Time Domain Modeling of Bridge Deck Flutter and Applications

Abstract

Time domain modeling of bridge deck flutter and its applications are examined in this article. The frequency dependent aerodynamic self-excited forces acting on a bridge deck are approximated in the Laplace domain by rational functions. The matrix formulation of the rational functions known as “Minimum State” is applied to aerodynamic data obtained experimentally from various types of decks. The precision of the approximations is calculated, and plots are drawn of the approximation functions compared to the available tabular data. The state-space equations of motion describing the aero elastic behavior of a section of a bridge deck are presented. Given the dynamic data of a bridge structure (mass, rotational mass moment of inertia, natural frequencies, stiffness and damping ratios), and assuming that a geometric similarity exists between the profiles of the full-scale bridge deck and the sectional model from which the frequency dependent aerodynamic data was extracted, it is possible to calculate the critical velocity of that particular bridge. This study shows that it is possible to build a catalog of several profiles, characterized by frequency dependent aerodynamic data and the corresponding rational functions. This catalog could form the basis for calculating a bridge’s aerodynamic stability without recurring to wind tunnels.