A simplified method for the free vibration and flutter analysis of bridge decks

A simplified method for the free vibration and flutter analysis of bridge decks is presented. Bending-torsion coupled beam theory with warping stiffness included is used in the structural idealization of bridge decks in order to derive explicit formulae for natural frequencies and mode shapes. These are used to perform the flutter analysis. The time-dependent aerodynamic forces are modelled using Theodorsen type flat plate theory. Expressions for generalized mass, generalized stiffness and generalized aerodynamic force terms are derived in compact explicit form. The flutter problem is then formulated by summing algebraically the analytical expressions for generalized mass, generalized stiffness and generalized aerodynamic forces, and the associated flutter determinant is expanded in analytical form. Finally, the flutter speed and flutter frequency are thereby determined by using a standard root finding procedure. The method is demonstrated by numerical results. This is followed by some concluding remarks.