Non-stationary flow forces for the numerical simulation of aeroelastic instability of bridge decks Claudio Borri a, * , Carlotta Costa a , Wolfhard Zahlten b a Dipartimento di Ing. Civile, Universit  a di Firenze, Via di S. Marta 3, 50142 Firenze, Italy b Inst. fuer Baumechanik, BUGH-Wuppertal, 42285 Wuppertal, Germany Accepted 13 March 2002 Abstract The aeroelastic wind forces acting on a streamlined bridge deck are analytically modeled and implemented in a finite element code for the investigation of aeroelastic instability and for structural analysis in non-linear dynamics. The present paper extends a previously introduced model, fully in the time domain, taking into account the ‘‘memory effect’’ of the aeroelastic processes, in order to reduce the computational effort. The implementation is tested on a two-DOF system and on a suspension bridge model. Ó 2002 Elsevier Science Ltd. All rights reserved. Keywords: Non-linear dynamics; Flutter instability; Aeroelastic derivatives; Indicial functions 1. Introduction In the last decades investigations of aeroelasticity have become indispensable in order to check the reli- ability of low-damped light structures, as for example suspension bridges. Effects of aeroelastic phenomena have been observed in wing aerodynamics (flutter of thin airfoils). The wings could suffer, at some critical wind speed, dangerous and uncontrolled vibrations. Analyti- cal and experimental studies aim to prevent these risks and to guarantee the safety of the airfoils at any speed. Analogous phenomena, with large displacements and rotations, have been observed also in bridges with spe- cific geometrical and structural characteristics. It is well known that Tacoma bridge collapsed due to wind effects (1940, Washington State): the failure happened after a long period of very uncomfortable oscillations. In order to clarify the reasons of the anomalous behavior of that bridge, studies have been developed in scientific litera- ture. The main reason of the collapse is likely that vortex shedding gave rise to the first vibrations, which were increased by the onset of flutter. The catastrophic aerodynamic behavior of the Ta- coma bridge is mainly attributed to the H-shape of the section that is, even at low velocities of the incoming wind, really sensitive to wind excitation. As the structure is invested by the wind, interaction occurs between fluid and structure. The wind supplies to the structure some energy, which depends on wind speed and turbulence characteristics, thus self-excited forces can arise on the bridge. The structure must be able to dissipate this energy supply during the motion and, if that is not possi- ble, the structural motion is excited, and the oscillations can grow indefinitely. The critical flutter speed is defined as the wind velocity for which the energy supplied by the fluid is exactly the same as the energy dissipated during the motion. In this eventuality the amplitude of the os- cillations would remain constant in time. The definition of the critical flutter speed is related to the study of structural reliability. In order to establish the safety of the local conditions, it is necessary to iden- tify the wind characteristics and the structural properties of the bridge, and to compare the critical and the local wind speed. The critical flutter speed must be higher than the local wind speed by some safety margin. The identification of flutter speed can be available by using analytical techniques, but in civil engineering the analytical methods do not allow a reliable evaluation of Computers and Structures 80 (2002) 1071–1079 www.elsevier.com/locate/compstruc * Corresponding author. E-mail address: cborri@dicea.unifi.it (C. Borri). 0045-7949/02/$ - see front matter Ó 2002 Elsevier Science Ltd. All rights reserved. PII:S0045-7949(02)00066-4