A consistent dynamic stiffness matrix for flutter analysis of bridge decks

Abstract

A consistent dynamic stiffness matrix is formulated for the flutter analysis of bridge decks. The equations of motion corresponding to the vertical, lateral, and torsional degrees of freedom are considered, and the associated self-excited lift, drag, and torsional moment are based on the unsteady linear model involving eighteen flutter derivatives. The velocity-dependent and the strain rate-dependent viscous damping coefficients, obtained in terms of the corresponding modal damping ratios, are also incorporated throughout the formulation. The flutter speed and the corresponding flutter frequency are determined through an iterative search of the determinant of the assembled dynamic stiffness matrix for flutter. Using the present formulation flutter analysis can be accurately performed with very few number of elements, as compared to the analyses with the conventional finite element approach. The flutter derivatives-based self-excited force model is especially suitable for the flutter analysis of a bluff-body bridge deck with experimentally available flutter derivatives. Numerical results for three examples verify the accuracy and efficacy of the present formulation.