equations are obtained via a direct total Lagrangian formulation where the kinematics for the deck, assumed to be linear, feature the vertical and the chord-wise displacements of the deck mean axis and the torsional rotations of the deck cross sections, while preserving their shape during rotation. The cables elasto-geometric stiffness contribution is obtained by condensing the equilibrium in the longitudinal direction assuming small horizontal displacements and neglecting the cable kinematics along the bridge chord-wise direction. The equations of motion are linearized about the prestressed static aeroelastic configuration and are obtained via an updated Lagrangian formulation.
The equations of motion governing the structural dynamics of the bridge are coupled with the incompressible unsteady aero-dynamic model obtained by a set of reduced-order indicial functions developed for the cross section of a suspension bridge, here represented by a rectangular cross-section. The space dependence of the governing equations is treated using the Galerkin approach borrowing as set of trial functions, the eigenbasis of the modal space. The time integration is subsequently performed by using a numerical scheme that includes the modal reduced dynamic aeroelastic Ordinary Differential Equations (ODEs) and the added aerodynamic states also represented in ODE form, the latter being associated with the lag-state formulation pertinent to the unsteady wind-induced loads.
The model is suitable to analyze the effect of a time and space non uniform gust load distributed on the bridge span. The obtained aeroelastic system is also suitable to study the onset of flutter and to investigate the sensitivity of the flutter condition on geometrical and aerodynamic parameters. The flutter instability is evaluated using appropriate frequency and time domain characteristics. The parametric continuum model is exploited to perform dynamic aeroelastic flutter analysis and gust response of the Runyang Suspension Bridge over the Yangtze river in China.