| Since the famous Tacoma Narrows Bridge failure of 1940, the bridge engineering community has been faced with the design consideration of aerodynamic flutter. Flutter is the instability which forms from the interaction of elastic, inertial, damping, and self-excited aerodynamic forces. This dissertation presents a matrix approach to flutter analysis as it pertains to any as-built cable-stayed bridge. The bridge is modeled as a three-dimensional structure with cable arrangements being of any configuration, lying in a single, double, or inclined plane.; The systematic approach to flutter is: first, linearize oscillatory behavior by performing a static analysis under the dead load condition accounting for nonlinearities due to cable sag, axial-flexural interaction, and large displacements; then, extract pure natural modes in the bending, torsional, and sway directions using an out-of-core subspace iteration technique with starting vectors generated by the Lanczos method; and finally, determine pre- and post-flutter vibratory behavior (frequency and logarithmic decrement) by the solution of the normal mode equations of motion, where aerodynamic forces are represented by wind tunnel generated flutter derivatives having aerodynamic stiffness and damping components.; The methods are applied to three of the proposed deck sections of the Luling Cable-Stayed Bridge, which was experimentally tested for flutter. Results indicate that the analytical methods compare well to previous investigations and that an advancement in the state-of-the-art of cable-stayed bridge computational methods is attained due to this study's generality and implementation. |
