Aerodynamic Theory of Bridge Oscillations

General equations are derived, expressing the aerodynamic forces of lift and torque on any oscillating section of two independent degrees of freedom. The parameters representing the distinctive aerodynamic characteristics of the section and the coefficients representing the variation with wind velocity are derived from static wind-tunnel tests on straight and curved section models. The effects of vertical velocity, angular displacement, and angular velocity are included, as well as the effects of the angle of incidence. The complete expressions for the aerodynamic forces are equated to the corresponding expressions for the dynamic forces acting on the section, including elastic (and gravitational) restoring force, inertia, and damping. The resulting general equations yield solutions for all practical problems of vertical, torsional, and coupled oscillations, including analytical determination and prediction of frequencies, critical velocities, instability response (rate of amplification), and amplitude response. Numerical examples are given, to illustrate the practical application of the derived relations and to confirm the validity of the underlying theory. Graphic methods are presented to facilitate application and visualization.